Showing papers on "S transform published in 2005"

The inverse S-transform in filters with time-frequency localization

Abstract: The S-transform provides a framework for data-adaptive filters which take advantage of time-frequency localized spectra. These filters basically consist in a data transformation to the time-frequency domain, the data-adaptive weighting of the localized spectra, and a back transformation. We illustrate that the inverse S-transform of manipulated spectra not necessarily transforms the localized signals as expected from the imposed weighting. The time localization is not directly translated and spurious signals and noise can be generated. We discuss this problem and suggest a new inverse S-transform, which may be helpful to many applications to take more advantage of the time-frequency localization.

System and method for progressively transforming and coding digital data

Abstract: A system and method facilitating progressively transforming and coding digital pictures is provided. The present invention via employment of a multi-resolution lapped transform provides for progressive rendering as well as mitigation of blocking artifacts and ringing artifacts as compared to many conventional compression systems. The invention includes a color space mapper, a multi-resolution lapped transform, a quantizer, a scanner and an entropy encoder. The multi-resolution lapped transform outputs transform coefficients, for example, first transform coefficients and second transform coefficients. A multi-resolution representation can be obtained utilizing second transform coefficients of the multi-resolution lapped transform. The color space mapper maps an input image to a color space representation of the input image. The color space representation of the input image is then provided to the multi-resolution lapped transform. The quantizer receives the first transform coefficients and/or the second transform coefficients and provides an output of quantized coefficients for use by the scanner and/or the entropy encoder. The scanner scans the quantized coefficients in order to produce a one-dimensional vector for use by the entropy encoder. The entropy encoder encodes the quantized coefficients received from the quantizer and/or the scanner resulting in data compression.

Maximum-likelihood detection in DWT domain image watermarking using Laplacian modeling

Abstract: Digital image watermarks can be detected in the transform domain using maximum-likelihood detection, whereby the decision threshold is obtained using the Neyman-Pearson criterion. A probability distribution function is required to correctly model the statistical behavior of the transform coefficients. Earlier work has considered modeling the discrete wavelet transform coefficients using a Gaussian distribution. Here, we introduce a Laplacian model and establish via simulation that it can result in a better performance than the Gaussian model.

The successive mean quantization transform

Abstract: This paper presents the successive mean quantization transform (SMQT). The transform reveals the organization or structure of the data and removes properties such as gain and bias. The transform is described and applied in speech processing and image processing. The SMQT is considered as an extra processing step for the mel frequency cepstral coefficients commonly used in speech recognition. In image processing the transform is applied in automatic image enhancement and dynamic range compression.

Hyperlog-a flexible log-like transform for negative, zero, and positive valued data.

Abstract: Background The remarkable success of cytometry over the past 30 years is largely due to its uncanny ability to display populations that vastly differ in numbers and fluorescence intensities on one scale. The log transform implemented in hardware as a log amplifier or in software normalizes signals or channels so that these populations appear as clearly discernible peaks. With the advent of multiple fluorescence cytometry, spectral crossover compensation of these signals has been necessary to properly interpret the data. Unfortunately, because compensation is a subtractive process, it can produce negative and zero valued data. The log transform is undefined for these values and, as a result, forces computer algorithms to truncate these values, creating a few problems for cytometrists. Data truncation biases displays making properly compensated data appear undercompensated; thus, enticing many operators to overcompensate their data. Also, events truncated into the first histogram channel are not normally visible with typical two-dimensional graphic displays, thus hiding a large number of events and obscuring the true proportionality of negative distributions. In addition, the log transform creates unequal binning that can dramatically distort negative population distributions. Methods and Results The HyperLog transform is a log-like transform that admits negative, zero, and positive values. The transform is a hybrid type of transform specifically designed for compensated data. One of its parameters allows it to smoothly transition from a logarithmic to linear type of transform that is ideal for compensated data. Conclusions The HyperLog transform is easily implemented in computer systems and results in display systems that present compensated data in an unbiased manner. © 2005 Wiley-Liss, Inc.

S-transform-based classification of power quality disturbance signals by support vector machines

Abstract: Based on Support Vector Machines (SVM) and S-transform, a novel approach to detect and classify various types of electric power quality disturbances is presented. The S-transform is an extension of the continuous wavelet transform and short time Fourier transform, it uses an analysis window whose width is decreasing with frequency and then providing a frequency dependent resolution. For its good time-frequency characteristic, it is suitable for feature extraction of power quality disturbance signals. At first the S-transform is applied to obtain useful features of the non-stationary power quality disturbance signals. Then disturbance types are identified through the pattern recognition classifier based on SVM. Numerical results show that the proposed classification method is an effective technique for building up a pattern recognition system for power network disturbance signals.

The Gabor transform, pseudodifferential operators, and seismic deconvolution

Abstract: Using the Gabor transform, we describe a technique to correct reflection seismograms for the effects of anelastic attenuation and source signature. Essentially we build a nonstationary deconvolution filter, estimated from the seismic data itself and applied by multiplication in the Gabor domain. In more detail, we estimate the time-frequency magnitude spectrum of the attenuation process and the source signature from the Gabor transform of a seismic signal; the phase then follows under the assumption of minimum phase. The deconvolution filter is the inverse of this estimate and is applied to the Gabor transform of the seismic signal by multiplication. An inverse Gabor transform completes the algorithm and gives a very high resolution estimate for the reflectivity of the earth. As a justification for our algorithm we present a model for a seismic trace that uses a pseudodifferential operator to describe anelastic attenuation. We then argue that the Gabor transform approximately renders this pseudodifferential operator expression into a product of time-frequency dependent factors. Attenuation processes and source signature are removed by multiplication with estimates of their inverses. With both real and synthetic data we illustrate the effectiveness of Gabor deconvolution and demonstrate its superiority over the established Wiener deconvolution.

Coding with improved time resolution for selected segments via adaptive block transformation of a group of samples from a subband decomposition

Abstract: A transform coder is described that performs a time-split transform in addition to a discrete cosine type transform. A time-split transform is selectively performed based on characteristics of media data. Transient detection identifies a changing signal characteristic, such as a transient in media data. After encoding an input signal from a time domain to a transform domain, a time-splitting transformer selectively perform an orthogonal sum-difference transform on adjacent coefficients indicated by a changing signal characteristic location. The orthogonal sum-difference transform on adjacent coefficients results in transforming a vector of coefficients in the transform domain as if they were multiplied by an identity matrix including at least one 2×2 time-split block along a diagonal of the matrix. A decoder performs an inverse of the described transforms.

Approximation of the Fourier Transform and the Dual Gabor Window

Abstract: Many results and problems in Fourier and Gabor analysis are formulated in the continuous variable case, i.e., for functions on ℝ. In contrast, a suitable setting for practical computations is the finite case, dealing with vectors of finite length. We establish fundamental results for the approximation of the continuous case by finite models, namely, the approximation of the Fourier transform and the approximation of the dual Gabor window of a Gabor frame. The appropriate function space for our approach is the Feichtinger space S0. It is dense in L2, much larger than the Schwartz space, and it is a Banach space.

The discrete Pascal transform and its applications

Abstract: We introduce a new discrete polynomial transform constructed from the rows of Pascal's triangle. The forward and inverse transforms are computed the same way in both the one- and two-dimensional cases, and the transform matrix can be factored into binary matrices for efficient hardware implementation. We conclude by discussing applications of the transform in digital image processing, such as bump and edge detection.

Improved denoising of images using modelling of a redundant contourlet transform

Abstract: In this work we investigate the image denoising problem. One common approach found in the literature involves manipulating the coefficients in the transform domain, e.g. shrinkage, followed by the inverse transform. Several advanced methods that model the inter-coefficient dependencies were developed recently, and were shown to yield significant improvement. However, these methods operate on the transform domain error rather than on the image domain one. These errors are in general entirely different for redundant transforms. In this work we propose a novel denoising method, based on the Basis-Pursuit Denoising (BPDN). Our method combines the image domain error with the transform domain dependency structure, resulting in a general objective function, applicable for any wavelet-like transform. We focus here on the Contourlet Transform (CT) and on a redundant version of it, both relatively new transforms designed to sparsely represent images. The performance of our new method is compared favorably with the state-of-the-art method of Bayesian Least Squares Gaussian Scale Mixture (BLS-GSM), which we adapted to the CT as well, with further improvements still to come.

An image compression scheme based on parametric Haar-like transform

Abstract: A new image compression scheme is presented, based on a fast orthogonal parametrically adaptive Haar-like transform, which is a discrete orthogonal transform such that it may be computed with a fast algorithm in structure similar to the classical fast Haar transform, and such that its matrix contains one or more predefined row(s) of an arbitrary order. The nature of the proposed image compression scheme is such that its performance (in terms of PSNR versus compression ratio) cannot be worse than that of the classical DCT (discrete cosine transform) based scheme. Simulations show that a significant performance improvement can be achieved for certain types of images such as medical X-ray images.

Fourier transform representation by frequency-time wavelets

Abstract: A new concept of the A-wavelet transform is introduced, and the representation of the Fourier transform by the A-wavelet transform is described. Such a wavelet transform uses a fully scalable modulated window but not all possible shifts. A geometrical locus of frequency-time points for the A-wavelet transform is derived, and examples are given. The locus is considered "optimal" for the Fourier transform when a signal can be recovered by using only values of its wavelet transform defined on the locus. The inverse Fourier transform is also represented by the A/sup */-wavelet transform defined on specific points in the time-frequency plane. The concept of the A-wavelet transform can be extended for representation of other unitary transforms. Such an example for the Hartley transform is described, and the reconstruction formula is given.

A comparison of flat and object-based transform coding techniques for the compression of multispectral images

Abstract: In this work we implement and compare several state-of-the-art transform coding schemes for the compression of multispectral images, in order to better understand which elements have a deeper impact on the overall performance, and which tools guarantee the best results. All schemes are based on Karhunen-Loeve transform and/or wavelet transform, in various combinations, and use SPIHT as the coding engine. Moreover, besides the ordinary techniques, their object-based counterparts are also examined, so as to study the viability of such approach [M. Cagnazzo et al., Oct 2004] for these images. Whenever possible, an optimal rate allocation strategy is applied. The experiments, performed on images acquired by two different sensors, highlight the superiority of KLT as spectral transform; the rough equivalence between object-based and ordinary techniques in terms of rate-distortion performance; and the importance of the optimal allocation.

Noise Reduction for NMR FID Signals via Oversampled Real-Valued Discrete Gabor Transform

Abstract: An efficient algorithm to reduce the noise from the Nuclear Magnetic Resonance Free Induction Decay (NMR FID) signals is presented, in this paper, via the oversampled real-valued discrete Gabor transform using the Gaussian synthesis window. An NMR FID signal in the Gabor transform domain (i.e., a joint time-frequency domain) is concentrated in a few number of Gabor transform coefficients while the noise is fairly distributed among all the coefficients. Therefore, the NMR FID signal can be significantly enhanced by performing a thresholding technique on the coefficients in the transform domain. Theoretical and simulation experimental analyses in this paper show that the oversampled Gabor transform using the Gaussian synthesis window is more suitable for the NMR FID signal enhancement than the critically-sampled one using the exponential synthesis window, because both the Gaussian synthesis window and its corresponding analysis window in the oversampling case can have better localization in the frequency domain than the exponential synthesis window and its corresponding analysis window in the critically-sampling case. Moreover, to speed up the transform, instead of the commonly-used complex-valued discrete Gabor transform, the real-valued discrete Gabor transform presented in our previous work is adopted in the proposed algorithm.

Transform-based methods for indexing and retrieval of 3D objects

Abstract: We compare two transform-based indexing methods for retrieval of 3D objects. We apply 3D discrete Fourier transform (DFT) and 3D radial cosine transform (RCT) to the voxelized data of 3D objects. Rotation invariant features are derived from the coefficients of these transforms. Furthermore we compare two different voxel representations, namely, binary denoting object and background space, and continuous after distance transformation. In the binary voxel representation the voxel values are simply set to 1 on the surface of the object and 0 elsewhere. In the continuous-valued representation the space is filled with a function of distance transform. The rotation invariance properties of the DFT and RCT schemes are analyzed. We have conducted retrieval experiments on the Princeton Shape Benchmark and investigated the retrieval performance of the methods using several quality measures.

The Gaussian Transform

Abstract: This paper introduces the general purpose Gaussian Transform, which aims at representing a generic symmetric distribution as an infinite mixture of Gaussian distributions. We start by the mathematical formulation of the problem and continue with the investigation of the conditions of existence of such a transform. Our analysis leads to the derivation of analytical and numerical tools for the computation of the Gaussian Transform, mainly based on the Laplace and Fourier transforms, as well as of the afferent properties set (e.g. the transform of sums of independent variables). Finally, the Gaussian Transform is exemplified in analytical form for typical distributions (e.g. Gaussian, Laplacian), and in numerical form for the Generalized Gaussian and Generalized Cauchy distributions families.

Feature Extraction Based on Mel-Scaled Wavelet Transform for Heart Sound Analysis

Abstract: To provide a robust representation of heart sound signal in an automatic heart disease diagnosis system, a mel-scaled wavelet transform has been developed. It combines the advantages of linear perceptual scale by mel mapping with the suitability of analyzing non-stationary signals by wavelet transform. The heart sound signal is firstly divided into windowing frames. A set of mel-scaled filterbank is then used to calculate the mel-warped spectrum, which is followed by a wavelet transform to extract the mel-scaled wavelet features. The performance of the proposed algorithm is evaluated for heart sound analysis using clean and noisy data, and compared with the standard mel-frequency cepstral coefficients. Results show that the proposed approach provides a robust representation of heart sound signal in noisy environment

A linear Euclidean distance transform algorithm based on the linear-time Legendre transform

Abstract: We introduce a new exact Euclidean distance transform algorithm for binary images based on the linear-time Legendre Transform algorithm. The three-step algorithm uses dimension reduction and convex analysis results on the Legendre-Fenchel transform to achieve linear-time complexity. First, computation on a grid (the image) is reduced to computation on a line, then the convex envelope is computed, and finally the squared Euclidean distance transform is obtained. Examples and an extension to non-binary images are provided.

Optimal correlating transform for erasure channels

Abstract: In this letter, we derive a gradient-based algorithm for computing the optimal transform when coefficients are transmitted over an erasure channel whose statistics are known. The discrete transform introduces correlation among the coefficients with consequent performance improvement against losses. Simulations show appreciable improvements over standard schemes and also good robustness when loss probabilities are only roughly estimated.

Inversion of the radon transform associated with the classical domain of type one

Abstract: Let D(Ω,Φ) be the unbounded realization of the classical domain of type one. In general, its Silov boundary is a nilpotent Lie group of step two. In this article we define the Radon transform on , and obtain an inversion formula in terms of a determinantal differential operator. Moreover, we characterize a subspace of on which the Radon transform is a bijection. By use of the suitable continuous wavelet transform we establish a new inversion formula of the Radon transform in weak sense without the assumption of differentiability.

Modified ICA algorithms for finding optimal transforms in transform coding

Abstract: In this paper we present two new algorithms that compute the linear optimal transform in high-rate transform coding, for non Gaussian data. One algorithm computes the optimal orthogonal transform, and the other the optimal linear transform. Comparison of the performances in high-rate transform coding between the classical Karhunen-Loeve Transform (KLT) and the transforms returned by the new algorithms are given. On synthetic data, the transforms given by the new algorithms perform significantly better that the KLT, however on real data all the transforms, included KLT, give roughly the same coding gain.

An analysis of real-Fourier domain-based adaptive algorithms implemented with the Hartley transform using cosine-sine symmetries

Abstract: The least mean squared (LMS) algorithm and its variants have been the most often used algorithms in adaptive signal processing. However the LMS algorithm suffers from a high computational complexity, especially with large filter lengths. The Fourier transform-based block normalized LMS (FBNLMS) reduces the computation count by using the discrete Fourier transform (DFT) and exploiting the fast algorithms for implementing the DFT. Even though the savings achieved with the FBNLMS over the direct-LMS implementation are significant, the computational requirements of FBNLMS are still very high, rendering many real-time applications, like audio and video estimation, infeasible. The Hartley transform-based BNLMS (HBNLMS) is found to have a computational complexity much less than, and a memory requirement almost of the same order as, that of the FBNLMS. This paper is based on the cosine and sine symmetric implementation of the discrete Hartley transform (DHT), which is the key in reducing the computational complexity of the FBNLMS by 33% asymptotically (with respect to multiplications). The parallel implementation of the discrete cosine transform (DCT) in turn can lead to more efficient implementations of the HBNLMS.

On Image Compression using Digital Curvelet Transform

Abstract: This paper describes a novel approach to digital image compression using a new mathematical transform: the curvelet transform. The transform has shown promising results over wavelet transform for 2D signals. Wavelets, though well suited to point singularities have limitations with orientation selectivity, and therefore, do not represent two-dimensional singularities (e.g. smooth curves) effectively. This paper employs the curvelet transform for image compression, exhibiting good approximation properties for smooth 2D functions. Curvelet improves wavelet by incorporating a directional component. The curvelet transform finds a direct discrete-space construction and is therefore computationally efficient. In this paper, we divided 2D spectrum into fine slices using iterated tree structured filter bank. Different amount of quantized curvelet coefficients were then selected for lossy compression and entropy encoding. A comparison with wavelet based compression was made for standard images like Lena, Barbara, etc. Curvelet transform has resulted in high quality image compression for natural images. Our implementation offers exact reconstruction, prone to perturbations, ease of implementation and low computational complexity. The algorithm works fairly well for grayscale and colored images

Complex wavelets versus Gabor wavelets for facial feature extraction: a comparative study

Abstract: In this paper two complex wavelet transforms, namely the Gabor wavelet transform and Kingsbury's Dual-Tree Complex wavelet transform (DT-CWT) are compared for their capabilities to extract facial features. The Gabor wavelets extract directional features from images and find frequent applications in computer vision problems of face detection and face recognition. The transform involves convolving an image with an ensemble of Gabor kernels, scale and directionally parameterized. As a result, a redundant image representation is obtained, where the number of transformed images is equal to the number of Gabor kernels used. However, repetitive convolution with 2-D Gabor kernels is a rather slow computational operation. The DT-CWT is a recently suggested transform, which provides good directional selectivity in six different fixed orientations at dyadic scales with the ability to distinguish positive and negative frequencies. It has a limited redundancy of four for images and is much faster than the Gabor transform to compute. Therefore, it arises as a good candidate to replace Gabor transform in applications, where the speed (i.e. on-line implementation) is a critical issue. We involve the two wavelet families in facial landmarks detection and compare their performance by statistical tests, e.g. by building Receiver Operating Characteristic (ROC) curves and by measuring the sensitivity of a particular feature extractor. We also compare results of Bayesian classification for the two families of feature extractors involved.

On unified architectures for synthesizing and implementation of fast parametric transforms

Abstract: In this paper a methodology to design VLSI architectures for parametric transform families is proposed. A parametric transform family consists of discrete orthogonal transforms such that they all may be computed with a fast algorithm of similar structure where parameters defining the transform within the family are used. In our previous work, an algorithm to synthesize transforms with predefined basis functions was introduced and efficiently applied to image compression. The methodology proposed in this paper allows of designing VLSI architectures that may not only switch from one transform of a family to another by setting parameters, but also to actually set these parameters so that the matrix of the resulting transform has predefined basis functions