Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Blind source separation using statistical nonnegative matrix factorization

PhD ThesisBlind Source Separation (BSS) attempts to automatically extract and track a signal of interest in real world scenarios with other signals present. BSS addresses the problem of recovering the original signals from an observed mixture without relying on training knowledge. This research studied three novel approaches for solving the BSS problem based on the extensions of non-negative matrix factorization model and the sparsity regularization methods. 1) A framework of amalgamating pruning and Bayesian regularized cluster nonnegative tensor factorization with Itakura-Saito divergence for separating sources mixed in a stereo channel format: The sparse regularization term was adaptively tuned using a hierarchical Bayesian approach to yield the desired sparse decomposition. The modified Gaussian prior was formulated to express the correlation between different basis vectors. This algorithm automatically detected the optimal number of latent components of the individual source. 2) Factorization for single-channel BSS which decomposes an information-bearing matrix into complex of factor matrices that represent the spectral dictionary and temporal codes: A variational Bayesian approach was developed for computing the sparsity parameters for optimizing the matrix factorization. This approach combined the advantages of both complex matrix factorization (CMF) and variational -sparse analysis. BLIND SOURCE SEPARATION USING STATISTICAL NONNEGATIVE MATRIX FACTORIZATION ii 3) An imitated-stereo mixture model developed by weighting and time-shifting the original single-channel mixture where source signals can be modelled by the AR processes. The proposed mixing mixture is analogous to a stereo signal created by two microphones with one being real and another virtual. The imitated-stereo mixture employed the nonnegative tensor factorization for separating the observed mixture. The separability analysis of the imitated-stereo mixture was derived using Wiener masking. All algorithms were tested with real audio signals. Performance of source separation was assessed by measuring the distortion between original source and the estimated one according to the signal-to-distortion (SDR) ratio. The experimental results demonstrate that the proposed uninformed audio separation algorithms have surpassed among the conventional BSS methods; i.e. IS-cNTF, SNMF and CMF methods, with average SDR improvement in the ranges from 2.6dB to 6.4dB per source.Payap Universit

Classification and Separation Techniques based on Fundamental Frequency for Speech Enhancement

[ES] En esta tesis se desarrollan nuevos algoritmos de clasificación y mejora de voz basados en las propiedades de la frecuencia fundamental (F0) de la señal vocal. Estas propiedades permiten su discriminación respecto al resto de señales de la escena acústica, ya sea mediante la definición de características (para clasificación) o la definición de modelos de señal (para separación). Tres contribuciones se aportan en esta tesis: 1) un algoritmo de clasificación de entorno acústico basado en F0 para audífonos digitales, capaz de clasificar la señal en las clases voz y no-voz; 2) un algoritmo de detección de voz sonora basado en la aperiodicidad, capaz de funcionar en ruido no estacionario y con aplicación a mejora de voz; 3) un algoritmo de separación de voz y ruido basado en descomposición NMF, donde el ruido se modela de una forma genérica mediante restricciones matemáticas.[EN]This thesis is focused on the development of new classification and speech enhancement algorithms based, explicitly or implicitly, on the fundamental frequency (F0). The F0 of speech has a number of properties that enable speech discrimination from the remaining signals in the acoustic scene, either by defining F0-based signal features (for classification) or F0-based signal models (for separation). Three main contributions are included in this work: 1) an acoustic environment classification algorithm for hearing aids based on F0 to classify the input signal into speech and nonspeech classes; 2) a frame-by-frame basis voiced speech detection algorithm based on the aperiodicity measure, able to work under non-stationary noise and applicable to speech enhancement; 3) a speech denoising algorithm based on a regularized NMF decomposition, in which the background noise is described in a generic way with mathematical constraints.Tesis Univ. Jaén. Departamento de Ingeniería de Telecomunición. Leída el 11 de enero de 201