Weyl-Heisenberg Spaces for Robust Orthogonal Frequency Division Multiplexing

Design of Weyl-Heisenberg sets of waveforms for robust orthogonal frequency division multiplex- ing (OFDM) has been the subject of a considerable volume of work. In this paper, a complete parameterization of orthogonal Weyl-Heisenberg sets and their corresponding biorthogonal sets is given. Several examples of Weyl-Heisenberg sets designed using this parameterization are pre- sented, which in simulations show a high potential for enabling OFDM robust to frequency offset, timing mismatch, and narrow-band interference

An optimally well-localized multi-channel parallel perfect reconstruction filter bank.

Joint uncertainty for the overall L-channel, one-dimensional, parallel filter bank is quantified by a metric which is a weighted sum of the time and frequency localizations of the individual filters. Evidence is presented to show that a filter bank possessing a lower joint filter bank uncertainty with respect to this metric results in a computed multicomponent AM-FM image model that yields lower reconstruction errors. This strongly supports the theory that there is a direct relationship between joint uncertainty as quantified by the measures developed and the degree of local smoothness or "local coherency" that may be expected in the filter bank channel responses. Thus, as demonstrated by the examples, these new measures may be used to construct new filter banks that offer excellent localization properties on par with those of Gabor filter banks.This dissertation defines a measure of uncertainty for finite length discrete-time signals. Using this uncertainty measure, a relationship analogous to the well known continuous-time Heisenberg-Weyl inequality is developed. This uncertainty measure is applied to quantify the joint discrete time-discrete frequency localization of finite impulse response filters, which are used in a quadrature mirror filter bank (QMF). A formulation of a biorthogonal QMF where the low pass analysis filter minimizes the newly defined measure of uncertainty is presented. The search algorithm used in the design of the length-N linear phase low pass analysis FIR filter is given for N = 6 and 8. In each case, the other three filters, which constitute a perfect reconstruction QMF, are determined by adapting a method due to Vetterli and Le Gall. From a set of well known QMFs comprised of length six filters, L-channel perfect reconstruction parallel filter banks (PRPFB) are constructed. The Noble identities are used to show that the L-channel PRPFB is equivalent to a L - 1 level discrete wavelet filter bank. Several five-channel PRPFBs are implemented. A separable implementation of a five-channel, one-dimensional filter bank produces twenty-five channel, two-dimensional filter bank. Each non-low pass, two-dimensional filter is decomposed in a novel, nonseparable way to obtain equivalent channel filters that possess orientation selectivity. This results in a forty-one channel, two-dimensional, orientation selective, PRPFB

Speckle Noise Reduction in Medical Ultrasound Images

Ultrasound imaging is an incontestable vital tool for diagnosis, it provides in non-invasive manner the internal structure of the body to detect eventually diseases or abnormalities tissues. Unfortunately, the presence of speckle noise in these images affects edges and fine details which limit the contrast resolution and make diagnostic more difficult. In this paper, we propose a denoising approach which combines logarithmic transformation and a non linear diffusion tensor. Since speckle noise is multiplicative and nonwhite process, the logarithmic transformation is a reasonable choice to convert signaldependent or pure multiplicative noise to an additive one. The key idea from using diffusion tensor is to adapt the flow diffusion towards the local orientation by applying anisotropic diffusion along the coherent structure direction of interesting features in the image. To illustrate the effective performance of our algorithm, we present some experimental results on synthetically and real echographic images

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Image Registration Using Redundant Wavelet Transforms

Imagery is collected much faster and in significantly greater quantities today compared to a few years ago. Accurate registration of this imagery is vital for comparing the similarities and differences between multiple images. Since human analysis is tedious and error prone for large data sets, we require an automatic, efficient, robust, and accurate method to register images. Wavelet transforms have proven useful for a variety of signal and image processing tasks, including image registration. In our research, we present a fundamentally new wavelet-based registration algorithm utilizing redundant transforms and a masking process to suppress the adverse effects of noise and improve processing efficiency. The shift-invariant wavelet transform is applied in translation estimation and a new rotation-invariant polar wavelet transform is effectively utilized in rotation estimation. We demonstrate the robustness of these redundant wavelet transforms for the registration of two images (i.e., translating or rotating an input image to a reference image), but extensions to larger data sets are certainly feasible. We compare the registration accuracy of our redundant wavelet transforms to the \u27critically sampled\u27 discrete wavelet transform using the Daubechies (7,9) wavelet to illustrate the power of our algorithm in the presence of significant additive white Gaussian noise and strongly translated or rotated images

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Wavelet Filter Evaluation for Image Coding

The wavelet transform has become the most interesting new algorithm for still image compression. Yet there are many parameters within a wavelet analysis and synthesis which govern the quality of a decoded image: decomposition strategy, image boundary policy, quantization threshold, etc. In this paper we discuss different image boundary policies and their implications for the decoded image. A focal point is the trade-off between the length of an orthogonal, compactly supported Daubechies-n wavelet filter bank and the decomposition depth of an image during analysis. An evaluation of the visual quality of images at different parameter settings leads to recommendations on the wavelet filter parameters to be used in image coding