Laura Rebollo-Neira
Effective sparse representation of X-Ray medical images within the context of data reduction is considered. The proposed framework is shown to render an enormous reduction in the cardinality of the data set required to represent this class of images at very good quality. The particularity of the approach is that it can be implemented at very competitive processing time and low memory requirements
Laura Rebollo-Neira, Miroslav Rozloznik, Pradip Sasmal
The convergence and numerical analysis of a low memory implementation of the Orthogonal Matching Pursuit greedy strategy, which is termed Self Projected Matching Pursuit, is presented. This approach renders an iterative way of solving the least squares problem with much less storage requirement than direct linear algebra techniques. Hence, it appropriate for solving large linear systems. The analysis highlights its suitability within the class of well posed problems.
Laura Rebollo-Neira
A codec for compression of music signals is proposed. The method belongs to the class of transform lossy compression. It is conceived to be applied in the high quality recovery range though. The transformation, endowing the codec with its distinctive feature, relies on the ability to construct high quality sparse approximation of music signals. This is achieved by a redundant trigonometric dictionary and a dedicated pursuit strategy. The potential of the approach is illustrated by comparison with the OGG Vorbis format, on a sample consisting of clips of melodic music. The comparison evidences remarkable improvements in compression performance for the identical quality of the decompressed signal.
Laura Rebollo-Neira, Gagan Aggarwal
A dedicated algorithm for sparse spectral representation of music sound is presented. The goal is to enable the representation of a piece of music signal, as a linear superposition of as few spectral components as possible. A representation of this nature is said to be sparse. In the present context sparsity is accomplished by greedy selection of the spectral components, from an overcomplete set called a dictionary. The proposed algorithm is tailored to be applied with trigonometric dictionaries. Its distinctive feature being that it avoids the need for the actual construction of the whole dictionary, by implementing the required operations via the Fast Fourier Transform. The achieved sparsity is theoretically equivalent to that rendered by the Orthogonal Matching Pursuit method. The contribution of the proposed dedicated implementation is to extend the applicability of the standard Orthogonal Matching Pursuit algorithm, by reducing its storage and computational demands. The suitability of the approach for producing sparse spectral models is illustrated by comparison with the traditional method, in the line of the Short Time Fourier Transform, involving only the corresponding orthonormal trigonometric basis.
Laura Rebollo-Neira, Ryszard Maciol, Shabnam Bibi
An approach for effective implementation of greedy selection methodologies, to approximate an image partitioned into blocks, is proposed. The method is specially designed for approximating partitions on a transformed image. It evolves by selecting, at each iteration step, i) the elements for approximating each of the blocks partitioning the image and ii) the hierarchized sequence in which the blocks are approximated to reach the required global condition on sparsity.
Laura Rebollo-Neira, James Bowley
Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies. Experiments are conducted to confirm: i)Effectiveness at producing sparse representations. ii)Competitiveness, with respect to the time required to process large images.The latter is a consequence of the suitability of the proposed dictionaries for approximating images in partitions of small blocks.This feature makes it possible to apply the effective greedy selection technique Orthogonal Matching Pursuit, up to some block size. For blocks exceeding that size a refinement of the original Matching Pursuit approach is considered. The resulting method is termed Self Projected Matching Pursuit, because is shown to be effective for implementing, via Matching Pursuit itself, the optional back-projection intermediate steps in that approach.
James Bowley, Laura Rebollo-Neira
Mixed dictionaries generated by cosine and B-spline functions are considered. It is shown that, by highly nonlinear approaches such as Orthogonal Matching Pursuit, the discrete version of the proposed dictionaries yields a significant gain in the sparsity of an image representation.