This paper studies the algorithms that reconstruct a signal from its wavelet extrema representation. We show that the existing reconstruction algorithms are inadequate in assuring a consistent reconstruction. We further propose a method that can be used with a number of existing algorithms to guarantee a consistent reconstruction. The new method provides a rigorous way to prevent artifacts resulting from the spurious wavelet extrema in the reconstructed signal.

In this paper we show that if wavelet domain processing is used with digital restoration, then pixel-scale features can be restored exactly in the absence of noise. In the presence of noise results are similar, except for some noise- amplification and ringing artifacts. Wavelet domain modeling eliminates the need to discretize the image acquisition kernel and helps formulate image restoration as a discrete least squares problem. The performance of this technique is analyzed by model-based simulation using a comprehensive model to account for system blur at the image formation level, for the potentially important effects of aliasing, and for additive noise.

We present a regularized method for wavelet thresholding in a multiresolution framework. For astronomical applications, classical methods perform a standard thresholding by setting to zero non-significant coefficients. The regularized thresholding uses a Tikhonov regularization constraint to give a value for the non-significant coefficients. This regularized multiresolution thresholding is used for various astronomical applications. In image filtering, the significant coefficients are kept, and we compute the new value for each non-significant coefficients according to the regularization constraint. In image compression, only the most significant wavelet coefficients are coded. With lossy compression algorithms such as hcompress, the compressed image has a block-like appearance because of coefficients that are set to zero over large areas. We apply the Tikhonov constraint to restore the coefficients lost during the compression. By this way the distortion is decreasing and the blocking effect is removed. This regularization applies with any kind of wavelet functions. We compare the performance of the regularized and non-regularized compression algorithms for Haar and spline filters. We show that the point spread function can be used as an additional constraint in the restoration of astronomical objects with complex shape. We present a regularized decompression scheme that includes filtering, compression and image deconvolution in a multiresolution framework.

Orthogonal bases of piecewise polynomial smooth functions on arbitrary partitions are constructed using techniques developed by the authors for constructing orthogonal multiwavelets. These bases are generated by a small number of functions that are translated and scaled to each of the intervals in the partition.

Many imaging systems rely on photon detection as the basis of image formation. One of the major sources of error in these systems is Poisson noise due to the quantum nature of the photon detection process. Unlike additive Gaussian noise, Poisson noise is signal-dependent, and consequently separating signal from noise is a very difficult task. In this paper, we develop a novel wavelet-domain filtering procedure for noise removal in photon imaging systems. The filter adapts to both the signal and the noise and balances the trade-off between noise removal and excessive smoothing of image details. Designed using the statistical method of cross-validation, the filter is simultaneously optimal in a small-sample predictive sum of squares sense and asymptotically optimal in the mean square error sense. The filtering procedure has a simple interpretation as a joint edge detection/estimation process. Moreover, we derive an efficient algorithm for performing the filtering that has the same order of complexity as the fast wavelet transform itself. The performance of the new filter is assessed with simulated data experiments and tested with actual nuclear medicine imagery.

One of the main advantages of the discrete wavelet representation is the near-optimal estimation of signals corrupted with noise. After the seminal work of De Vore and Lucier (1992) and Donoho and Johnstone (1995), new techniques for choosing appropriate threshold and/or shrinkage functions have recently been explored by Bayesian and likelihood methods. This work is motivated by a Bayesian approach and is based on the complex representation of signals by the Symmetric Daubechies Wavelets. Applications for two dimensional signals are discussed.

We present a comparative study between a complex Wavelet Coefficient Shrinkage (WCS) filter and several standard speckle filters that are widely used in the radar imaging community. The WCS filter is based on the use of Symmetric Daubechies wavelets which share the same properties as the real Daubechies wavelets but with an additional symmetry property. The filtering operation is an elliptical soft- thresholding procedure with respect to the principal axes of the 2D complex wavelet coefficient distributions. Both qualitative and quantitative results (signal to mean square error ratio, equivalent number of looks, edgemap figure of merit) are reported. Tests have been performed using simulated speckle noise as well as real radar images. It is found that the WCS filter performs equally well as the standard filters for low-level noise and slightly outperforms them for higher-level noise.

This paper presents the results of the development of an adaptive method for reducing signal-dependent noise, such as speckle noise, in a coherent imaging system signal, such as in medical ultrasound imaging. Speckle noise is filtered using nonlinear adaptive thresholding of received echo wavelet transform coefficients. Filtering speckle noise in ultrasound imaging enhances the resultant image by improving the signal-to-noise ratio. This method includes the steps of transforming the imaging system signal using discrete wavelet transformation to provide wavelet transform coefficients for each of the wavelet scales having different levels of resolution ranging from a finest wavelet scale to a coarsest wavelet scale; deleting the wavelet transform coefficients representing the finest wavelet scale; identifying, for each wavelet scale other than the finest wavelet scale, which of the wavelet transform coefficients are related to noise and which are related to a true signal through the use of adaptive nonlinear thresholding; selecting those wavelet transform coefficients which are identified as being related to a true signal; and inverse transforming the selected wavelet transform coefficients using an inverse discrete wavelet transformation to provide an enhanced true signal with reduced noise. This method is shown to improve the signal-to-noise ratio by 2 - 5 dB in digital ultrasound images of real and phantom objects for a range of thresholding levels while preserving the contrast differences between regions and maintaining feature edges. The filtered images have an enhanced apparent contrast resulting from the reduction in the speckle noise and the preservation of the contrast differences.

The conditions for optimality of uniform orthonormal subband coders are reviewed. A number of properties of optimal filter banks are then summarized. The case of nonuniform orthonormal filter banks is also considered, and it is shown that the well known connection between optimal coding gain, energy compaction, and principle component property does not extend to the nonuniform case.

Wavelet transform coding image compression is applied to two raw seismic data sets. The parameters of filter length, depth of decomposition, and quantization method are varied through 36 parameter settings and the rate-distortion relation is plotted and fitted with a line. The lines are compared to judge which parameter setting produces the highest quality for a given compression ratio on the sample data. It is found that long filters, moderate decomposition depths, and frequency-weighted, variance-adjusted quantization yield the best results.

The traditional mean-squared-error or peak-signal-to-noise error measures are mainly focused on the pixel-by-pixel difference between the original and compressed images. Such metrics are improper for subjective quality or fidelity assessment, since human perception is very sensitive to correlations between adjacent pixels. In this work, we explore the Haar wavelet to model the space-frequency localization property of human visual system (HVS). It is shown that the physical contrast in different resolutions can be easily represented in terms of transform coefficients. We model HVS with the Haar filter with several visual mechanisms and develop a subjective quality measure which is more consistent with human observation experience.

In this paper we give a brief introduction to filter banks over commutative rings. In contrast to filter banks over the real numbers, we employ finite ring arithmetic to control the number of bits in the signal representations. This way we avoid the coefficient swell problem that is preeminent in rings of characteristic zero. We derive decompositions for images that are tailored to dedicated hardware implementations. These decompositions reduce the size of line-buffers which dominate the silicon area in integrated circuit implementations. As an application, we derive a lossless compression scheme for 8 bit monochrome images using wavelet filters with values in the ring Z/256Z.

In this paper, the relationship between wavelet transform and Differential Mapping Singularities Theory (DMST) is discussed in the context of image compression. DMST maps 3D surfaces accurately, with exact results, and to construct an image compression algorithm based on an expanded set of operations. This set includes shift, scaling rotation, and homogeneous nonlinear transformations. This approach permits the mathematical description of a full set of singularities that describe edges and other specific points of objects. The edges and specific points (degenerate critical points) are the product of mapping smooth 3D surfaces, which can be described by a simple set of polynomials that are suitable for image compression and Automatic Target Recognition.

In this paper, an in depth investigation and comparison of the performance obtainable with short wavelet filters for low bit rate perceptual audio coding is presented. This a priori knowledge of the short wavelet filters performance evaluation open new horizons in their usage, especially, when combined with the Moving Pictures Expert Group (MPEG-4) requirements for segmental signal to noise ratio scalable audio coding.

In this contribution a preprocessing technique for information flow control in compressed video sequences is presented. It consists of resolution adaptation in spatial and temporal domains and is based on a wavelet multiresolution representation. The technique allows to reduce information peaks during frames sequences characterized by large motion and to reduce artifacts introduced by coders operating at high compression rates. Extending previous works, the contribution exploits the decreasing perceptive resolution versus the angular distance from the visual line of sight (foveal zone) providing additional features related to motion activity.

A complete wavelet-based image storage and indexing system for progressive coding, indexing, retrieval, and transmission of images over the network is proposed in this research. New wavelet domain features which include subband significance, decomposition structure, luminance and chrominance histograms, and the significance map of the lowest frequency channel are used to achieve content-based indexing and retrieval. The proposed indexing features take into account of the color, brightness, texture, frequency, and spatial information of a given query image. All features can be naturally extracted as a byproduct during the image compression stage with wavelets. Since coding and indexing are integrated in an unified framework in the proposed system, the database management is greatly simplified. Extensive experimental results are given to demonstrate the retrieval performance of the new approach.

The problem of image feature extraction for classification is difficult because of the high dimensionality inherent in image data. By extracting only relevant image features we reduce the dimensionality of the problem and improve classification accuracy. We further enhance classification performance by finding an optimal representation of the extracted image features which maximizes separability distance among classes. The principal tools used are Fourier series, wavelet packets, local discriminant basis analysis, and neural networks.

We present an improved type of image pyramid based on general approximation functions. The type of pyramid proposed maintains the good properties of symmetry and consistent boundary conditions of the Haar pyramid. Moreover, it is not restricted to a piece-wise constant image model, but allows the use of any generating sequence. The centered topology guarantees a clearly defined up- projection of labels and may be employed in applications for contour detection, object recognition and segmentation. We start by introducing the general discrete framework for the design of least squares pyramids using the standard filtering and decimation tools based on arbitrary basis functions. Our design criterion is to minimize the l₂ norm of the approximation error. We then define the centered pyramid and give explicit filter coefficients for odd and even spline approximation functions. Finally, we compare the centered pyramid to the ordinary one and highlight some applications.

In this work, a multi-resolution procedure based on a generalized Laplacian pyramid (GLP), with p:q (i.e. rational) scale factor, is proposed to merge image data of any resolution and represent them at any scale. The GLP- based data fusion is shown to be slightly superior to those of a similar scheme based on the discrete wavelet transform (WT), according to a set of parameters established in the literature. Not only fused images look sharper than their original versions, but also textured regions are enhanced without losing their spectral signatures. The pyramid- generating filters can be easily designed for data of any resolutions, differently from the WT, whose filter-bank design is non-trivial when the ratio between the scales of the images to be merged is not a power of two. Eventually, remotely sensed images from LandSat TM and from Panchromatic SPOT are fused together. The resulting bands capture multi- spectral features with enhanced contrast and texture, and an increased spatial resolution, thereby expediting automatic analyses for contextual interpretation of the environment.

We propose a new optimizer for multiresolution image registration. It is adapted to a criterion known as mutual information and is well suited to inter-modality. Our iteration strategy is inspired by the Marquardt-Levenberg algorithm, even though the underlying problem is not least- squares. We develop a framework based on a continuous polynomial spline representation of images. Together with the use of Parzen histogram estimates, it allows for closed- form expressions of the gradient and Hessian of the criterion. Tremendous simplifications result from the choice of Parzen windows satisfying the partition of unity, also based on B-splines. We use this framework to compute an image pyramid and to set our optimizer in a multiresolution context. We perform several experiments and show that it is particularly well adapted to a coarse-to-fine optimization strategy. We compare our approach to the popular Powell algorithm and conclude that our proposed optimizer is faster, at no cost in robustness or precision.

Most wavelet-based statistical signal and image processing techniques treat the wavelet coefficients as though they were statistically independent. This assumption is unrealistic; considering the statistical dependencies between wavelet coefficients can yield substantial performance improvements. In this paper, we develop a new framework for wavelet-based signal processing that employs hidden Markov models to characterize the dependencies between wavelet coefficients.

This paper illustrates a seismic tomographic imaging technique sing stochastic a priori information about structural geological morphology. The method is based on a multiresolution representation, which allows incorporating into conventional Markov Random Field models probabilistic constraints between different scales. A MAP Bayesian iterative solution is proposed to perform inversion of largely ill conditioned problems in presence of a limited angular coverage and a limited number of ray-paths.

Earth Observation satellites are often considered to deliver a high spatial resolution image and a set of high spectral resolution images with a lower spatial resolution. Users often want to take advantage of both the high spatial and high spectral resolutions. The ARSIS concept was specially designed to fulfill this requirement and to produce high spectral resolution images with the best spatial resolution available in the set of images with respect to the original spectral content. This concept is based on the wavelet transform and the multiresolution analysis. In this paper, the concept is presented and the different parameters are discussed. Examples of application of ARSIS to real case- studies are provided. Perspectives of use of such a concept are proposed and the benefits to user discussed.

See text for formula.

We present a theory and algorithms of 2D multi-Gabor representations (2DMGR) using a set of nonseparable 2D window waveforms. These windows can be customized to have different spatial and frequency orientations, and different shapes and variances. Together, they form a frame in a 2D space. 2DMGRs have clear values in applications where different spatial and frequency contents and orientations of an image are important features, e.g., in texture analysis, synthesis and segmentations, and in studies of mammalian visual systems, etc.. Numerical recipe and simulation examples are also provided.

We give many examples of bivariate nonseparable compactly supported orthonormal wavelets which are supported over [0,3] X [0,3]. The Holder continuity properties of these wavelets are studied.

If G is an orthonormal system in IL₂ then for any function g (epsilon) G the function g² is a probability density. In this paper we discuss the properties of wavelet based densities and corresponding random variables.

A wavelet-based deformable contour called the wavelet snake has been developed, and applied to distinction of tumors from false detections reported by our computer-aided diagnosis (CAD) scheme for detection of pulmonary nodules in digital chest radiographs. In this technique, multiscale edge representation using spline wavelets was employed as a preprocessing step for extraction of an approximate boundary of a candidate nodule in each region of interest (ROI) reported by our CAD scheme. These multiscale edges are then used to `guide' the wavelet snake to estimate the true boundary of the nodule. The wavelet snake is designed to deform its shape based on a maximum a posteriori estimation performed by a gradient descent algorithm. The degree of overlap between the resulting snake and the multiscale edges were calculated at two scales, and a combination of the overlap measures at these scales were used as a measure for distinction between the ROIs containing nodules and non- nodules. A set of ROIs consisting of 94 nodules and 518 false positives were used for evaluation of our method by means of the receiver operating characteristic (ROC) analysis. Our method yielded an area under the ROC curve of 0.79 in classification performance, which reduced 19% of the false positives with sacrifice of only one nodule.

We present a viewpoint of studying biorthogonal wavelets by using wavelet operators. A characterization of MRA biorthogonal wavelets is given in the framework of wavelet operators. An efficient wavelet filtering algorithm based on this characterization is applied to Z-ray computerized tomography (CT) for multiresolution reconstruction and reduced X-ray exposure. Simulation results indicate that wavelet based reconstruction allows satisfactory image quality in a region of interest from local wavelet and global scaling components of projection data. The results are directly applicable to medical X-ray CT.

As the leading cause of death for adult women under 54 years of age in the United States, breast cancer accounts for 29% of all cancers in women. Early diagnosis of breast cancer is the most effective approach to reduce death rate. The rapid climbing of the health care cost further reiterates the importance of cost-effective, accurate screening tools for breast cancer. This paper proposes a wavelet frame based computer algorithm for screening of microcalcifications on digitized mammographical imagery. Despite its simplicity, the discrete wavelet transform (DWT) of compactly supported wavelets has been effectively used for detection of various types of signals. However, the shifting variant property of DWT makes it very unstable for detection of minute microcalcifications. Although increasing the sampling rate will improve the detection probability, this approach will drastically increase the size of mammographical images. The wavelet frame transform can be easily derived from the DWT algorithm by eliminating its down sampling step. The subtle difference between DWT and WF in down sampling is shown to be critical to the accuracy of microcalcifications detection. Without any down sampling, local image information at different scales is preserved. By joint thresholding of wavelet coefficients at different scales, one can accurately pin point suspected microcalcifications. A simple partitioning technique enables the detection algorithm to process image blocks independently. Four different partitioning techniques have been compared, and the method of repeating the end value on each partition boundary has the least significant impact on the detection accuracy.

Combined use of the X-ray (Radon) transform and the wavelet transform has proved to be useful in application areas such as diagnostic medicine and seismology. In the present paper, the wavelet X-ray transform is introduced. This transform performs 1D wavelet transforms along line in Rⁿ, which are parameterized in the same fashion as for the X-ray transform. It is shown that the transform has the same convenient inversion properties as the wavelet transform. The reconstruction formula receives further attention in order to obtain usable discretizations of the transform. Finally, a connection between the wavelet X-ray transform and the filtered backprojection formula is discussed.

Maximum likelihood detectors of narrowband, non-stationary random echos in Gaussian noise can be efficiently implemented in the time-frequency domain. When the transmitted signals have large time-bandwidth products, the natural implementation of estimators and detectors is the time-scale or wavelet transform domain implementation. This paper extends the wavelet transform implementations to include weighted time-frequency or time-scale (TF/TS) transforms. We define weighted TF/TS transforms using Reproducing Kernel Hilbert Space inner products. Inverses of these weighted TF/TS transforms are also given. The particular case of the weight being the inverse noise covariance is presented. We show how weighted transforms are used in the estimator-correlator detection statistic for complex scattering environments in conjunction with cascaded scattering functions so that the resulting detection statistic is much more robust. The weighted TF/TS transform turns out to be a natural transform for solving nonstationary detector, estimation, and filtering problems and has important applications to transient signal estimation in multipath channels with colored non-stationary Gaussian noise.

This paper investigates the relationship between the traditional wavelet (or matched filter) detector and the estimator correlator (EC) detector formulated in the wavelet domain. The EC detector is actually a weighted wavelet detector, weighted by the scattering function that describes the medium and/or model. The wavelet detector is the optimum detector for point objects but it does not incorporate knowledge of the scattering environment. However, when imaging distributed objects, it is advantageous to take a priori information into account. The EC incorporates this information as a weight on the wavelet image and formulates an estimated spreading function which essentially achieves recombination of highlights and multipath energy. It can be shown that the EC reduces to the wavelet detector when a point object is being imaged.

Wavelet shrinkage is a signal estimation technique that exploits the remarkable abilities of the wavelet transform for signal compression. Wavelet shrinkage using thresholding is asymptotically optimal in a minimax mean-square error (MSE) sense over a variety of smoothness spaces. However, for any given signal, the MSE-optimal processing is achieved by the Wiener filter, which delivers substantially improved performance. In this paper, we develop a new algorithm for wavelet denoising that uses a wavelet shrinkage estimate as a means to design a wavelet-domain Wiener filter. The shrinkage estimate indirectly yields an estimate of the signal subspace that is leveraged into the design of the filter. A peculiar aspect of the algorithm is its use of two wavelet bases: one for the design of the empirical Wiener filter and one for its application. Simulation results show up to a factor of 2 improvement in MSE over wavelet shrinkage, with a corresponding improvement in visual quality of the estimate. Simulations also yield a remarkable observation: whereas shrinkage estimates typically improve performance by trading bits for variance or vice versa, the proposed scheme typically decreases both bias and variance compared to wavelet shrinkage.

In this paper, we consider the problem of detecting changes in dynamical systems from the analysis of the signals they produce. A notion of continuous multiresolution entropy is introduced, which combine advantages stemming from both classical entropy and wavelet analysis. The relevance of the approach, together with its robustness in the presence of moderate noise, is supported by numerical investigations.

This paper introduces a novel filter bank structure called the perfect reconstruction circular convolution (PRCC) filter bank. These filters satisfy the perfect reconstruction properties, namely, the paraunitary conditions, in the discrete frequency domain. The development of the PRCC framework has been motivated by the need for an efficient, invertible algorithm for the implementation of the discrete wavelet transform (DWT) based on bandlimited scaling functions and wavelets. As a motivation, we show how bandlimited scaling functions arise naturally in the context of interpolation and approximation sampling systems with the filters matched to the input process. Next, we show how the PRCC filter bank framework serves as a basis for a frequency sampled implementation of DWT based on bandlimited scaling functions and wavelets, and in general, of matched filters in the above sampling systems. Finally, we present simulation results sing the PRCC framework which verify that the matched interpolating function gives the smallest mean squared error between the input and the reconstructed signal, as compared to other interpolating functions.

The purpose of this note is to highlight some of the unique properties of spline wavelets. These wavelets can be classified in four categories: orthogonal (Battle-Lemarie), semi-orthogonal (e.g., B-spline), shift-orthogonal, and biorthogonal (Cohen-Daubechies-Feauveau). Unlike most other wavelet bases, splines have explicit formulae in both the time and frequency domain, which greatly facilitates their manipulation. They allow for a progressive transition between the two extreme cases of a multiresolution: Haar's piecewise constant representation (spline of degree zero) versus Shannon's bandlimited model (which corresponds to a spline of infinite order). Spline wavelets are extremely regular and usually symmetrical or anti-symmetric. They can be designed to have compact support and to achieve optimal time-frequency localization (B-spline wavelets). The underlying scaling functions are the B-splines, which are the shortest and most regular scaling functions of order L. Finally, splines have the best approximation properties among all known wavelets of a given order L. In other words, they are the best for approximating smooth functions.

We discuss a method for initializing the multi-wavelet decomposition algorithm by pre-filtering. The proposed pre- filtering operation projects the input signal into the space defined by the multi-scaling function associated with the multi-wavelet. Since the approach is projection based, it is guaranteed to always have a solution. The space in which the original signal is contained is defined by multiple generating functions, making this work a generalization of our previous results.

The design of modulated filter bank with nonuniform frequency allocations is considered. The nonuniform subband filters are formed by merging the subband filters of an uniform modulated filter bank. This simple merge preserved the spectral properties and the structure of the uniform modulated filter bank in the resulting nonuniform filter bank. The merge of subband filters of paraunitary modulated filter bank preserve the perfect reconstruction property. As a result, this seemingly idea gives rise to a simple design method for a large class of nonuniform modulate filter banks that are perfectly reconstruct. Design example of a nonuniform cosine modulated filter bank is derived. The performance of nonuniform cosine modulated filter bank under the presented framework is discussed.

In this paper, the concept of cosine-modulated multifilter (CMMF) and the formulation of a class of cosine-modulated multifilters are proposed in order to take advantages of both cosine-modulated filter banks and multifilters. Specifically, the low-complexity in implementation of cosine-modulated filter bank can provide a way to overcome the high-complexity in design of the multifilters. Constrains on the prototype filter for the resulting CMMF to be paraunitary are stated and the design method is presented. Besides providing all the advantages that multifilters have, the proposed method has two major advantages over the existing multifilter design methods. First, all the filters in an M-band N-channel multifilter are cosine-modulated version of a single prototype filter, hence design complexity is significantly reduced. Second, the implementation is greatly simplified and efficient, especially when fast algorithm, such as fast DCT and FFT, are used in the cosine modulation case and exponential modulation case. Design examples are also presented.

Most of the information in a typical image is concentrated in a few regions. These are dominated by structures characterized by discontinuities in intensity. Inherent to the identification of significant structures is determining the location of the structures and assigning saliency values to them. In this paper, we present a wavelet based algorithm that identifies significant structures in an image. We first decompose the image using the wavelet transform. Then, for each pixel, a combining process computes a function that collects all the information available at the sub-band scales. The rationale of the method relies on the assumption that images and volumes possess scale-coherent structures. A structure is scale-coherent if it persists across the scales, or contains all frequencies. The detection of these features forms the core of our approach. We construct a combining function of the image by multiplying the sub-bands obtained from the wavelet transform. The result of this operation is a mask that delineates regions comprising of significant structures. This mask can then be used to provide saliency values at each pixel. Additional processing and image enhancement algorithms can now concentrate their efforts in regions where the mask has high values. We show how our method can be employed to remove noise, enhance, and smooth features in images arising from medical imaging modalities including MRI and mammography.

Severe weather such as tornadoes and large hail often emanates from thunderstorms that have persistent, well organized, rotating updrafts. These rotating updrafts, which are generally referred to as mesocyclones, appear as couplets of incoming and outgoing radial velocities to a single Doppler radar. Observations of mesocyclones reveal useful information on the kinematics in the vicinity of the storm updraft that, if properly interpreted, can be used to assess the likelihood and intensity of the severe weather. Automated algorithms for such assessments exist, but are inconsistent in their wind shear estimations and are prone to high false alarm rates. Reported here are the elements of a new approach that we believe will alleviate the shortcomings of previous mesocyclone detection algorithms. This wavelet-based approach enables us to focus on the known scales where mesocyclones reside. Common data quality problems associated with radar data such as noise and data gaps are handled effectively by the approach presented here. We demonstrate our approach with a 1D test pattern, then with a 2D synthetic mesocyclone vortex, and finally with a case study.

In this paper, we present improvements over the original scale-cepstrum proposed. The scale-cepstrum was proposed as an acoustic feature for speech analysis and was motivated by a desire to normalize the first-order effects of differences in vocal-tract lengths for a given vowel. Our subsequent work has shown that a more appropriate frequency-warping than the log-warping used is necessary to account for the frequency dependency of the scale-factor. Using this more appropriate frequency-warping and a modified method of computing the scale-cepstrum we have obtained improved features that provide better separability between vowels than before, and are also robust to noise. We have used the generalized F-ratio test as a measure of separability and have compared the proposed improved features with the melcepstral features. The data used in the comparison consist of ten vowels extracted from sentences spoken by different speakers in the TIMIT database.

The use of space-scale representations for the frequential analysis of oriented textures is investigated. For this purpose, the Continuous Wavelet Transform is considered. Its discretization in the framework of the Mellin-Transform is described. The behavior of this transformation as a tool for space-frequency representation is compared to the Wigner Distribution on test images. Parameters measuring shape and orientation of local spectra are extracted from these representations, and illustrated on natural textures.

An approach is proposed for detecting macro defects in color LCDs (liquid crystal displays) by using a family of 2D Gabor wavelets. The absolute values of the wavelet coefficients are used to detect macro defects such as periodic or streak patterns. To measure the filter performance, we introduced the improvement rate of the signal-to-noise ratio. The paper also proposes a new method for reconstructing images with enhanced defects by using linear combinations of the real parts of Gabor wavelet coefficients. We obtained the frame bounds of 2D Gabor wavelets which have a discrete sampling step. The reconstructed images can help human evaluators to verify defects. The uniqueness of this method is that not all coefficients are used, but only those that contribute to defect detection. This method is practical in terms of its computational simplicity, and can therefore be used for on- line automatic inspection. Experiments using actual images with defects showed the effectiveness of the method.

Wavelet transform has been widely used in many signal and image processing applications such as edge detection and data compression. For applications that tolerate a slight compromise in accuracy for faster speed, a fast approximation of wavelet transform is favorable. In this paper we propose a simple yet effective algorithm for fast wavelet transform. The use of fixed point numbers simplifies the hardware design and computational complexity than the use of a floating point arithmetic unit. Calculations are further reduced using our thresholding-in-calculation (TIC) technique to omit calculations of small terms that are negligible to the accumulated sum. The TIC technique basically determines whether a multiplication followed by an addition shall be executed using a look-up table with the quantized magnitude of multiplication operands as input parameters. Knowing the levels of quantization, any combination of the quantized multiplication operands can approximate the product and be compared to a predetermined threshold value. If the approximated product is greater than or equal to the threshold value, the corresponding entry in the look-up table is marked for multiplication; otherwise, no multiplication will be executed. Our simulation results show that our approximation algorithm is effective for wavelet transform of audio signals. In addition, when our algorithm is applied to a simple wavelet based edge detection algorithm, the detection result is almost the same as the one using precise calculation of the wavelet transform.

Optimal mechanisms are determined for the hierarchical decomposition of wire-frame surfaces. A family of box- splines with compact support, suitable for the approximation of wire-frames is first defined, generated by arbitrary sampling matrices with integer eigenvalues. For each such box-spline, the optimal positioning of the wire-frame nodes is determined for each level of the hierarchical wire-frame decomposition. Criterion of optimality is the minimization of the variance of the error difference between the original surface and its representation at each resolution level. This is needed so as to ensure that the wire mesh produces at each resolution as close a replica of the original surface as possible. The application of the proposed scheme to the hierarchical coding of 3D wire meshes is experimentally evaluated.

Integer based-matrix algorithms for discrete Haar transform and discrete wavelet transform are proposed with relation to the multiresolution representation. A recursive wavelet transform technique is used with a view to demonstrating simply lossy reconstructed images in contrast to an original image under the specified resolution size. A visual effect of reconstructed images with different appearance and image quality, caused by modifying or throwing away a part of the 2D evaluation such as similarity and/or modified similarity, and fidelity: RMSE and/or PSNR.

A new approach to FPGA implementation of 2D discrete wavelet transform is presented. This architecture allow high accurate and sampling rate DWT realization based on FIR filters of substantial length to be implemented on current generation FPGAs. The scheme is based on two parallel pipelined linear phase 17-tap FIR filters with common shift register, partial adders and look-up tables as coefficient multipliers with 4-stage pipelined architecture. The transform is realized in three stages controlled by the state machine, where temporary (L and H) and final subimages (LL, LH, HL, and HH) are created. High throughput (1050 MIPS) and external memory controller allow efficiency concurrent cooperation with external processors.

Atrial fibrillation (AF) is a common arrhythmia associated with many heart diseases and has a high rate of incidence in the older population. Many of the symptoms of AF are poorly tolerated by patients and if not properly managed, may lead to fatal conditions like embolic stroke. The atrial electrograms during AF show a high degree of non- stationarity. AF being progressive in nature, we aim to link the degree of non-stationarity of the atrial electrogram to the stage of advancement of the disease, the duration of episodes of AF, possibility of spontaneous reversion to sinus rhythm and the defibrillation energy requirement. In this paper we describe a novel algorithm for classifying bipolar electrograms from the right atrium of sheep into four groups--normal sinus rhythm, atrial flutter, paroxysmal AF, chronic AF. This algorithm uses features derived from a wavelet transform representation of the signal to train an artificial neural network which is then used to classify the different arrhythmia. The success rates achieved for each subclass indicates that this approach is well suited for the study of the atrial arrhythmia.

Pyramidal decomposition is known to be highly useful for progressive and lossless image coding. The present paper presents a methodology for the optimal construction of pyramids by selecting the analysis prefilters and interpolation synthesis postfilters so as to minimize the error variance at each level of the pyramid. This establishes optimally efficient pyramidal lossless compression. It also has the added advantage of producing lossy replicas of the original which, at lower resolutions retain as much similarity to the original as possible. Thus, optimal progressive coding of signals or images is produced, as is needed for many applications such as fast browsing through image databases or hybrid lossless/lossy medical image coding. To achieve efficient lossless coding a scheme is utilized for the reduction of the number of data needed to be transmitted to reconstruct the original from the low resolution image and the errors produced at the various pyramid stages. This scheme in effect renders the pyramid into a `reduced' pyramid without sacrificing, however, the optimal analysis prefilters of the pyramid. Experimental application of this methodology shows that is outperforms existing methods for lossless and progressive image coding.

Our goal in this article is to present a quantitative study about speech recognition and the inherent problems of its applications and the computer processing. Our approach is characterized by independent speaker and we made use of pre- processing the concept as Wavelets Transform and as pattern recognition an Artificial Neural Network (ANN--Multilayer Perceptron--Backpropagation Algorithm).

EMG signals can be considered as the sum of scaled and delayed versions of a single prototype. We have applied the Wavelet Transform choosing the mother wavelet so as to match the known shape of the basic component, and have compared the results obtained with different wavelets. The results in terms of MUAP detection and resolution are very encouraging even in the presence of asymmetric shape and high levels of additive noise.

Given multiple images of a diffuse surface taken from the same point of view, a photometric approach yields the surface normals which provide a good representation for a 1- 1 surface. This representation can be filtered and compressed using wavelets. In this work, two different applications based upon the wavelet approximations of the surface normals are presented. For the first application, surface reconstruction, compressed wavelet transforms of the images are used to reconstruct a surface. The surface shape is first interpolated from a 3D triangulated description, and then transformed into two and three images based solely upon the surface normals and the lighting direction. When the surface is compressed, the rational wavelets used in integrating the surface can produce singularities. A technique for handling compression of rational wavelets is presented. The second application is object differentiation, a subset of object recognition. The surface normals are used to derive the Gaussian curvature of an object. The Gaussian curvature is used as a primitive for classification. The actual object signature comes from the high magnitude coefficients in the Haar wavelet decomposition. By storing a library of objects indexed by extreme wavelet coefficients as opposed to the object name, a fast query can be performed to find a list of possible matches.

We study the decomposition and compression of one-way wave propagation and imaging operation using wavelet transform. We show that the matrix representation of the Kirchhoff imaging operator (Kirchhoff migration operator) in space domain is a dense matrix, while the compressed beamlet- operator matrix which is the wavelet decomposition in the Kirchhoff operator, is a highly sparse matrix. The beamlet imaging operator represents the backpropagation of multiscale orthonormal beams (beamlets) at different positions with different angles. The beamlet-operator behaves differently in different wavelet bases. For sharp and short bases, such as the Daubechies 4, both the interscale and intrascale coupling are strong. On the other hand, the interscale coupling is relatively weak for smooth bases, such as higher-order Daubechies wavelets, Coiflets, and spline wavelets. The images obtained by the compressed beamlet operators are almost identical to the images from a full-aperture Kirchhoff operator. Compared with the conventional limited-aperture Kirchhoff migration (imaging), beamlet migration (imaging) can retain the wide effective aperture of a full-aperture operator, and hence achieves higher resolution and image quality with reduced computational cost. The compression ratio of the imaging operator ranges from a few times to a few hundred times, depending on the frequency, step length and the wavelet basis.

We investigate the application of adaptive wavelets for the representation and classification of signals in digitized speech and medical images. A class of wavelet basis functions are used to extract features from the regions of interest. These features are then used in an artificial neural network to classify the region are containing the desired object or belonging to the background clutter. The dilation and shift parameters of the wavelet functions are not fixed. These parameters are included in the training scheme. In this way the wavelets are adaptive to the expected shape and size of the signals. The results indicate that adaptive wavelet functions may outperform the classical fixed wavelet analysis in detection of subtle objects.