• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.12
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• pp.739-745
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• 2014

It has been shown in compressive sensing that every s-sparse $x{\in}R^N$ can be recovered from the measurement vector y=Ax or the noisy vector y=Ax+e via ${\ell}_1$-minimization as soon as the 3s-restricted isometry constant of the sensing matrix A is smaller than 1/2 or smaller than $1/\sqrt{3}$ by applying the Iterative Hard Thresholding (IHT) algorithm. However, recovery can be guaranteed by practical algorithms for some certain assumptions of acquisition schemes. One of the key assumption is that the sensing matrix must satisfy the Restricted Isometry Property (RIP), which is often violated in the setting of many practical applications. In this paper, we studied a generalization of RIP, called Restricted Biorthogonality Property (RBOP) for anisotropic cases, and the new recovery algorithms called oblique pursuits. Then, we provide an analysis on the success of sparse recovery in terms of restricted biorthogonality constant for the IHT algorithms.

• Journal of Broadcast Engineering
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• v.17 no.6
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• pp.954-963
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• 2012

As a greedy algorithm reconstructing the sparse signal from underdetermined system, orthogonal matching pursuit (OMP) algorithm has received much attention. In this paper, we multiple candidate matching pursuit (MuCaMP), which builds up candidate support set in every iteration and uses the minimum residual at last iteration. Using the restricted isometry property (RIP), we derive the sufficient condition for MuCaMP to recover the sparse signal exactly. The MuCaMP guarantees to reconstruct the K-sparse signal when the sensing matrix satisfies the RIP constant ${\delta}_{N+K}<\frac{\sqrt{N}}{\sqrt{K}+3\sqrt{N}}$. In addition, we show a recovery performance both noiseless and noisy measurements.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.49 no.2
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• pp.122-129
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• 2012

As a greedy algorithm reconstructing the sparse signal from underdetermined system, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we present an extension of OMP for pursuing efficiency of the index selection. Our approach, referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple (N) columns are identified per step. Using the restricted isometry property (RIP), we derive the condition for gOMP to recover the sparse signal exactly. The gOMP guarantees to reconstruct sparse signal when the sensing matrix satisfies the RIP constant ${\delta}_{NK}$ < $\frac{\sqrt{N}}{\sqrt{K}+2\sqrt{N}}$. In addition, we show recovery performance and the reduced number of iteration required to recover the sparse signal.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.689-701
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• 2019

We study the recovery results of ${\ell}_p$-constrained compressive sensing (CS) with $p{\geq}1$ via robust width property and determine conditions on the number of measurements for standard Gaussian matrices under which the property holds with high probability. Our paper extends the existing results in Cahill and Mixon from ${\ell}_2$-constrained CS to ${\ell}_p$-constrained case with $p{\geq}1$ and complements the recovery analysis for robust CS with ${\ell}_p$ loss function.

• Journal of Satellite, Information and Communications
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• v.8 no.4
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• pp.130-134
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• 2013

This paper describes the basic principles of 3D broadcast system and proposes new 3D broadcast technology that reduce the amount of data by applying CS(Compressed Sensing). Differences between Sampling theory and the CS technology concept was described. Recently proposed CS algorithm AMP(Approximate Message Passing) and CoSaMP(Compressive Sampling Matched Pursuit) was described. Image data that compressed and restored by these algorithm was compared. Calculation time of the algorithm having a low complexity is determined.

• Journal of Satellite, Information and Communications
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• v.10 no.3
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• pp.57-61
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• 2015

This paper describes the basic principles of 3D broadcast system and proposes new 3D broadcast technology that reduces the amount of data by applying CS(Compressed Sensing). Differences between Sampling theory and the CS technology concept was described. CS algorithm SS-CoSaMP(Single-Space Compressive Sampling Matched Pursuit) and AMP(Approximate Message Passing) was described. Image data compressed and restored by these algorithm was compared. Calculation time of the algorithm having a low complexity is determined.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2015.11a
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• pp.51-53
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• 2015

In this paper, we propose an efficient sparse signal recovery algorithm referred to as the matching pursuit with a tree pruning (TMP). Two key ingredients of TMP are the pre-selection to put a restriction on columns of the sensing matrix to be investigated and the tree pruning to eliminate unpromising paths from the search tree. In our analysis, we show that the sparse signal is accurately reconstructed when the sensing matrix satisfies the restricted isometry property. In our simulations, we confirm that TMP is effective in recovering sparse signals and outperforms conventional sparse recovery algorithms.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.5
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• pp.15-24
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• 2009

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 fie 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.

• Journal of Satellite, Information and Communications
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• v.9 no.3
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• pp.59-63
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• 2014

This paper describes the basic principles of 3D broadcast system and proposes new 3D broadcast technology that reduces the amount of data by applying CS(Compressed Sensing). Differences between Sampling theory and the CS technology concept were described. Recently proposed CS algorithm AMP(Approximate Message Passing) and CoSaMP(Compressive Sampling Matched Pursuit) were described. This paper compared an accuracy between two algorithms and a calculation time that image data compressed and restored by these algorithms. As result determines a low complexity algorithm for 3D broadcast system.

• Journal of Satellite, Information and Communications
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• v.9 no.2
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• pp.63-68
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• 2014

This paper proposed a novel compressed sensing (CS) technique for an efficient video transmission of multi-copter. The proposed scheme is focused on reduction of the amount of data based on CS technology. First, we describe basic principle of Spectrum sensing. And then we compare AMP(Approximate Message Passing) with CoSaMP(Compressive Sampling Matched Pursuit) through mathematical analysis and simulation results. They are evaluated in terms of calculation time and complexity, then the promising algorithm is suggestd for multicopter operation. The result of experiment in this paper shows that AMP algorithm is more efficient than CoSaMP algorithm when it comes to calculation time and image error probability.