The M-Term Pursuit for Image Representation and Progressive Compression

This paper introduces a sparse signal representation algorithm in redundant dictionaries, called the M-Term Pursuit (MTP), with an application to image representation and scalable coding. The MTP algorithm belongs to the framework of the matching pursuit (MP); it expands the image into a linear combination of atoms, selected from a large collection of spatial atoms. The MTP relies on the concept of dictionary partitioning, i.e., as splitting the dictionary into $L$ disjoint sub-dictionaries, each carrying some specific information. Then, it iteratively finds a $K$-term approximation, by selecting $M$ atoms at a time, where $

Role of homeostasis in learning sparse representations

Neurons in the input layer of primary visual cortex in primates develop edge-like receptive fields. One approach to understanding the emergence of this response is to state that neural activity has to efficiently represent sensory data with respect to the statistics of natural scenes. Furthermore, it is believed that such an efficient coding is achieved using a competition across neurons so as to generate a sparse representation, that is, where a relatively small number of neurons are simultaneously active. Indeed, different models of sparse coding, coupled with Hebbian learning and homeostasis, have been proposed that successfully match the observed emergent response. However, the specific role of homeostasis in learning such sparse representations is still largely unknown. By quantitatively assessing the efficiency of the neural representation during learning, we derive a cooperative homeostasis mechanism that optimally tunes the competition between neurons within the sparse coding algorithm. We apply this homeostasis while learning small patches taken from natural images and compare its efficiency with state-of-the-art algorithms. Results show that while different sparse coding algorithms give similar coding results, the homeostasis provides an optimal balance for the representation of natural images within the population of neurons. Competition in sparse coding is optimized when it is fair. By contributing to optimizing statistical competition across neurons, homeostasis is crucial in providing a more efficient solution to the emergence of independent components

Feature detection using spikes: the greedy approach

A goal of low-level neural processes is to build an efficient code extracting the relevant information from the sensory input. It is believed that this is implemented in cortical areas by elementary inferential computations dynamically extracting the most likely parameters corresponding to the sensory signal. We explore here a neuro-mimetic feed-forward model of the primary visual area (VI) solving this problem in the case where the signal may be described by a robust linear generative model. This model uses an over-complete dictionary of primitives which provides a distributed probabilistic representation of input features. Relying on an efficiency criterion, we derive an algorithm as an approximate solution which uses incremental greedy inference processes. This algorithm is similar to 'Matching Pursuit' and mimics the parallel architecture of neural computations. We propose here a simple implementation using a network of spiking integrate-and-fire neurons which communicate using lateral interactions. Numerical simulations show that this Sparse Spike Coding strategy provides an efficient model for representing visual data from a set of natural images. Even though it is simplistic, this transformation of spatial data into a spatio-temporal pattern of binary events provides an accurate description of some complex neural patterns observed in the spiking activity of biological neural networks.Comment: This work links Matching Pursuit with bayesian inference by providing the underlying hypotheses (linear model, uniform prior, gaussian noise model). A parallel with the parallel and event-based nature of neural computations is explored and we show application to modelling Primary Visual Cortex / image processsing. http://incm.cnrs-mrs.fr/perrinet/dynn/LaurentPerrinet/Publications/Perrinet04tau

Applications of sparse approximation in communications

Sparse approximation problems abound in many scientific, mathematical, and engineering applications. These problems are defined by two competing notions: we approximate a signal vector as a linear combination of elementary atoms and we require that the approximation be both as accurate and as concise as possible. We introduce two natural and direct applications of these problems and algorithmic solutions in communications. We do so by constructing enhanced codebooks from base codebooks. We show that we can decode these enhanced codebooks in the presence of Gaussian noise. For MIMO wireless communication channels, we construct simultaneous sparse approximation problems and demonstrate that our algorithms can both decode the transmitted signals and estimate the channel parameters

Comparison Of Sparse Coding And Jpeg Coding Schemes For Blurred Retinal Images.

Overcomplete representations are currently one of the highly researched areas especially in the field of signal processing due to their strong potential to generate sparse representation of signals. Sparse representation implies that given signal can be represented with components that are only rarely significantly active. It has been strongly argued that the mammalian visual system is highly related towards sparse and overcomplete representations. The primary visual cortex has overcomplete responses in representing an input signal which leads to the use of sparse neuronal activity for further processing. This work investigates the sparse coding with an overcomplete basis set representation which is believed to be the strategy employed by the mammalian visual system for efficient coding of natural images. This work analyzes the Sparse Code Learning algorithm in which the given image is represented by means of linear superposition of sparse statistically independent events on a set of overcomplete basis functions. This algorithm trains and adapts the overcomplete basis functions such as to represent any given image in terms of sparse structures. The second part of the work analyzes an inhibition based sparse coding model in which the Gabor based overcomplete representations are used to represent the image. It then applies an iterative inhibition algorithm based on competition between neighboring transform coefficients to select subset of Gabor functions such as to represent the given image with sparse set of coefficients. This work applies the developed models for the image compression applications and tests the achievable levels of compression of it. The research towards these areas so far proves that sparse coding algorithms are inefficient in representing high frequency sharp image features. So this work analyzes the performance of these algorithms only on the natural images which does not have sharp features and compares the compression results with the current industrial standard coding schemes such as JPEG and JPEG 2000. It also models the characteristics of an image falling on the retina after the distortion effects of the eye and then applies the developed algorithms towards these images and tests compression results

Wavelet Features for Recognition of First Episode of Schizophrenia from MRI Brain Images

Machine learning methods are increasingly used in various fields of medicine, contributing to early diagnosis and better quality of care. These outputs are particularly desirable in case of neuropsychiatric disorders, such as schizophrenia, due to the inherent potential for creating a new gold standard in the diagnosis and differentiation of particular disorders. This paper presents a scheme for automated classification from magnetic resonance images based on multiresolution representation in the wavelet domain. Implementation of the proposed algorithm, utilizing support vector machines classifier, is introduced and tested on a dataset containing 104 patients with first episode schizophrenia and healthy volunteers. Optimal parameters of different phases of the algorithm are sought and the quality of classification is estimated by robust cross validation techniques. Values of accuracy, sensitivity and specificity over 71% are achieved