arXiv subjects

Laura Rebollo-Neira

Publications and source records attributed to Laura Rebollo-Neira.

At least 19 recordsLinked to original sources

arXiv2024

Recursive construction of biorthogonal polynomials for handling polynomial regression

An adaptive procedure for constructing polynomials which are biorthogonal to the basis of monomials in the same finite-dimensional inner product space is proposed. By taking advantage of available orthogonal polynomials, the proposed methodology reduces the well-known instability problem arising from the matrix inversion involved in classical polynomial regression. The recurrent generation of the biorthogonal basis facilitates the upgrading of all its members to include an additional one. Moreover, it allows for a natural downgrading of the basis. This convenient feature leads to a straightforward approach for reducing the number of terms in the polynomial regression approximation. The merit of this approach is illustrated through a series of examples where the resulting biorthogonal basis is derived from Legendre, Laguerre, and Chebyshev orthogonal polynomials.

math.NA↗

arXiv2024

Simultaneous Optimized Orthogonal Matching Pursuit with Application to ECG Compression

A greedy pursuit strategy which finds a common basis for approximating a set of similar signals is proposed. The strategy extends the Optimized Orthogonal Matching Pursuit approach to selecting the subspace containing the approximation of all the signals in the set. The method, called Simultaneous Optimized Orthogonal Matching Pursuit, is stepwise optimal in the sense of minimizing at each iteration the mean error norm of the joint approximation. When applied to compression of electrocardiograms, significant gains over other transformation based compression techniques are demonstrated on the MIT-BIH Arrhythmia dataset.

eess.SP↗

arXiv2023

Sparsity based morphological identification of heartbeats

The electrocardiogram (ECG) is one of the most common primary tests to evaluate the health of the heart. Reliable automatic interpretation of ECG records is crucial to the goal of improving public health. It can enable a safe inexpensive monitoring. This work presents a new methodology for morphological identification of heartbeats, which is placed outside the usual machine learning framework. The proposal considers the sparsity of the representation of a heartbeat as a parameter for morphological identification. The approach involves greedy algorithms for selecting elements from redundant dictionaries, which should be previously learnt from examples of the classes to be identified. Using different metrics of sparsity, the dictionary rendering the smallest sparsity value, for the equivalent approximation quality of a new heartbeat, classifies the morphology of that beat. This study focuses on a procedure of learning the dictionaries for representing heartbeats and compares several metrics of sparsity for morphological identification on the basis of those metrics. The suitability of the method is illustrated by binary differentiation of Normal and Ventricular heartbeats in the MIT-BIH Arrhythmia data set. In general classification 99.7% of the Normal beats and 97.6% of the Ventricular beats in the testing sets are correctly identified. In interpatient assessment 91.8% of the Normal beats and 91.0% of Ventricular beats are correctly identified. Even more important than these scores is the fact that they are produced on the bases of a single parameter. The numerical tests, designed to emphasise the interpretability and reliability of the approach, demonstrate the potential of the method to contribute towards the development of a well grounded expert system for classification of heartbeats in ECG records.

eess.SP↗

arXiv2021

Enhancing sparse representation of color images by cross channel transformation

Transformations for enhancing sparsity in the approximation of color images by 2D atomic decomposition are discussed. The sparsity is firstly considered with respect to the most significant coefficients in the wavelet decomposition of the color image. The discrete cosine transform is singled out as an effective transformation for this purpose. The enhanced feature is further exploited by approximating the transformed arrays using an effective greedy strategy with a separable highly redundant dictionary. The relevance of the achieved sparsity is illustrated by a simple encoding procedure. On a set of typical test images the compression at high quality recovery is shown to significantly improve upon JPEG and WebP formats. The results are competitive with those produced by the JPEG2000 standard.

eess.IV↗

arXiv2020

Analysis of the Self Projected Matching Pursuit Algorithm

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.

cs.CV↗

arXiv2019

Construction of wavelet dictionaries for ECG modelling

The purpose of sparse modelling of ECG signals is to represent an ECG record, given by sample points, as a linear combination of as few elementary components as possible. This can be achieved by creating a redundant set, called a dictionary, from where the elementary components are selected. The success in sparsely representing an ECG record depends on the nature of the dictionary being considered. In this paper we focus on the construction of different families of wavelet dictionaries, which are appropriate for the purpose of reducing dimensionality of ECG signals through sparse representation modelling. The suitability of wavelet dictionaries for ECG modelling, applying the Optimized Orthogonal Matching Pursuit approach for the selection process, was demonstrated in a previous work on the MIT-BIH Arrhythmia database consisting of 48 records each of which of 30 min length. This paper complements the previous one by presenting the technical details, methods, algorithms, and MATLAB software facilitating the construction of different families of wavelet dictionaries. The implementation allows for straightforward further extensions to include additional wavelet families. The sparsity in the representation of an ECG record significantly improves in relation to the sparsity produced by the corresponding wavelet basis. This result holds true for the 17 wavelet families considered here.

math.NA↗

arXiv2019

Mixed-transform based codec for 2D compression of ECG signals

A method for ECG compression, by imaging the record as a 2D array and implementing a transform lossy compression strategy, is advanced. The particularity of the proposed transformation consists in applying a Discrete Wavelet Transform along one of the dimensions and the Discrete Cosine Transform along the other dimension. The performance of the method is demonstrated on the MIT-BIH Arrhythmia database. Significant improvements upon the 1D version of the codec, and on benchmarks for 2D ECG compression, are achieved.

eess.SP↗

arXiv2019

Sparse Representation of 3D Images for Piecewise Dimensionality Reduction with High Quality Reconstruction

Sparse representation of 3D images is considered within the context of data reduction. The goal is to produce high quality approximations of 3D images using fewer elementary components than the number of intensity points in the 3D array. This is achieved by means of a highly redundant dictionary and a dedicated pursuit strategy especially designed for low memory requirements. The benefit of the proposed framework is illustrated in the first instance by demonstrating the gain in dimensionality reduction obtained when approximating true color images as very thin 3D arrays, instead of performing an independent channel by channel approximation. The full power of the approach is further exemplified by producing high quality approximations of hyper-spectral images with a reduction of up to 371 times the number of data points in the representation.

eess.IV↗

arXiv2019

Wavelet Based Dictionaries for Piecewise Dimensionality Reduction of ECG Signals

Dimensionality reduction of ECG signals is considered within the framework of sparse representation. The approach constructs the signal model by selecting elementary components from a redundant dictionary via a greedy strategy. The proposed wavelet dictionaries are built from the multiresolution scheme, but translating the prototypes within a shorter step than that corresponding to the wavelet basis. The reduced representation of the signal is shown to be suitable for compression at low level distortion. In that regard, compression results are superior to previously reported benchmarks on the MIT-BIH Arrhythmia data set.

eess.SP↗

arXiv2019

Effective high compression of ECG signals at low level distortion

An effective method for compression of ECG signals, which falls within the transform lossy compression category, is proposed. The transformation is realized by a fast wavelet transform. The effectiveness of the approach, in relation to the simplicity and speed of its implementation, is a consequence of the efficient storage of the outputs of the algorithm which is realized in compressed Hierarchical Data Format. The compression performance is tested on the MIT-BIH Arrhythmia database producing compression results which largely improve upon recently reported benchmarks on the same database. For a distortion corresponding to a percentage root-mean-square difference PRD of 0.53, in mean value, the achieved average compression ratio is 23.17 with quality score of 43.93. For a mean value of PRD up to 1.71 the compression ratio increases up to 62.5. The compression of a 30 min record is realized in an average time of 0.14 s. The insignificant delay for the compression process, together with the high compression ratio achieved at low level distortion and the negligible time for the signal recovery, uphold the suitability of the technique for supporting distant clinical health care.

eess.SP↗

arXiv2018

A dedicated codec for compression of Gravitational Waves Sound

A dedicated codec for compression of gravitational waves sound with high quality recovery is proposed. The performance is tested on the available set of gravitational sound signals that has been theoretically generated at the Massachusetts Institute of Technology (MIT). The approach is based on a model for data reduction rendering high quality approximation of the signals. The reduction of dimensionality is achieved by selecting elementary components from a redundant set called a dictionary. Comparisons with the compression standard MP3 demonstrate the merit of the dedicated technique for compressing this type of sound.

eess.SP↗

arXiv2017

Sparse Representation of Gravitational Sound

Gravitational Sound clips produced by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the Massachusetts Institute of Technology (MIT) are considered within the particular context of data reduction. It is shown that these types of signals can be approximated at high quality using much less elementary components than those required within the standard orthogonal basis framework. Furthermore, a measure a local sparsity is shown to render meaningful information about the variation of a signal along time, by generating a set of local sparsity values which is much smaller than the dimension of the signal. This point is stressed further by recourse to a more complex signal, generated by Milde Science Communication to divulge Gravitational Sound in the form a ring tone.

physics.data-an↗

arXiv2016

Effective sparse representation of X-Ray medical images

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

cs.CV↗

arXiv2016

A dedicated greedy pursuit algorithm for sparse spectral representation of music sound

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.

cs.SD↗

arXiv2015

Trigonometric dictionary based codec for music compression with high quality recovery

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.

cs.SD↗

arXiv2015

Cooperative Greedy Pursuit Strategies for Sparse Signal Representation by Partitioning

Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly coherent redundant dictionaries. The cooperation takes place by ranking the partition units for their sequential stepwise approximation, and is realized by means of i)forward steps for the upgrading of an approximation and/or ii) backward steps for the corresponding downgrading. The advantage of the strategy is illustrated by producing high quality approximations of music signals using redundant trigonometric dictionaries. In addition to rendering stunning improvements in sparsity with respect to the concomitant trigonometric basis, these dictionaries enable a fast implementation of the approach via the Fast Fourier Transform.

cs.DS↗

arXiv2013

Hierarchized block wise image approximation by greedy pursuit strategies

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.

cs.CV↗

arXiv2012

Self Contained Encrypted Image Folding

The recently introduced approach for Encrypted Image Folding is generalized to make it Self Contained. The goal is achieved by enlarging the folded image so as to embed all the necessary information for the image recovery. The need for extra size is somewhat compensated by considering a transformation with higher folding capacity. Numerical examples show that the size of the resulting cipher image may be significantly smaller than the plain text one. The implementation of the approach is further extended to deal also with color images.

math-ph↗