Engineering, Technology & Applied Science Research Vol. 8, No. 2, 2018, 2809-2813 2809 www.etasr.com Ebrahim et al.: A Performance Comparative Analysis of Block Based Compressive Sensing and Line … A Performance Comparative Analysis of Block Based Compressive Sensing and Line Based Compressive Sensing Mansoor Ebrahim Department of Computer Science Iqra University Karachi, Pakistan mebrahim@iqra.edu.pk Syed Hasan Adil Department of Computer Science Iqra University Karachi, Pakistan hasan.adil@iqra.edu.pk Daniyal Nawaz Department of Computer Science Iqra University Karachi, Pakistan daniyal.nawaz@iqra.edu.pk Abstract—Compressive sensing (CS) is an innovative idea that has opened new areas for viable communication of correlated data. In this paper, a comparative performance analysis of two different variants of compressive sensing i.e. block based compressive sensing (BCS) and line based compressive censing (LCS) schemes is performed for natural images. The idea is to evaluate which variant performs better in terms of reconstruction quality and provides easy initial solution. The experimental analysis demonstrates that LCS scheme can enhance the image reconstruction at lower subrates by 0.5 dB to 2.5 dB, when compared to the BCS scheme. Keywords-compressive sensing; block based approach; line based approach; reconstruction; image I. INTRODUCTION Compressive sensing (CS) is one of the latest techniques that have achieved popularity recently and is applied to various imaging applications [1], such as magnetic resonance imaging (MRI) [2, 3] and seismic identification [4]. CS [5, 6] idea is to express a signal (image/video) with sample estimation rate much lower than that of the Nyquist rate which is essential for the recovery of the signal. One of the innovative of this is the single-pixel camera [1] that openly condenses the sampling and amount of data that will be transmitted, but increases the difficulty of recovering the original signal. In other words, the recovery of the original signal from small number of sample measurements is difficult. Numerous earlier researches have already examined the utilization of CS in image compression [3-8]. Many researchers concentrated their work on proposing how natural images can be compressed utilizing CS and the recovery of the encoded signal (image) from such little estimation. In CS we concentrate mostly towards discrete signs instead of constant time space signals. In addition, compressive sensing of natural images is exposed to few issues such as computationally complex reconstruction algorithm and requirement of large memory to store the random sampling operator Φ. In order to encounter the aforementioned issue different approaches were developed i.e. block based compressive sensing and line based compressive sensing. The block-based approach is far more developed and widely employed as compared to the newly developed line based approach to reduce of the computationally complexity of CS scheme [9-14]. Such methodologies value CS because (i) block/line based estimation is more convenient for applications where the sample image data don't need to be encoded completely in a block/line form until the point when the estimation of the whole image is completed, (ii) the application and capacity of the estimation operator are straightforward, (iii) the individual handling of each block/line of image data brings about simple initial solution with considerably quick and better recovery process. In this paper, a performance comparison of two different variants of compressive sensing i.e. block based compressive sensing and line based compressive sensing for images is performed. The purpose is to find out which variant works best to solve the issues related to CS. The variants are evaluated based on computational complexity and reconstruction quality at various subrates for different test image datasets. In addition, block based and line based approaches are also compared at various block/line sizes to validate the effectiveness of each scheme. The paper is structured as follows. The fundamentals of the CS along with block based and line based approaches are presented in section II. Section III presents and discusses the simulation results. Section IV concludes the paper. II. THEORY OF COMPRESSIVE SENSING The CS theory [5] states that a sparse (original or some transform domain) signal can be completely recovered from a number of samples below than that stated by the Nyquist theorem. The CS scheme efficiently eases the computational prerequisites, for example, memory, processing power, and transmission data transfer capacity at the encoder by relating signal acquirement and dimensionality reduction into a distinct stage. CS is effective in two circumstances. When direct measurements of a high-resolution signal are hard to attain and when multiple high-resolution signals are complex to encode. In literature, CS is a standard and isn’t stated for any particular signal other than underlying sparsity assumptions. CS permits great prospect of signal reconstruction by utilizing least amount of unsystematic measurements, as long as the signal/image is spa sch me red me tra as Fig me vec ma ma est X= by com can the CS sim sig sam iss ma A. the red div sep con sam enc ma app bri pri rec pro Engineerin www.etasr arse and inc hemes, in C easurements r ducing the com Consider a easurementsis ansformation d shown in Figu Y=Φ·X g. 1. Compres asurement matrix X∈RN and Y ctor respectiv atrix Φ is orth atrix. In addi timation is no =Φ-1 Y is ill-po CS ought to mpleted by ta n be expressedx argmin However, mo eoretical and a S requires a multaneously gnals difficult mpled signals sue, various res ainly include b Block Based Block based e sparse natur duce storage s vided in term parately based nstrained (bloc Φ = Φ ⋯⋮ ⋱0 ⋯ The key plu mpled image coder until the aking block-ba plications, (iii) ing informatio imarily quick construction i ojection land ng, Technology r.com coherent. 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PSN VARIOUS DATA Subrate 0.0 BCS 24.3 LCS 24.8 Gain 0.5 Subrate 0.0 BCS 28.9 LCS 29.7 Gain 0.7 Subrate 0.0 BCS 25.9 LCS 26.7 Gain 0.8 Subrate 0.0 BCS 25.7 LCS 26.6 Gain 0.8 Subrate 0.0 BCS 24 LCS 25.8 Gain 1.1 Subrate 0.0 BCS 24.9 LCS 26.0 Gain 1.0 Visual Result Since LCS an ential to certif ually detectab ected represen ults shown in ages of the en S using two d t the reconstru ect present in coded measure ions (red dotte rformed by us oother and p asurements. 8. Visual res LCS encoded me 018, 2809-2813 of Block Based NR ACCOMPLISHED ASET IMAGES AT B A 05 0.1 35 25.25 85 25.89 5 0.64 B 05 0.1 98 30.68 75 31.48 77 0.8 Mon 05 0.1 91 28.03 74 28.94 83 0.91 Middl 05 0.1 79 28.99 65 29.89 86 0.9 Co 05 0.1 .7 26.98 83 28.27 13 1.29 Te 05 0.1 96 26.99 02 28.18 06 1.19 t Comparison nd BCS are e fy that the sub ble images. Tw nting medium n Figures 8 a ncoded measur different subrat ucted images f n the image ements. 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It can be no prove the disto d using the ng the empha that reconstru ements looks m struction of opoly image usin ine … NCODE 3 69 87 8 3 89 03 4 3 1 57 47 3 66 98 2 3 07 65 8 3 07 51 44 , it is create ts are . The ucted S and oticed orting BCS asized uction much BCS g BCS Fig BC blo sen and app 1d [1] [2] [3] [4] [5] [6] [7] [8] [9] [10 [11 [12 [13 Engineerin www.etasr g. 9. Visual re CS and LCS encod This article ock based com nsing for diffe d sizes. The e proach perfor dB to 3dB at va M. F. Duarte, Kelly, R. G. sampling”, IEE 2008 M. Lustig, D. Sensing MRI” 72-82, 2008 M. Lustig, D. L compressed se Medicine, Vol W. Tang, J. M Seismic Data R D. L. Dono Information Th E. J. Candes, M IEEE Signal Pr A. Chambolle minimization a No. 2, pp. 167- M. A. T. Figue sparse reconst inverse probl Processing, Vo L. Gan, “Bl International C 403–406, July 0] S. Mun, J. E. Directional Tra Processing, Ca ] J. E. Fowler, S of images & vi No. 4, pp. 297- 2] F. Shi, J. 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