An enhanced block-based Compressed Sensing technique using orthogonal matching pursuit
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ORIGINAL PAPER
An enhanced block-based Compressed Sensing technique using orthogonal matching pursuit Sujit Das1 · Jyotsna Kumar Mandal1 Received: 17 March 2020 / Revised: 8 August 2020 / Accepted: 4 September 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract The theory of compressed sensing asserts that one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some orthonormal basis; from non-adaptive linear measurements by solving a L1 norm minimisation problem. The non-adaptive measurements have the character of random linear combinations of the basis or frame elements. However, for large-scale 2D image signals, the randomized sensing matrix consumes enormous computational resources that makes it impractical. The problem has been addressed in the paper as a block compressed sensing (BCS) with sparsity normalization in the transformed domain in the preprocessing stage. The blocks obtained are converted to non-adaptive measurements using identically independent weighted Gaussian random matrices. The feasibility of reconstruction is verified using orthogonal matching pursuit. Simulation results show that better reconstruction performance can be achieved by the proposed technique in comparison with the existing BCS approaches. Keywords Compress Sensing · OMP · Rotation · Wavelets · Block CS
1 Introduction Compressed sensing (CS) is build upon the groundbreaking theory by Candes and Tao [3] and Donoho [7] and who showed that a finite-dimensional signal having a sparse or compressible representation can be recovered from a small set of linear, non-adaptive incoherent measurements. The design of these measurement schemes and their extensions to practical data models and acquisition schemes are one of the most central challenges in the field of compressed sensing. CS differs from classical sampling in two important respects. First, rather than sampling the signal at specific points in time or space, CS systems typically acquire measurements in the form of inner products between the signal and a more general test function called sensing matrix. Randomness often plays a key role in the design of these test functions. Second, the two frameworks differ in the manner in which they deal with
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Jyotsna Kumar Mandal [email protected] Sujit Das [email protected]
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Department of Computer Science and Engineering, University of Kalyani, Kalyani, Nadia, India
signal recovery, i.e., the problem of recovering the original signal from the compressive measurements. n n ∈ Rn be the signal of interest, θ = {θi }i=1 Let x = {xi }i=1 and x = Ψ θ in the basis or frame Ψ . Then, x is k-sparse if and only if ||θ ||0 = #k{k; θk = 0}, k 0 otherwise,
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where X i is ith block of transformed signal X and X ij is the jth coefficient of ith block. The columns of weighted sensing matrix is modified as follows: Aˆ ij = Aij wij ,
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where Aij is the jth column in of ith sensing matrix and elements of Ai is drawn from N (0, m1i ), m i is number of meas
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