Sparse Signal and Image Recovery From Compressive Samples

Candès, Emmanuel J.; Braun, Noah; Wakin, Michael B.

doi:10.1109/isbi.2007.357017

Cited by 54 publications

(33 citation statements)

References 11 publications

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“…This signal, x, can be represented in terms of a basis of vectors [ ] =1 . Let = [ 1 2 ⋅ ⋅ ⋅ ] be a × orthonormal basis matrix with the vectors as column [4], [13]. The signal, x, can be written as…”

Section: Methodsmentioning

confidence: 99%

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Compressed sensing for multi-lead electrocardiogram signals

Sharma

Dandapat

2012

2012 World Congress on Information and Communication Technologies

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Compressed sensing is widely used due to its ability to reconstruct the signal accurately from a set of samples which is smaller than the set of samples produced using Nyquist rate. Multi-lead electrocardiogram signals show sparseness in wavelet domain. In this work, compressive sensing is applied for electrocardiogram signals in transform domain using random sensing matrix with independent identically distributed (i.i.d.) entries formed by sampling a Gaussian distribution. The reconstruction of sparsely represented signal is performed by convex optimization problem by L1-norm minimization. The quality of processed signal is satisfactory. Signal distortions are evaluated using percentage root mean square difference (PRD), root mean square error (RMSE), normalized root mean square difference (NRMSD), normalized maximum amplitude error (NMAX) and maximum absolute error (MAE). The lowest PRD value, 1.723%, is found for lead-V5 signal at sparsity level of 26.76%, using database of CSE multi-lead measurement library for simulation.

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Section: Methodsmentioning

confidence: 99%

“…It can recover signals or images from highly incomplete measurements which are conventionally believed to be insufficient information. For signal and image processing, this has been applied successfully [4], [5].…”

Section: Introductionmentioning

confidence: 99%

Compressed sensing for multi-lead electrocardiogram signals

Sharma

Dandapat

2012

2012 World Congress on Information and Communication Technologies

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“…In practice, the optimal choice for σ , τ and μ may not be obvious, especially when the noise level is not well known in advance. The interesting feature of these solutions is that they yield a sparse v, that is they produce a v with very few non-zero entries and this has been explained and justified in a series of papers, see e.g., [6,9,25] and the references therein.…”

Section: Sparse Representations and 1 -Optimizationmentioning

confidence: 98%

“…Fundamental theoretical contributions from a number of researchers [3,4,5,6,7,8,9,29] has sparked this rapidly developing field which is driven by a wide spectrum of applications from robust statistics, data compression, compressed sensing, image processing, estimation, and high resolution signal analysis. The present work builds on the well-paved paradigm of sparse representations by focusing on a problem of system/source identification known as blind source separation.…”

Section: Introductionmentioning

confidence: 99%

Sparse Blind Source Separation via ℓ1-Norm Optimization

Georgiou

Tannenbaum

2010

Perspectives in Mathematical System Theory, Control, and Signal Processing

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Abstract. The title of the paper refers to an extension of the classical blind source separation where the mixing of unknown sources is assumed in the form of convolution with impulse response of unknown linear dynamics. A further key assumption of our approach is that source signals are considered to be sparse with respect to a known dictionary, and thereby, an 1 -optimization is a natural formalism for solving the un-mixing problem. We demonstrate the effectiveness of the framework numerically.

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“…If image signals are regarded, it is widely known that they can be sparsely represented in the Fourier domain [37]. That is to say that most signal energy is concentrated into a small number of transform coefficients while all other coefficients are equal or close to zero.…”

Section: A Consequences From Non-regular Subsampling and Frequency Smentioning

confidence: 99%

Resampling Images to a Regular Grid From a Non-Regular Subset of Pixel Positions Using Frequency Selective Reconstruction

Seiler

Jonscher

Schöberl

et al. 2015

IEEE Trans. on Image Process.

100

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Even though image signals are typically defined on a regular 2D grid, there also exist many scenarios where this is not the case and the amplitude of the image signal only is available for a non-regular subset of pixel positions. In such a case, a resampling of the image to a regular grid has to be carried out. This is necessary since almost all algorithms and technologies for processing, transmitting or displaying image signals rely on the samples being available on a regular grid. Thus, it is of great importance to reconstruct the image on this regular grid, so that the reconstruction comes closest to the case that the signal has been originally acquired on the regular grid. In this paper, Frequency Selective Reconstruction is introduced for solving this challenging task. This algorithm reconstructs image signals by exploiting the property that small areas of images can be represented sparsely in the Fourier domain. By further considering the basic properties of the optical transfer function of imaging systems, a sparse model of the signal is iteratively generated. In doing so, the proposed algorithm is able to achieve a very high reconstruction quality, in terms of peak signal-to-noise ratio (PSNR) and structural similarity measure as well as in terms of visual quality. The simulation results show that the proposed algorithm is able to outperform state-of-the-art reconstruction algorithms and gains of more than 1 dB PSNR are possible.

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Sparse Signal and Image Recovery From Compressive Samples

Cited by 54 publications

References 11 publications

Compressed sensing for multi-lead electrocardiogram signals

Compressed sensing for multi-lead electrocardiogram signals

Sparse Blind Source Separation via ℓ1-Norm Optimization

Resampling Images to a Regular Grid From a Non-Regular Subset of Pixel Positions Using Frequency Selective Reconstruction

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