Compressed sensing with preconditioning for sparse recovery with subsampled matrices of Slepian prolate functions

2012 ◽  
Vol 59 (1) ◽  
pp. 81-116 ◽  
Author(s):  
Laurent Gosse
Keyword(s):  
Compressed Sensing ◽  
Sparse Recovery

scholarly journals Sparse Recovery Algorithm for Compressed Sensing Using Smoothed l0 Norm and Randomized Coordinate Descent

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 834
Author(s):  
Jin ◽  
Yang ◽  
Li ◽  
Liu
Keyword(s):  
Compressed Sensing ◽  
Image Denoising ◽  
Signal To Noise Ratio ◽  
Sparse Recovery ◽  
Coordinate Descent ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Signal Recovery ◽  
Recovery Algorithm ◽  
Core Concepts

Compressed sensing theory is widely used in the field of fault signal diagnosis and image processing. Sparse recovery is one of the core concepts of this theory. In this paper, we proposed a sparse recovery algorithm using a smoothed l0 norm and a randomized coordinate descent (RCD), then applied it to sparse signal recovery and image denoising. We adopted a new strategy to express the (P0) problem approximately and put forward a sparse recovery algorithm using RCD. In the computer simulation experiments, we compared the performance of this algorithm to other typical methods. The results show that our algorithm possesses higher precision in sparse signal recovery. Moreover, it achieves higher signal to noise ratio (SNR) and faster convergence speed in image denoising.

scholarly journals A Fast Sparse Recovery Algorithm for Compressed Sensing Using Approximate l0 Norm and Modified Newton Method

Materials ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 1227 ◽  
Author(s):  
Dingfei Jin ◽  
Yue Yang ◽  
Tao Ge ◽  
Daole Wu
Keyword(s):  
Compressed Sensing ◽  
Newton Method ◽  
Simulation Experiment ◽  
Sparse Recovery ◽  
Signal Recovery ◽  
Recovery Efficiency ◽  
Recovery Algorithm ◽  
Modified Newton Method ◽  
Computer Simulation Experiment ◽  
Recovery Algorithms

In this paper, we propose a fast sparse recovery algorithm based on the approximate l0 norm (FAL0), which is helpful in improving the practicability of the compressed sensing theory. We adopt a simple function that is continuous and differentiable to approximate the l0 norm. With the aim of minimizing the l0 norm, we derive a sparse recovery algorithm using the modified Newton method. In addition, we neglect the zero elements in the process of computing, which greatly reduces the amount of computation. In a computer simulation experiment, we test the image denoising and signal recovery performance of the different sparse recovery algorithms. The results show that the convergence rate of this method is faster, and it achieves nearly the same accuracy as other algorithms, improving the signal recovery efficiency under the same conditions.

Nonuniform recovery of fusion frame structured sparse signals

2017 ◽  
Vol 15 (03) ◽  
pp. 333-352
Author(s):  
Yu Xia ◽  
Song Li
Keyword(s):  
Probability Distribution ◽  
Compressed Sensing ◽  
Fourier Coefficients ◽  
A Priori ◽  
Sparse Recovery ◽  
A Priori Knowledge ◽  
Sparse Signals ◽  
Fusion Frame ◽  
Redundant Representation ◽  
Vector Valued

This paper considers the nonuniform sparse recovery of block signals in a fusion frame, which is a collection of subspaces that provides redundant representation of signal spaces. Combined with specific fusion frame, the sensing mechanism selects block-vector-valued measurements independently at random from a probability distribution [Formula: see text]. If the probability distribution [Formula: see text] obeys a simple incoherence property and an isotropy property, we can faithfully recover approximately block sparse signals via mixed [Formula: see text]-minimization in ways similar to Compressed Sensing. The number of measurements is significantly reduced by a priori knowledge of a certain incoherence parameter [Formula: see text] associated with the angles between the fusion frame subspaces. As an example, the paper shows that an [Formula: see text]-sparse block signal can be exactly recovered from about [Formula: see text] Fourier coefficients combined with fusion frame [Formula: see text], where [Formula: see text].

scholarly journals Radar Array Diagnosis from Undersampled Data Using a Compressed Sensing/Sparse Recovery Technique

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
S. Costanzo ◽  
A. Borgia ◽  
G. Di Massa ◽  
D. Pinchera ◽  
M. D. Migliore
Keyword(s):  
Compressed Sensing ◽  
Sparse Recovery ◽  
Accurate Diagnosis ◽  
Small Set ◽  
Recovery Technique ◽  
Radar Applications ◽  
Experimental Validations ◽  
Slotted Waveguide ◽  
Recovery Approach ◽  
Undersampled Data

A Compressed Sensing/Sparse Recovery approach is adopted in this paper for the accurate diagnosis of fault array elements from undersampled data. Experimental validations on a slotted waveguide test array are discussed to demonstrate the effectiveness of the proposed procedure in the failures retrieval from a small set of measurements with respect to the number of radiating elements. Due to the sparsity feature of the proposed formulation, the method is particularly appealing for the diagnostics of large arrays, typically adopted for radar applications.

scholarly journals Multitrack Compressed Sensing for Faster Hyperspectral Imaging

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5034
Author(s):  
Sharvaj Kubal ◽  
Elizabeth Lee ◽  
Chor Yong Tay ◽  
Derrick Yong
Keyword(s):  
Compressed Sensing ◽  
Hyperspectral Imaging ◽  
Sparse Recovery ◽  
Reconstruction Accuracy ◽  
Recovery Algorithm ◽  
Additional Information ◽  
Different Types ◽  
Block Compressed Sensing ◽  
Speed And Accuracy ◽  
Reconstruction Time

Hyperspectral imaging (HSI) provides additional information compared to regular color imaging, making it valuable in areas such as biomedicine, materials inspection and food safety. However, HSI is challenging because of the large amount of data and long measurement times involved. Compressed sensing (CS) approaches to HSI address this, albeit subject to tradeoffs between image reconstruction accuracy, time and generalizability to different types of scenes. Here, we develop improved CS approaches for HSI, based on parallelized multitrack acquisition of multiple spectra per shot. The multitrack architecture can be paired up with either of the two compatible CS algorithms developed here: (1) a sparse recovery algorithm based on block compressed sensing and (2) an adaptive CS algorithm based on sampling in the wavelet domain. As a result, the measurement speed can be drastically increased while maintaining reconstruction speed and accuracy. The methods were validated computationally both in noiseless as well as noisy simulated measurements. Multitrack adaptive CS has a ∼10 times shorter measurement plus reconstruction time as compared to full sampling HSI without compromising reconstruction accuracy across the sample images tested. Multitrack non-adaptive CS (sparse recovery) is most robust against Poisson noise at the expense of longer reconstruction times.

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