scholarly journals An efficient algorithm for compression-based compressed sensing

2018 ◽  
Vol 8 (2) ◽  
pp. 343-375 ◽  
Author(s):  
Sajjad Beygi ◽  
Shirin Jalali ◽  
Arian Maleki ◽  
Urbashi Mitra
Keyword(s):  
Compressed Sensing ◽  
Video Compression ◽  
State Of The Art ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Robustness Analysis ◽  
Rate Distortion ◽  
Low Complexity ◽  
Signal Recovery ◽  
Recovery Algorithm

Abstract Modern image and video compression codes employ elaborate structures in an effort to encode them using a small number of bits. Compressed sensing (CS) recovery algorithms, on the other hand, use such structures to recover the signals from a few linear observations. Despite the steady progress in the field of CS, the structures that are often used for signal recovery are still much simpler than those employed by state-of-the-art compression codes. The main goal of this paper is to bridge this gap by answering the following question: can one employ a compression code to build an efficient (polynomial time) CS recovery algorithm? In response to this question, the compression-based gradient descent (C-GD) algorithm is proposed. C-GD, which is a low-complexity iterative algorithm, is able to employ a generic compression code for CS and therefore enlarges the set of structures used in CS to those used by compression codes. Three theoretical contributions are provided: a convergence analysis of C-GD, a characterization of the required number of samples as a function of the rate-distortion function of the compression code and a robustness analysis of C-GD to additive white Gaussian noise and other non-idealities in the measurement process. Finally, the presented simulation results show that, in image CS, using compression codes such as JPEG2000, C-GD outperforms state-of-the-art methods, on average, by about $2$–$3$ dB in peak signal-to-noise ratio.

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 Low-Complexity Biosignal Recovery Algorithm using Compressed Sensing and Independent Component Analysis

2020 ◽  
Author(s):  
Yahia Alghorani ◽  
salama Ikki
Keyword(s):  
Independent Component Analysis ◽  
Compressed Sensing ◽  
Low Cost ◽  
Vital Signs ◽  
Low Complexity ◽  
Component Analysis ◽  
Independent Component ◽  
Signal Recovery ◽  
Recovery Algorithm ◽  
Ica Algorithm

<div>The aim of this study is to propose a low-complexity algorithm that can be used for the joint sparse recovery of biosignals. The framework of the proposed algorithm supports real-time patient monitoring systems that enhance the detection, tracking, and monitoring of vital signs via wearable biosensors. Specifically, we address the problem of sparse signal recovery and acquisition in wearable biosensor networks, where we develop an efficient computational framework using compressed sensing (CS) and independent component analysis (ICA) to reduce and eliminate artifacts and interference in sparse biosignals. Our analysis and examples indicate that the CS-ICA algorithm helps to develop low-cost, low-power wearable biosensors while improving data quality and accuracy for a given measurement. We also show that, under noisy measurement conditions, the CS-ICA algorithm can outperform the standard CS method, where a biosignal can be retrieved in only a few measurements. By implementing the sensing framework, the error in reconstructing biosignals is reduced, and a digital-to-analog converter operates at low-speed and low-resolution</div>

scholarly journals Low-Complexity Rate-Distortion Optimization of Sampling Rate and Bit-Depth for Compressed Sensing of Images

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 125
Author(s):  
Qunlin Chen ◽  
Derong Chen ◽  
Jiulu Gong ◽  
Jie Ruan
Keyword(s):  
Compressed Sensing ◽  
Signal To Noise Ratio ◽  
Sampling Rate ◽  
Rate Distortion ◽  
Image Transmission ◽  
Low Complexity ◽  
Rate Model ◽  
Bit Rate ◽  
Compression Performance ◽  
The Relationship

Compressed sensing (CS) offers a framework for image acquisition, which has excellent potential in image sampling and compression applications due to the sub-Nyquist sampling rate and low complexity. In engineering practices, the resulting CS samples are quantized by finite bits for transmission. In circumstances where the bit budget for image transmission is constrained, knowing how to choose the sampling rate and the number of bits per measurement (bit-depth) is essential for the quality of CS reconstruction. In this paper, we first present a bit-rate model that considers the compression performance of CS, quantification, and entropy coder. The bit-rate model reveals the relationship between bit rate, sampling rate, and bit-depth. Then, we propose a relative peak signal-to-noise ratio (PSNR) model for evaluating distortion, which reveals the relationship between relative PSNR, sampling rate, and bit-depth. Finally, the optimal sampling rate and bit-depth are determined based on the rate-distortion (RD) criteria with the bit-rate model and the relative PSNR model. The experimental results show that the actual bit rate obtained by the optimized sampling rate and bit-depth is very close to the target bit rate. Compared with the traditional CS coding method with a fixed sampling rate, the proposed method provides better rate-distortion performance, and the additional calculation amount amounts to less than 1%.

scholarly journals A New Regularized Reconstruction Algorithm Based on Compressed Sensing for the Sparse Underdetermined Problem and Applications of One-Dimensional and Two-Dimensional Signal Recovery

Algorithms ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 126 ◽  
Author(s):  
Bin Wang ◽  
Li Wang ◽  
Hao Yu ◽  
Fengming Xin
Keyword(s):  
Compressed Sensing ◽  
Reconstruction Algorithm ◽  
Steepest Descent Method ◽  
Signal Recovery ◽  
Two Dimensional ◽  
Reconstruction Algorithms ◽  
Experimental Conditions ◽  
One Dimensional ◽  
Recovery Algorithm ◽  
Reconstruction Performance

The compressed sensing theory has been widely used in solving undetermined equations in various fields and has made remarkable achievements. The regularized smooth L0 (ReSL0) reconstruction algorithm adds an error regularization term to the smooth L0(SL0) algorithm, achieving the reconstruction of the signal well in the presence of noise. However, the ReSL0 reconstruction algorithm still has some flaws. It still chooses the original optimization method of SL0 and the Gauss approximation function, but this method has the problem of a sawtooth effect in the later optimization stage, and the convergence effect is not ideal. Therefore, we make two adjustments to the basis of the ReSL0 reconstruction algorithm: firstly, we introduce another CIPF function which has a better approximation effect than Gauss function; secondly, we combine the steepest descent method and Newton method in terms of the algorithm optimization. Then, a novel regularized recovery algorithm named combined regularized smooth L0 (CReSL0) is proposed. Under the same experimental conditions, the CReSL0 algorithm is compared with other popular reconstruction algorithms. Overall, the CReSL0 algorithm achieves excellent reconstruction performance in terms of the peak signal-to-noise ratio (PSNR) and run-time for both a one-dimensional Gauss signal and two-dimensional image reconstruction tasks.

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.

RBF-network based sparse signal recovery algorithm for compressed sensing reconstruction

2015 ◽  
Vol 63 ◽  
pp. 66-78 ◽  
Author(s):  
Vidya L. ◽  
Vivekanand V. ◽  
Shyamkumar U. ◽  
Deepak Mishra
Keyword(s):  
Compressed Sensing ◽  
Sparse Signal ◽  
Sparse Signal Recovery ◽  
Signal Recovery ◽  
Rbf Network ◽  
Recovery Algorithm

scholarly journals Encrypted message transmission in a QO-STBC encoded MISO wireless Communication system under implementation of low complexity ML decoding algorithm

2012 ◽  
Vol 2 (2) ◽  
pp. 53-58
Author(s):  
Shaikh Enayet Ullah ◽  
Md. Golam Rashed ◽  
Most. Farjana Sharmin
Keyword(s):  
Fading Channels ◽  
Gaussian Noise ◽  
Communication System ◽  
Channel Coding ◽  
Signal To Noise Ratio ◽  
Additive White Gaussian Noise ◽  
Text Message ◽  
Low Complexity ◽  
White Gaussian Noise ◽  
Message Transmission

In this paper, we made a comprehensive BER simulation study of a quasi- orthogonal space time block encoded (QO-STBC) multiple-input single output(MISO) system. The communication system under investigation has incorporated four digital modulations (QPSK, QAM, 16PSK and 16QAM) over an Additative White Gaussian Noise (AWGN) and Raleigh fading channels for three transmit and one receive antennas. In its FEC channel coding section, three schemes such as Cyclic, Reed-Solomon and ½-rated convolutionally encoding have been used. Under implementation of merely low complexity ML decoding based channel estimation and RSA cryptographic encoding /decoding algorithms, it is observable from conducted simulation test on encrypted text message transmission that the communication system with QAM digital modulation and ½-rated convolutionally encoding techniques is highly effective to combat inherent interferences under Raleigh fading and additive white Gaussian noise (AWGN) channels. It is also noticeable from the study that the retrieving performance of the communication system degrades with the lowering of the signal to noise ratio (SNR) and increasing in order of modulation.

scholarly journals On Compressed Sensing of Binary Signals for the Unsourced Random Access Channel

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 605
Author(s):  
Elad Romanov ◽  
Or Ordentlich
Keyword(s):  
Compressed Sensing ◽  
Additive White Gaussian Noise ◽  
Random Access ◽  
Monte Carlo Algorithm ◽  
Parity Check ◽  
Sensing Matrix ◽  
Recovery Algorithm ◽  
Access Channel ◽  
Check Matrix ◽  
Sparse Sensing

Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix A and a recovery algorithm, such that the sparse binary vector x can be recovered reliably from the measurements y=Ax+σz, where z is additive white Gaussian noise. We propose to design A as a parity check matrix of a low-density parity-check code (LDPC) and to recover x from the measurements y using a Markov chain Monte Carlo algorithm, which runs relatively fast due to the sparse structure of A. The performance of our scheme is comparable to state-of-the-art schemes, which use dense sensing matrices, while enjoying the advantages of using a sparse sensing matrix.

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