Signal Recovery From Incomplete and Inaccurate Measurements Via Regularized Orthogonal Matching Pursuit

Needell, Deanna; Vershynin, Roman

doi:10.1109/jstsp.2010.2042412

Cited by 779 publications

(492 citation statements)

References 20 publications

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“…However, recent research has clarified that Greedy methods succeed empirically and theoretically in many situations where convex relaxation works. Some Greedy methods can actually have performance guarantees that match those obtained for convex optimization approaches [39]. In this paper, we focus on the convex optimization methods with the application to SAIRs.…”

Section: Principles Of Csmentioning

confidence: 99%

A Compressive Sensing Approach for Synthetic Aperture Imaging Radiometers

Li¹,

Zhou²,

Ren³

et al. 2013

PIER

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Abstract-The aperture synthesis technology represents a promising new approach to microwave radiometers for high-resolution observations of the Earth from geostationary orbit. However, the future application of the new technology may be limited by its large number of antennas, receivers, and correlators. In order to reduce significantly the complexity of the on-board hardware requirements, a novel method based on the recently developed theory of compressive sensing (CS) is proposed in this paper. Due to the fact that the brightness temperature distributions of the Earth have a sparse representation in some proper transform domain -for example, in terms of spatial finite-differences or their wavelet coefficients, we use the CS approach to significantly undersample the visibility function. Thus the number of antennas, receivers, and correlators can be further reduced than those based on the traditional methods that obey the Shannon/Nyquist sampling theorem. The reconstruction is performed by minimizing the 1 norm of a transformed image. The effectiveness of the proposed approach is validated by numerical simulations using the image corresponding to AMSU-A over the Pacific.

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Section: Principles Of Csmentioning

confidence: 99%

A Compressive Sensing Approach for Synthetic Aperture Imaging Radiometers

Li¹,

Zhou²,

Ren³

et al. 2013

PIER

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“…Tropp and Gilbert point out that matching pursuit (MP) algorithm and Orthogonal matching pursuit (OMP) [2] algorithm can guarantee a good reconstruction result with lower computational complexity. With the development and progress of CS, many algorithms based on the principle of Matching pursuit are proposed, for example: Stagewise orthogonal matching pursuit (StOMP) [5], Regularized orthogonal matching pursuit (ROMP) [6], etc. At the same time, in order to achieve a better reconstruction result, another kind of algorithm is proposed, which uses sparse matrix as measurements matrix taking sample.…”

Section: Donoho In 2006mentioning

confidence: 99%

Construction of Deterministic Measurements Matrix Using Decimated Legendre Sequences

Cui

2015

MATEC Web of Conferences

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This paper proposed and constructed a new class of deterministic measurements matrix by using decimated binary Legendre sequences for convolutional Compressed Sensing. The author proves that when the measurement matrix is constructed by a random subsampling, it can offer a stable sparse reconstruction. Besides, the simulation results shows that when a deterministic subsampler is used, the proposed matrix can also guarantee the stable reconstruction as good as random Gaussian or Bernoulli matrixes do, which are commonly used in CS.

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“…Based on the theory of sparse representation [8], we formulate the following optimization problem to restore the feature vector from Eq. (9):…”

Section: The Restoration Of the Phase Contrast Imagesmentioning

confidence: 99%

“…We propose an iterative optimization algorithm to solve this min-ℓ 1 optimization problem since it is known that there is no closed-form solution for such a problem. We first search the best-matching N bases in the dictionary {H m } with the matching pursuit algorithm [8], and then utilize a non-negative multiplicative updating method [9] to obtain the nonnegative feature vectors {Ψ m k }. The procedure is described in Algorithm 1.…”

Section: The Restoration Of the Phase Contrast Imagesmentioning

confidence: 99%

Phase Contrast Image Restoration via Dictionary Representation of Diffraction Patterns

Yin

Kanade

et al. 2012

Lecture Notes in Computer Science

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Abstract. The restoration of microscopy images makes the segmentation and detection of cells easier and more reliable, which facilitates automated cell tracking and cell behavior analysis. In this paper, the authors analyze the image formation process of phase contrast images and propose an image restoration method based on the dictionary representation of diffraction patterns. By formulating and solving a min-ℓ1 optimization problem, each pixel is restored into a feature vector corresponding to the dictionary representation. Cells in the images are then segmented by the feature vector clustering. In addition to segmentation, since the feature vectors capture the information on the phase retardation caused by cells, they can be used for cell stage classification between intermitotic and mitotic/apoptotic stages. Experiments on three image sequences demonstrate that the dictionary-based restoration method can restore phase contrast images containing cells with different optical natures and provide promising results on cell stage classification.

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Signal Recovery From Incomplete and Inaccurate Measurements Via Regularized Orthogonal Matching Pursuit

Cited by 779 publications

References 20 publications

A Compressive Sensing Approach for Synthetic Aperture Imaging Radiometers

A Compressive Sensing Approach for Synthetic Aperture Imaging Radiometers

Construction of Deterministic Measurements Matrix Using Decimated Legendre Sequences

Phase Contrast Image Restoration via Dictionary Representation of Diffraction Patterns

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