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

Multiscale Adaptive Representation of Signals: I. The Basic Framework

We introduce a framework for designing multi-scale, adaptive, shift-invariant frames and bi-frames for representing signals. The new framework, called AdaFrame, improves over dictionary learning-based techniques in terms of computational efficiency at inference time. It improves classical multi-scale basis such as wavelet frames in terms of coding efficiency. It provides an attractive alternative to dictionary learning-based techniques for low level signal processing tasks, such as compression and denoising, as well as high level tasks, such as feature extraction for object recognition. Connections with deep convolutional networks are also discussed. In particular, the proposed framework reveals a drawback in the commonly used approach for visualizing the activations of the intermediate layers in convolutional networks, and suggests a natural alternative

A Deep Learning Approach to Structured Signal Recovery

In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy algorithms, we introduce a deep learning framework that supports both linear and mildly nonlinear measurements, that learns a structured representation from training data, and that efficiently computes a signal estimate. In particular, we apply a stacked denoising autoencoder (SDA), as an unsupervised feature learner. SDA enables us to capture statistical dependencies between the different elements of certain signals and improve signal recovery performance as compared to the CS approach

WAVELET BASED NONLINEAR SEPARATION OF IMAGES

This work addresses a real-life problem corresponding to the separation of the nonlinear mixture of images which arises when we scan a paper document and the image from the back page shows through. The proposed solution consists of a non-iterative procedure that is based on two simple observations: (1) the high frequency content of images is sparse, and (2) the image printed on each side of the paper appears more strongly in the mixture acquired from that side than in the mixture acquired from the opposite side. These ideas had already been used in the context of nonlinear denoising source separation (DSS). However, in that method the degree of separation achieved by applying these ideas was relatively weak, and the separation had to be improved by iterating within the DSS scheme. In this paper the application of these ideas is improved by changing the competition function and the wavelet transform that is used. These improvements allow us to achieve a good separation in one shot, without the need to integrate the process into an iterative DSS scheme. The resulting separation process is both nonlinear and non-local. We present experimental results that show that the method achieves a good separation quality