1,028 research outputs found
Fast Orthonormal Sparsifying Transforms Based on Householder Reflectors
Dictionary learning is the task of determining a data-dependent transform
that yields a sparse representation of some observed data. The dictionary
learning problem is non-convex, and usually solved via computationally complex
iterative algorithms. Furthermore, the resulting transforms obtained generally
lack structure that permits their fast application to data. To address this
issue, this paper develops a framework for learning orthonormal dictionaries
which are built from products of a few Householder reflectors. Two algorithms
are proposed to learn the reflector coefficients: one that considers a
sequential update of the reflectors and one with a simultaneous update of all
reflectors that imposes an additional internal orthogonal constraint. The
proposed methods have low computational complexity and are shown to converge to
local minimum points which can be described in terms of the spectral properties
of the matrices involved. The resulting dictionaries balance between the
computational complexity and the quality of the sparse representations by
controlling the number of Householder reflectors in their product. Simulations
of the proposed algorithms are shown in the image processing setting where
well-known fast transforms are available for comparisons. The proposed
algorithms have favorable reconstruction error and the advantage of a fast
implementation relative to the classical, unstructured, dictionaries
Image Compression Techniques: A Survey in Lossless and Lossy algorithms
The bandwidth of the communication networks has been increased continuously as results of technological advances. However, the introduction of new services and the expansion of the existing ones have resulted in even higher demand for the bandwidth. This explains the many efforts currently being invested in the area of data compression. The primary goal of these works is to develop techniques of coding information sources such as speech, image and video to reduce the number of bits required to represent a source without significantly degrading its quality. With the large increase in the generation of digital image data, there has been a correspondingly large increase in research activity in the field of image compression. The goal is to represent an image in the fewest number of bits without losing the essential information content within. Images carry three main type of information: redundant, irrelevant, and useful. Redundant information is the deterministic part of the information, which can be reproduced without loss from other information contained in the image. Irrelevant information is the part of information that has enormous details, which are beyond the limit of perceptual significance (i.e., psychovisual redundancy). Useful information, on the other hand, is the part of information, which is neither redundant nor irrelevant. Human usually observes decompressed images. Therefore, their fidelities are subject to the capabilities and limitations of the Human Visual System. This paper provides a survey on various image compression techniques, their limitations, compression rates and highlights current research in medical image compression
A unified approach to sparse signal processing
A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, compo-nent analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding i
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