Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message Passing

In this work the dynamic compressive sensing (CS) problem of recovering sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear measurements is explored from a Bayesian perspective. While there has been a handful of previously proposed Bayesian dynamic CS algorithms in the literature, the ability to perform inference on high-dimensional problems in a computationally efficient manner remains elusive. In response, we propose a probabilistic dynamic CS signal model that captures both amplitude and support correlation structure, and describe an approximate message passing algorithm that performs soft signal estimation and support detection with a computational complexity that is linear in all problem dimensions. The algorithm, DCS-AMP, can perform either causal filtering or non-causal smoothing, and is capable of learning model parameters adaptively from the data through an expectation-maximization learning procedure. We provide numerical evidence that DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety of operating conditions. We further describe the result of applying DCS-AMP to two real dynamic CS datasets, as well as a frequency estimation task, to bolster our claim that DCS-AMP is capable of offering state-of-the-art performance and speed on real-world high-dimensional problems.Comment: 32 pages, 7 figure

Proceedings of the 35th WIC Symposium on Information Theory in the Benelux and the 4th joint WIC/IEEE Symposium on Information Theory and Signal Processing in the Benelux, Eindhoven, the Netherlands May 12-13, 2014

Compressive sensing (CS) as an approach for data acquisition has recently received much attention. In CS, the signal recovery problem from the observed data requires the solution of a sparse vector from an underdetermined system of equations. The underlying sparse signal recovery problem is quite general with many applications and is the focus of this talk. The main emphasis will be on Bayesian approaches for sparse signal recovery. We will examine sparse priors such as the super-Gaussian and student-t priors and appropriate MAP estimation methods. In particular, re-weighted l2 and re-weighted l1 methods developed to solve the optimization problem will be discussed. The talk will also examine a hierarchical Bayesian framework and then study in detail an empirical Bayesian method, the Sparse Bayesian Learning (SBL) method. If time permits, we will also discuss Bayesian methods for sparse recovery problems with structure; Intra-vector correlation in the context of the block sparse model and inter-vector correlation in the context of the multiple measurement vector problem

Development of Some Spatial-domain Preprocessing and Post-processing Algorithms for Better 2-D Up-scaling

Image super-resolution is an area of great interest in recent years and is extensively used in applications like video streaming, multimedia, internet technologies, consumer electronics, display and printing industries. Image super-resolution is a process of increasing the resolution of a given image without losing its integrity. Its most common application is to provide better visual effect after resizing a digital image for display or printing. One of the methods of improving the image resolution is through the employment of a 2-D interpolation. An up-scaled image should retain all the image details with very less degree of blurring meant for better visual quality. In literature, many efficient 2-D interpolation schemes are found that well preserve the image details in the up-scaled images; particularly at the regions with edges and fine details. Nevertheless, these existing interpolation schemes too give blurring effect in the up-scaled images due to the high frequency (HF) degradation during the up-sampling process. Hence, there is a scope to further improve their performance through the incorporation of various spatial domain pre-processing, post-processing and composite algorithms. Therefore, it is felt that there is sufficient scope to develop various efficient but simple pre-processing, post-processing and composite schemes to effectively restore the HF contents in the up-scaled images for various online and off-line applications. An efficient and widely used Lanczos-3 interpolation is taken for further performance improvement through the incorporation of various proposed algorithms. The various pre-processing algorithms developed in this thesis are summarized here. The term pre-processing refers to processing the low-resolution input image prior to image up-scaling. The various pre-processing algorithms proposed in this thesis are: Laplacian of Laplacian based global pre-processing (LLGP) scheme; Hybrid global pre-processing (HGP); Iterative Laplacian of Laplacian based global pre-processing (ILLGP); Unsharp masking based pre-processing (UMP); Iterative unsharp masking (IUM); Error based up-sampling(EU) scheme. The proposed algorithms: LLGP, HGP and ILLGP are three spatial domain preprocessing algorithms which are based on 4th, 6th and 8th order derivatives to alleviate nonuniform blurring in up-scaled images. These algorithms are used to obtain the high frequency (HF) extracts from an image by employing higher order derivatives and perform precise sharpening on a low resolution image to alleviate the blurring in its 2-D up-sampled counterpart. In case of unsharp masking based pre-processing (UMP) scheme, the blurred version of a low resolution image is used for HF extraction from the original version through image subtraction. The weighted version of the HF extracts are superimposed with the original image to produce a sharpened image prior to image up-scaling to counter blurring effectively. IUM makes use of many iterations to generate an unsharp mask which contains very high frequency (VHF) components. The VHF extract is the result of signal decomposition in terms of sub-bands using the concept of analysis filter bank. Since the degradation of VHF components is maximum, restoration of such components would produce much better restoration performance. EU is another pre-processing scheme in which the HF degradation due to image upscaling is extracted and is called prediction error. The prediction error contains the lost high frequency components. When this error is superimposed on the low resolution image prior to image up-sampling, blurring is considerably reduced in the up-scaled images. Various post-processing algorithms developed in this thesis are summarized in following. The term post-processing refers to processing the high resolution up-scaled image. The various post-processing algorithms proposed in this thesis are: Local adaptive Laplacian (LAL); Fuzzy weighted Laplacian (FWL); Legendre functional link artificial neural network(LFLANN). LAL is a non-fuzzy, local based scheme. The local regions of an up-scaled image with high variance are sharpened more than the region with moderate or low variance by employing a local adaptive Laplacian kernel. The weights of the LAL kernel are varied as per the normalized local variance so as to provide more degree of HF enhancement to high variance regions than the low variance counterpart to effectively counter the non-uniform blurring. Furthermore, FWL post-processing scheme with a higher degree of non-linearity is proposed to further improve the performance of LAL. FWL, being a fuzzy based mapping scheme, is highly nonlinear to resolve the blurring problem more effectively than LAL which employs a linear mapping. Another LFLANN based post-processing scheme is proposed here to minimize the cost function so as to reduce the blurring in a 2-D up-scaled image. Legendre polynomials are used for functional expansion of the input pattern-vector and provide high degree of nonlinearity. Therefore, the requirement of multiple layers can be replaced by single layer LFLANN architecture so as to reduce the cost function effectively for better restoration performance. With single layer architecture, it has reduced the computational complexity and hence is suitable for various real-time applications. There is a scope of further improvement of the stand-alone pre-processing and postprocessing schemes by combining them through composite schemes. Here, two spatial domain composite schemes, CS-I and CS-II are proposed to tackle non-uniform blurring in an up-scaled image. CS-I is developed by combining global iterative Laplacian (GIL) preprocessing scheme with LAL post-processing scheme. Another highly nonlinear composite scheme, CS-II is proposed which combines ILLGP scheme with a fuzzy weighted Laplacian post-processing scheme for more improved performance than the stand-alone schemes. Finally, it is observed that the proposed algorithms: ILLGP, IUM, FWL, LFLANN and CS-II are better algorithms in their respective categories for effectively reducing blurring in the up-scaled images

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Speech Enhancement Exploiting the Source-Filter Model

Imagining everyday life without mobile telephony is nowadays hardly possible. Calls are being made in every thinkable situation and environment. Hence, the microphone will not only pick up the user’s speech but also sound from the surroundings which is likely to impede the understanding of the conversational partner. Modern speech enhancement systems are able to mitigate such effects and most users are not even aware of their existence. In this thesis the development of a modern single-channel speech enhancement approach is presented, which uses the divide and conquer principle to combat environmental noise in microphone signals. Though initially motivated by mobile telephony applications, this approach can be applied whenever speech is to be retrieved from a corrupted signal. The approach uses the so-called source-filter model to divide the problem into two subproblems which are then subsequently conquered by enhancing the source (the excitation signal) and the filter (the spectral envelope) separately. Both enhanced signals are then used to denoise the corrupted signal. The estimation of spectral envelopes has quite some history and some approaches already exist for speech enhancement. However, they typically neglect the excitation signal which leads to the inability of enhancing the fine structure properly. Both individual enhancement approaches exploit benefits of the cepstral domain which offers, e.g., advantageous mathematical properties and straightforward synthesis of excitation-like signals. We investigate traditional model-based schemes like Gaussian mixture models (GMMs), classical signal processing-based, as well as modern deep neural network (DNN)-based approaches in this thesis. The enhanced signals are not used directly to enhance the corrupted signal (e.g., to synthesize a clean speech signal) but as so-called a priori signal-to-noise ratio (SNR) estimate in a traditional statistical speech enhancement system. Such a traditional system consists of a noise power estimator, an a priori SNR estimator, and a spectral weighting rule that is usually driven by the results of the aforementioned estimators and subsequently employed to retrieve the clean speech estimate from the noisy observation. As a result the new approach obtains significantly higher noise attenuation compared to current state-of-the-art systems while maintaining a quite comparable speech component quality and speech intelligibility. In consequence, the overall quality of the enhanced speech signal turns out to be superior as compared to state-of-the-art speech ehnahcement approaches.Mobiltelefonie ist aus dem heutigen Leben nicht mehr wegzudenken. Telefonate werden in beliebigen Situationen an beliebigen Orten geführt und dabei nimmt das Mikrofon nicht nur die Sprache des Nutzers auf, sondern auch die Umgebungsgeräusche, welche das Verständnis des Gesprächspartners stark beeinflussen können. Moderne Systeme können durch Sprachverbesserungsalgorithmen solchen Effekten entgegenwirken, dabei ist vielen Nutzern nicht einmal bewusst, dass diese Algorithmen existieren. In dieser Arbeit wird die Entwicklung eines einkanaligen Sprachverbesserungssystems vorgestellt. Der Ansatz setzt auf das Teile-und-herrsche-Verfahren, um störende Umgebungsgeräusche aus Mikrofonsignalen herauszufiltern. Dieses Verfahren kann für sämtliche Fälle angewendet werden, in denen Sprache aus verrauschten Signalen extrahiert werden soll. Der Ansatz nutzt das Quelle-Filter-Modell, um das ursprüngliche Problem in zwei Unterprobleme aufzuteilen, die anschließend gelöst werden, indem die Quelle (das Anregungssignal) und das Filter (die spektrale Einhüllende) separat verbessert werden. Die verbesserten Signale werden gemeinsam genutzt, um das gestörte Mikrofonsignal zu entrauschen. Die Schätzung von spektralen Einhüllenden wurde bereits in der Vergangenheit erforscht und zum Teil auch für die Sprachverbesserung angewandt. Typischerweise wird dabei jedoch das Anregungssignal vernachlässigt, so dass die spektrale Feinstruktur des Mikrofonsignals nicht verbessert werden kann. Beide Ansätze nutzen jeweils die Eigenschaften der cepstralen Domäne, die unter anderem vorteilhafte mathematische Eigenschaften mit sich bringen, sowie die Möglichkeit, Prototypen eines Anregungssignals zu erzeugen. Wir untersuchen modellbasierte Ansätze, wie z.B. Gaußsche Mischmodelle, klassische signalverarbeitungsbasierte Lösungen und auch moderne tiefe neuronale Netzwerke in dieser Arbeit. Die so verbesserten Signale werden nicht direkt zur Sprachsignalverbesserung genutzt (z.B. Sprachsynthese), sondern als sogenannter A-priori-Signal-zu-Rauschleistungs-Schätzwert in einem traditionellen statistischen Sprachverbesserungssystem. Dieses besteht aus einem Störleistungs-Schätzer, einem A-priori-Signal-zu-Rauschleistungs-Schätzer und einer spektralen Gewichtungsregel, die üblicherweise mit Hilfe der Ergebnisse der beiden Schätzer berechnet wird. Schließlich wird eine Schätzung des sauberen Sprachsignals aus der Mikrofonaufnahme gewonnen. Der neue Ansatz bietet eine signifikant höhere Dämpfung des Störgeräuschs als der bisherige Stand der Technik. Dabei wird eine vergleichbare Qualität der Sprachkomponente und der Sprachverständlichkeit gewährleistet. Somit konnte die Gesamtqualität des verbesserten Sprachsignals gegenüber dem Stand der Technik erhöht werden

A study on different linear and non-linear filtering techniques of speech and speech recognition

In any signal noise is an undesired quantity, however most of thetime every signal get mixed with noise at different levels of theirprocessing and application, due to which the information containedby the signal gets distorted and makes the whole signal redundant.A speech signal is very prominent with acoustical noises like bubblenoise, car noise, street noise etc. So for removing the noises researchershave developed various techniques which are called filtering. Basicallyall the filtering techniques are not suitable for every application,hence based on the type of application some techniques are betterthan the others. Broadly, the filtering techniques can be classifiedinto two categories i.e. linear filtering and non-linear filtering.In this paper a study is presented on some of the filtering techniqueswhich are based on linear and nonlinear approaches. These techniquesincludes different adaptive filtering based on algorithm like LMS,NLMS and RLS etc., Kalman filter, ARMA and NARMA time series applicationfor filtering, neural networks combine with fuzzy i.e. ANFIS. Thispaper also includes the application of various features i.e. MFCC,LPC, PLP and gamma for filtering and recognition

Image Deblurring and Super-resolution by Adaptive Sparse Domain Selection and Adaptive Regularization

As a powerful statistical image modeling technique, sparse representation has been successfully used in various image restoration applications. The success of sparse representation owes to the development of l1-norm optimization techniques, and the fact that natural images are intrinsically sparse in some domain. The image restoration quality largely depends on whether the employed sparse domain can represent well the underlying image. Considering that the contents can vary significantly across different images or different patches in a single image, we propose to learn various sets of bases from a pre-collected dataset of example image patches, and then for a given patch to be processed, one set of bases are adaptively selected to characterize the local sparse domain. We further introduce two adaptive regularization terms into the sparse representation framework. First, a set of autoregressive (AR) models are learned from the dataset of example image patches. The best fitted AR models to a given patch are adaptively selected to regularize the image local structures. Second, the image non-local self-similarity is introduced as another regularization term. In addition, the sparsity regularization parameter is adaptively estimated for better image restoration performance. Extensive experiments on image deblurring and super-resolution validate that by using adaptive sparse domain selection and adaptive regularization, the proposed method achieves much better results than many state-of-the-art algorithms in terms of both PSNR and visual perception.Comment: 35 pages. This paper is under review in IEEE TI

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Image Restoration

This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with