• 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.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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.9
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• pp.4418-4437
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• 2017

In this paper a three-phase secure compressive sensing (CS) and received signal strength (RSS) based target localization approach is proposed to mitigate the effect of malicious node attack. RSS measurements are first arranged into a group of subsets where the same measurement can be included in multiple subsets. Intermediate target position estimates are then produced using individual subsets of RSS measurements and the CS technique. From the intermediate position estimates, the residual error vector and residual error square vector are formed. The least median of residual error square is utilized to define a verifier parameter. The selected residual error vector is utilized along with a threshold to determine whether a node or measurement is under attack. The final target positions are estimated by using only the attack-free measurements and the CS technique. Further, theoretical analysis is performed for parameter selection and computational complexity evaluation. Extensive simulation studies are carried out to demonstrate the advantage of the proposed CS-based secure localization approach over the existing algorithms.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38C no.11
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• pp.1029-1043
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• 2013

We introduce Approximate Message Passing (AMP) algorithm which is one of the efficient recovery algorithms in Compressive Sensing (CS) area. Recently, AMP algorithm has gained a lot of attention due to its good performance and yet simple structure. This paper provides not only a understanding of the AMP algorithm but its relationship with a classical (Sum-Product) Message Passing (MP) algorithm. Numerical experiments show that the AMP algorithm outperforms the classical MP algorithms in terms of time and phase transition.

• IEIE Transactions on Smart Processing and Computing
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• v.3 no.1
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• pp.10-18
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• 2014

From the perspective of reducing the sampling cost of color images at high resolution, block-based compressive sensing (CS) has attracted considerable attention as a promising alternative to conventional Nyquist/Shannon sampling. On the other hand, for storing/transmitting applications, CS requires a very efficient way of representing the measurement data in terms of data volume. This paper addresses this problem by developing a measurement-coding method with the proposed customized Huffman coding. In addition, by noting the difference in visual importance between the luma and chroma channels, this paper proposes measurement coding in YCbCr space rather than in conventional RGB color space for better rate allocation. Furthermore, as the proper use of the image property in pursuing smoothness improves the CS recovery, this paper proposes the integration of a low pass filter to the CS recovery of color images, which is the block-based ${\ell}_{20}$-norm minimization. The proposed coding scheme shows considerable gain compared to conventional measurement coding.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.6
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• pp.2748-2766
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• 2016

Compared with traditional patch-based sparse representation, recent studies have concluded that group-based sparse representation (GSR) can simultaneously enforce the intrinsic local sparsity and nonlocal self-similarity of images within a unified framework. This article investigates an accelerated split Bregman method (SBM) that is based on GSR which exploits image compressive sensing (CS). The computational efficiency of accelerated SBM for the measurement matrix of a partial Fourier matrix can be further improved by the introduction of a fast Fourier transform (FFT) to derive the enhanced algorithm. In addition, we provide convergence analysis for the proposed method. Experimental results demonstrate that accelerated SBM is potentially faster than some existing image CS reconstruction methods.

• Current Optics and Photonics
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• v.6 no.3
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• pp.288-296
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• 2022

We propose and experimentally demonstrate a novel photonic compressive sensing (CS) scheme for acquiring sparse radio frequency signals with adjustable compression ratio in this paper. The sparse signal to be measured and a pseudo-random binary sequence are modulated on consecutively connected chirped pulses. The modulated pulses are compressed into short pulses after propagating through a dispersive element. A programmable optical filter based on spatial light modulator is used to realize spectral segmentation and demultiplexing. After spectral segmentation, the compressed pulses are transformed into several sub-pulses and each of them corresponds to a measurement in CS. The major advantage of the proposed scheme lies in its adjustable compression ratio, which enables the system adaptive to the sparse signals with variable sparsity levels and bandwidths. Experimental demonstration and further simulation results are presented to verify the feasibility and potential of the approach.

• The Magazine of the IEIE
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• v.41 no.6
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• pp.18-26
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• 2014

신호의 표현과 압축은 밀접하게 연관되어 있다. 만약 매우 효과적인 신호 표현 방식을 찾을 수 있다면 매우 높은 비율로 신호 압축이 가능하다. 또한 효과적인 신호 표현 방식을 통해 우수한 성능과 낮은 복잡도를 갖는 신호 추정 방식을 유도할 수도 있다. 효과적인 신호 표현 방식은 대상 신호 자체의 성질과 관련되어 있다. 영상 신호등 매우 일반적인 신호가 적절한 변환을 통해 산재된 신호(sparse signal)가 될 수 있음을 많은 연구를 통해 볼 수 있다. 이러한 사실이 compressive sensing(CS)의 기반이다. 즉 신호가 어떠한 변환을 통해 산재된 신호로 표현될 수 있다면 매우 적은 수의 샘플로 이러한 신호를 알아낼 수 있다는 것을 Donoho와 Candes 등이 보였고 이것이 가능한 다양한 조건에 등에 대해 연구되었다. CS는 신호 처리에 근본적인 문제인 효과적인 신호 표현 방식에 직접 연관되어 매우 다양한 분야에 적용될 수 있다. 이 논문에서 CS의 기본적인 개념을 소개한 후 CS가 레이더 신호 처리에 어떻게 도움이 될 수 있는지 살펴본다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.12
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• pp.746-755
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• 2014

Compressive sensing (CS) has drawn much interest as a new sampling technique that enables signals to be sampled at a much lower than the Nyquist rate. By noting that the block-based compressive sensing can still keep spatial correlation in measurement domain, in this paper, we propose a novel encoding technique for measurement data obtained in the block-based CS of natural image. We apply discrete wavelet transform (DWT) to decorrelate CS measurements and then assign a proper quantization scheme to those DWT coefficients. Thus, redundancy of CS measurements and bitrate of system are reduced remarkably. Experimental results show improvements in rate-distortion performance by the proposed method against two existing methods of scalar quantization (SQ) and differential pulse-code modulation (DPCM). In the best case, the proposed method gains up to 4 dB, 0.9 dB, and 2.5 dB compared with the Block-based CS-Smoothed Projected Landweber plus SQ, Block-based CS-Smoothed Projected Landweber plus DPCM, and Multihypothesis Block-based CS-Smoothed Projected Landweber plus DPCM, respectively.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.10
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• pp.118-128
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• 2015

Compressive sensing (CS) has to face with two challenges of computational complexity reconstruction and low coding efficiency. As a solution, this paper presents a novel spatially scalable Kronecker two layer compressive sensing framework which facilitates reconstruction up to three spatial resolutions as well as much improved CS coding performance. We propose a dual-resolution sensing matrix based on the quincunx sampling grid which is applied to the base layer. This sensing matrix can provide a fast-preview of low resolution image at encoder side which is utilized for predictive coding. The enhancement layer is encoded as the residual measurement between the acquired measurement and predicted measurement data. The low resolution reconstruction is obtained from the base layer only while the high resolution image is jointly reconstructed using both two layers. Experimental results validate that the proposed scheme outperforms both conventional single layer and previous multi-resolution schemes especially at high bitrate like 2.0 bpp by 5.75dB and 5.05dB PSNR gain on average, respectively.