From cardinal spline wavelet bases to highly coherent dictionaries

Andrle, Miroslav; Rebollo-Neira, Laura

doi:10.1088/1751-8113/41/17/172001

Cited by 11 publications

(9 citation statements)

References 31 publications

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“…Moreover the performance is superior to that of the Chui-Wang spline wavelet basis [19] even for signal f 3 , which was specially selected because, due to the abrupt edges delimiting the smooth lines, is very appropriate to be approximated by wavelets. It is also worth stressing that for signal f 1 and f 2 the performance is similar to the cardinal Chui-Wang dictionary, which is known to render a very good representation for these signals [20]. However, whilst the Chui-Wang cardinal spline wavelet dictionaries introduced in [20] are significantly redundant with respect to the corresponding basis (about twice as larger) the non-uniform B-spline dictionaries introduced here contain a few more functions than the basis.…”

Section: Dictionariesmentioning

confidence: 70%

“…It is also worth stressing that for signal f 1 and f 2 the performance is similar to the cardinal Chui-Wang dictionary, which is known to render a very good representation for these signals [20]. However, whilst the Chui-Wang cardinal spline wavelet dictionaries introduced in [20] are significantly redundant with respect to the corresponding basis (about twice as larger) the non-uniform B-spline dictionaries introduced here contain a few more functions than the basis. Nevertheless, as the examples of this section indicate, the improvement in the sparseness of the approximation a dictionary may yield with respect to the B-spline basis is enormous.…”

Section: Numerical Examplesmentioning

confidence: 70%

“…3) The orthogonal cosine bases used by the discrete cosine transform (dct). 4) The semi-orthogonal cardinal Chui-Wang spline wavelet basis [19] and 5) the Chui-Wang cardinal spline dictionary for the same space [20]. For signals f 1 and f 2 we use cubic spline wavelets and for signal f 3 linear spline wavelets.…”

Section: Dictionariesmentioning

confidence: 99%

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Sparse signal representation by adaptive non-uniform B-spline dictionaries on a compact interval

Rebollo-Neira¹,

Xu²

2010

Signal Processing

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Non-uniform B-spline dictionaries on a compact interval are discussed in the context of sparse signal representation. For each given partition, dictionaries of B-spline functions for the corresponding spline space are built up by dividing the partition into subpartitions and joining together the bases for the concomitant subspaces. The resulting slightly redundant dictionaries are composed of B-spline functions of broader support than those corresponding to the B-spline basis for the identical space. Such dictionaries are meant to assist in the construction of adaptive sparse signal representation through a combination of stepwise optimal greedy techniques.

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Section: Dictionariesmentioning

confidence: 70%

Section: Numerical Examplesmentioning

confidence: 70%

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Sparse signal representation by adaptive non-uniform B-spline dictionaries on a compact interval

Rebollo-Neira¹,

Xu²

2010

Signal Processing

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“…Now, we choose a parameter

such that

for some integer

. We define functions

and

which form a redundant dictionary [1] , [2] , [21] . Obviously,

corresponds to a basis.…”

Section: Wavelet Dictionariesmentioning

confidence: 99%

Construction of wavelet dictionaries for ECG modeling

Černá

Rebollo-Neira

2021

MethodsX

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Technical details, algorithms, and MATLAB implementation for a method advanced in the paper ``Wavelet Based Dictionaries for Dimensionality Reduction of ECG Signals'', are presented. This work aims to be the companion of that publication, in which an adaptive mathematical model for a given ECG record is proposed. The method comprises the following building blocks. Construction of a suitable redundant set, called 'dictionary', for decomposing an ECG signal as a superposition of elementary components, called 'atoms', selected from that dictionary. Implementation of the greedy strategy Optimized Orthogonal Matching Pursuit (OOMP) for selecting the atoms intervening in the signal decomposition. This paper gives the details of the algorithms for implementing stage (i), which is not fully elaborated in the previous publication. The proposed dictionaries are constructed from known wavelet families, but translating the prototypes with a shorter step than that corresponding to a wavelet basis. Stage (ii) is readily implementable by the available function OOMP. The use of the software and the power of the technique is illustrated by reducing the dimensionality of ECG records taken from the MIT-BIH Arrhythmia Database. The MATLAB software has been made publicly available on a dedicated website. We provide the explanations, algorithms and software for the construction of scaling functions and wavelet prototypes for 17 different wavelet families. The procedure is designed to allow for straightforward extension of the software by the inclusion of additional options for the wavelet families.

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“…The work proposed by M. Fira et al [54] proposed a data-driven dictionary design by building the dictionary using the EEG signal from the training dataset itself rather than using any fixed dictionary. Furthermore, apart from these mainstream dictionaries for EEG signal, few other studies also used B-Spline dictionary [55,56], linear and cubic-Spline dictionaries [57], Spline dictionary [58], Meyer wavelet function dictionary [59], or Daubechies wavelets function dictionary [60] to obtain the sparse representation of the input signal.…”

Section: Sparse Representationmentioning

confidence: 99%

Trends in Compressive Sensing for EEG Signal Processing Applications

Gurve

Delisle-Rodríguez

Bastos

et al. 2020

Sensors

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The tremendous progress of big data acquisition and processing in the field of neural engineering has enabled a better understanding of the patient’s brain disorders with their neural rehabilitation, restoration, detection, and diagnosis. An integration of compressive sensing (CS) and neural engineering emerges as a new research area, aiming to deal with a large volume of neurological data for fast speed, long-term, and energy-saving purposes. Furthermore, electroencephalography (EEG) signals for brain–computer interfaces (BCIs) have shown to be very promising, with diverse neuroscience applications. In this review, we focused on EEG-based approaches which have benefited from CS in achieving fast and energy-saving solutions. In particular, we examine the current practices, scientific opportunities, and challenges of CS in the growing field of BCIs. We emphasized on summarizing major CS reconstruction algorithms, the sparse basis, and the measurement matrix used in CS to process the EEG signal. This literature review suggests that the selection of a suitable reconstruction algorithm, sparse basis, and measurement matrix can help to improve the performance of current CS-based EEG studies. In this paper, we also aim at providing an overview of the reconstruction free CS approach and the related literature in the field. Finally, we discuss the opportunities and challenges that arise from pushing the integration of the CS framework for BCI applications.

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From cardinal spline wavelet bases to highly coherent dictionaries

Cited by 11 publications

References 31 publications

Sparse signal representation by adaptive non-uniform B-spline dictionaries on a compact interval

Sparse signal representation by adaptive non-uniform B-spline dictionaries on a compact interval

Construction of wavelet dictionaries for ECG modeling

Trends in Compressive Sensing for EEG Signal Processing Applications

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