Deterministic Construction of Compressed Sensing Matrix Based on Q-Matrix

Yang Nie,Xin-Le Yu,Zhan-Xin Yang 보안공학연구지원센터 2016 International Journal of Grid and Distributed Comp Vol.9 No.10

Compressed sensing is an innovative technology, which provides a new sampling mode. The key problem in compressed sensing is the construction of sensing matrix, which has an important influence on the signal sampling and reconstruction algorithm. At present, in most cases the sensing matrix is a random structure, and is difficult to realize due to its huge storage in practical applications. In this paper, we introduce a novel deterministic construction of sensing matrix via Q-matrix, which is calculated by solving the N-queens problem. The proposed sensing matrix has good orthogonality and circularity. Using the circularity of Q-matrix, we can construct sensing matrix for compressed sensing. A large number of simulation results show that the proposed sensing matrix in this paper can obtain a better quality of the reconstructed image, and it is easily realized owing to its cyclic characteristic.

Compressed Sensing 기법을 이용한 Dynamic MR Imaging

정홍(Hong Jung),예종철(Jong Chul Ye) 大韓電子工學會 2009 電子工學會論文誌-SP (Signal processing) Vol.46 No.5

Compressed sensing 은 기존의 Nyquist sampling 이론에 기반을 두었던 dynamic MRI 에서의 시·공간 해상도의 제한을 획기적으로 향상시킴으로써, 최근 몇 년 사이, MR reconstruction 분야에서 가장 큰 이슈가 되고 있는 연구주제이다. Dynamic MRI 는 대부분 시간방향의 redundancy 가 매우 크므로, 쉽게 sparse 변환이 가능하다. 따라서 sparsity를 기본 조건으로 하는 compressed sensing 은 거의 모든 dynamic MRI 에 대해 효과적으로 적용될 수 있다. 본 review 페이퍼에서는 최근 compressed sensing 에 기반을 두거나 영상의 sparsity를 이용하여 개발된 dynamic MR imaging algorithm 들을 간략히 소개하고, 비교·분석함으로써, compressed sensing과 같은 새로운 접근 방식의 dynamic MRI 가 실제 임상에서 가져다 줄 발전 가능성을 제시한다. The recently developed sampling theory, “compressed sensing” is gathering huge interest in MR reconstruction area because of its feasibility of high spatio-temporal resolution of dynamic MRI which has been limited in conventional methods based on Nyquist sampling theory. Since dynamic MRI usually has high redundant information along temporal direction, this can be very sparsely represented in most of cases. Therefore, compressed sensing that exploits the sparsity of unknown images can be effectively applied in most of dynamic MRI. This review article briefly introduces currently proposed compressed sensing based dynamic MR imaging algorithms and other methods exploiting sparsity. By comparing them with conventional methods, you may have insight how the compressed sensing based methods can impact nearly every area of clinical dynamic MRI.

The Multi-target Localization Algorithm via Compressed Sensing

Nan Xue,Yan Hu 보안공학연구지원센터 2014 International Journal of Multimedia and Ubiquitous Vol.9 No.11

A multi-target localization algorithm based on compressed sensing was proposed in this paper. The issue of multi-target localization was transformed into compressed sensing. The algorithm greatly reduced the amount of wireless network’s communication data by transferring most of the computing work to the central server. This method made full uses of the priori information of the signal and the support set. It combined Kalman filter with Bayesian compressed sensing to improve the localization accuracy and noise immunity. Simulation results showed that the proposed method has good noise immunity, robustness and localization accuracy compared with traditional localization methods.

Adaptive Adjustment of Compressed Measurements for Wideband Spectrum Sensing

( Yulong Gao ),( Wei Zhang ),( Yongkui Ma ) 한국인터넷정보학회 2016 KSII Transactions on Internet and Information Syst Vol.10 No.1

Compressed sensing (CS) possesses the potential benefits for spectrum sensing of wideband signal in cognitive radio. The sparsity of signal in frequency domain denotes the number of occupied channels for spectrum sensing. This paper presents a scheme of adaptively adjusting the number of compressed measurements to reduce the unnecessary computational complexity when priori information about the sparsity of signal cannot be acquired. Firstly, a method of sparsity estimation is introduced because the sparsity of signal is not available in some cognitive radio environments, and the relationship between the amount of used data and estimation accuracy is discussed. Then the SNR of the compressed signal is derived in the closed form. Based on the SNR of the compressed signal and estimated sparsity, an adaptive algorithm of adjusting the number of compressed measurements is proposed. Finally, some simulations are performed, and the results illustrate that the simulations agree with theoretical analysis, which prove the effectiveness of the proposed adaptive adjusting of compressed measurements.

Block Compressed Sensing of Self-adaptive Measurement and Combinatorial Optimization

Li Mingxing,Chen Xiuxin,Su Weijun,Yu Chongchong 보안공학연구지원센터 2015 International Journal of Hybrid Information Techno Vol.8 No.5

The block compressed sensing has brought forth the problem that the reconstructed image is of lower quality compared with that of the compressed sensing. A new method is proposed in this paper, named as Block Compressed Sensing of Self-adaptive Measurement and Combinatorial Optimization, which capably solves the problem. According to different sparsity of each image block, we firstly measure the blocks by using different projections; then, we choose measurement with the optimal reconstruction as the final measurement. Eventually, reconstruct the original image using the optimal measurement we got. The proposed method outperforms the compressed sensing in terms of real-time and better reconstruction quality is achieved than the block compressed sensing. Our experimental results verify the superiority of the proposed method.

확률적 희소 신호 복원 알고리즘 개발

성진택(Jin-Taek Seong) 한국정보전자통신기술학회 2017 한국정보전자통신기술학회논문지 Vol.10 No.5

본 논문은 유한체(finite fields)에서 압축센싱(compressed sensing) 프레임워크를 살펴본다. 하나의 측정 샘플은 센싱행렬의 행과 희소 신호 벡터와의 내적으로 연산되며, 본 논문에서 제안하는 확률적 희소 신호 복원 알고리즘을 이용하여 그 압축센싱의 해를 찾고자 한다. 지금까지 압축센싱은 실수(real-valued)나 복소수(complex-valued) 평면에서 주로 연구되어 왔지만, 이와 같은 원신호를 처리하는 경우 이산화 과정으로 정보의 손실이 뒤따르게 된다. 이에 대한 연구배경은 이산(discrete) 신호에 대한 희소 신호를 복원하고자 하는 노력으로 이어지고 있다. 본 연구에서 제안하는 프레임워크는 센싱행렬로써 코딩 이론에서 사용된 LDPC(Low-Density Parity-Check) 코드의 패러티체크 행렬을 이용한다. 그리고 본 연구에서 제안한 확률적 복원 알고리즘을 이용하여 유한체의 희소 신호를 복원한다. 기존의 코딩이론에서 발표한 LDPC 복호화와는 달리 본 논문에서는 희소 신호의 확률분포를 이용한 반복적 알고리즘을 제안한다. 그리고 개발된 복원 알고리즘을 통하여 우리는 유한체의 크기가 커질수록 복원 성능이 우수한 결과를 얻었다. 압축센싱의 센싱행렬이 LDPC 패러티체크 행렬과 같은 저밀도 행렬에서도 좋은 성능을 보여줌에 따라 이산 신호를 고려한 응용 분야에서 적극적으로 활용될 것으로 기대된다. In this paper, we consider a framework of compressed sensing over finite fields. One measurement sample is obtained by an inner product of a row of a sensing matrix and a sparse signal vector. A recovery algorithm proposed in this study for sparse signals based probabilistic decoding is used to find a solution of compressed sensing. Until now compressed sensing theory has dealt with real-valued or complex-valued systems, but for the processing of the original real or complex signals, the loss of the information occurs from the discretization. The motivation of this work can be found in efforts to solve inverse problems for discrete signals. The framework proposed in this paper uses a parity-check matrix of low-density parity-check (LDPC) codes developed in coding theory as a sensing matrix. We develop a stochastic algorithm to reconstruct sparse signals over finite field. Unlike LDPC decoding, which is published in existing coding theory, we design an iterative algorithm using probability distribution of sparse signals. Through the proposed recovery algorithm, we achieve better reconstruction performance as the size of finite fields increases. Since the sensing matrix of compressed sensing shows good performance even in the low density matrix such as the parity-check matrix, it is expected to be actively used in applications considering discrete signals.

뇌혈관자기공영영상에서 Compressed SENSE(CS) 기법에 대한 영상의 질 평가 : SENSE 기법과 비교

구은회(Eun-Hoe Goo) 한국방사선학회 2021 한국방사선학회 논문지 Vol.15 No.7

본 연구에서는 검사시간을 단축시키면서 해상도를 증가시키는 Compressed SENSE를 TOF에 적용하여 SENSE와 CS 기법에 대한 영상의 질을 비교하고 SNR, CNR을 평가하여 최적의 기법을 알아보고 이러한 정보를 토대로 임상적 기초자료로 제공하고자 한다. 충청도 소재 한 대학병원에서 TOF MRA 검사를 시행한 환자 32명(남자 15명, 여자 17명, ICA stenosis:10, M1 aneurysm:10, 평균나이 53 ± 4.15)을 대상으로 데이터를 분석하였다. 검사에 적용된 장비는 Ingenia CX 3.0T, Archieva 3.0 T 두 기기를 이용하였고 데이터 획득을 위한 방법으로 32 Channel Head Coil과 3D Gradient echo 이었다. 정량적 분석으로 각 영상의 SNR과 CNR을 측정하고 정성적 평가를 위해 관찰자의 시각적 견해에 대하여 5등급으로 나누어 영상의 질을 평가하였다. 영상평가는 paired t-test와 Wilcoxon 검정을 하였으며 p 값이 0.05 이하 일 때 유의성이 있는 것으로 간주하였다. TOF MRA 영상에서 SNR과 CNR에 대한 정량적 분석 결과 SENSE 기법에 비해 CS 기법이 높게 측정되었다(p<0.05). 관찰자의 시각적 평가로서 혈관의 선예도: CS(4.45 ± 0.41), 전반적인 영상의질: CS(4.77 ± 0.18), 영상의 배경소거: CS(4.57 ± 0.18)는 모두 CS 기법이 높은 결과를 얻었다(p=0.000). 결론적으로, 유속증가 자기공명혈관 조영술에서 SENSE 와 Compressed SENSE 기법을 비교하여 평가했을 때 Compressed SENSE TOF MRA 기법이 우위의 결과를 보여주었다. 이러한 결과는 뇌 질환 3D TOF MRA 검사에서 향후 임상적 기초자료가 될 것이라고 생각한다. The object of this research is CS, which increases resolution while shortening inspection time, is applied to MRA to compare the quality of images for SENSE and CS techniques and to evaluate SNR and CNR to find out the optimal techniques and to provide them as clinical basic data based on this information. Data were analyzed on 32 patients who performed TOF MRA tests at a university hospital in Chung cheong-do (15 males, 17 females), ICA stenosis:10, M1 Aneurysm:10, and average age 53 ± 4.15). In the inspection, the inspection equipment was Ingenia CX 3.0T, Archieva 3.0T, and 32 channel head coil and 3D gradient echo as a method for equipment data. SNR and CNR of each image were measured by quantitative analysis, and the quality of the image was evaluated by dividing the observer s observation into 5 grades for qualitative evaluation. Imaging evaluation is described as being significant when the p-value is 0.05 or less when the paired T-test and Wilcoxon test are performed. Quantitative analysis of SNR and CNR in TOF MRA images Compared to the SENSE method, the CS method is a method measurement method (p <0.05). As an observer s evaluation, the sharpness of blood vessels: CS (4.45 ± 0.41), overall image quality: CS (4.77 ± 0.18), background suppression of images: CS (4.57 ± 0.18) all resulted in high CS technique (p = 0.000). In conclusion, the Compressed SENSE TOF MRA technique shows superior results when comparing and evaluating the SENSE and Compressed SENSE techniques in increased flow rate magnetic resonance angiography. The results are thought to be the clinical basis material in the 3D TOF MRA examination for brain disease.

Compressed Sensing-Based Multi-Layer Data Communication in Smart Grid Systems

( Md. Tahidul Islam ),( Insoo Koo ) 한국인터넷정보학회 2013 KSII Transactions on Internet and Information Syst Vol.7 No.9

Compressed sensing is a novel technology used in the field of wireless communication and sensor networks for channel estimation, signal detection, data gathering, network monitoring, and other applications. It plays a significant role in highly secure, real-time, well organized, and cost-effective data communication in smart-grid (SG) systems, which consist of multi-tier network standards that make it challenging to synchronize in power management communication. In this paper, we present a multi-layer communication model for SG systems and propose compressed-sensing based data transmission at every layer of the SG system to improve data transmission performance. Our approach is to utilize the compressed-sensing procedure at every layer in a controlled manner. Simulation results demonstrate that the proposed monitoring devices need less transmission power than conventional systems. Additionally, secure, reliable, and real-time data transmission is possible with the compressed-sensing technique.

Compressed Sensing of Low-Rank Matrices : A Brief Survey on Efficient Algorithms

이기륭(Kiryung Lee),예종철(Jong Chul Ye) 大韓電子工學會 2009 電子工學會論文誌-SP (Signal processing) Vol.46 No.5

Compressed sensing은 소수의 선형 관측으로부터 sparse 신호를 복원하는 문제를 언급하고 있다. 최근 벡터 경우에서의 성공적인 연구 결과가 행렬의 경우로 확장되었다. Low-rank 행렬의 compressed sensing은 ill-posed inverse problem을 low-rank 정보를 이용하여 해결한다. 본 문제는 rank 최소화 혹은 low-rank 근사의 형태로 나타내질 수 있다. 본 논문에서는 최근 제안된 여러 가지 효율적인 알고리즘에 대한 survey를 제공한다. Compressed sensing addresses the recovery of a sparse vector from its few linear measurements. Recently, the success for the vector case has been extended to the matrix case. Compressed sensing of low-rank matrices solves the ill-posed inverse problem with the low-rank prior. The problem can be formulated as either the rank minimization or the low-rank approximation. In this paper, we survey recently proposed efficient algorithms to solve these two formulations.

Small-block sensing and larger-block recovery in block-based compressive sensing of images

Dinh, Khanh Quoc,Shim, Hiuk Jae,Jeon, Byeungwoo Elsevier 2017 SIGNAL PROCESSING-IMAGE COMMUNICATION - Vol.55 No.-

<P><B>Abstract</B></P> <P>In the block-based compressive sensing (CS) of images, a small block is more practical due to its low-cost sensing in terms of the required memory and the computational complexity. A large block, however, is more effective in CS recovery because of the high probability of a smaller mutual coherence and a more-compressible representation of the images. This paper proposes a block-based CS scheme that is applicable to images with a small-block sensing and larger-block recovery (SBS-LBR), whereby a block-diagonal sensing matrix is used to arbitrarily set a recovery-block size that is multiple-times larger than the sensing block size; subsequently, a more compressible transform signal is generated with large-sized sparsifying basis. The proposed SBS-LBR not only facilitates a low sampling cost, but also improves the recovered images from the larger recovery-block size. Our experiment results confirm a theoretical analysis of the scheme, and have shown the improvement from the proposed SBS-LBR with the suggested proper choices regarding the sensing- and recovery-block sizes.</P> <P><B>Highlights</B></P> <P> <UL> <LI> ACS scheme employs different block sizes in the sensing and the recovery. </LI> <LI> The scheme is analyzed with mutual coherence and compressibility of transform signal. </LI> <LI> The scheme achieves both low sampling cost and more-favorable recovery performance. </LI> </UL> </P>