Iterative Selection and Correction Based Adaptive Greedy Algorithm for Compressive Sensing Reconstruction
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Iterative Selection and Correction Based Adaptive Greedy Algorithm for Compressive Sensing Reconstruction Ahmed Aziz1,2 · Walid Osamy1,3 · Ahmed M. Khedr4,5 Accepted: 14 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Compressive sensing (CS) is a new sampling theory used in many signal processing applications due to its simplicity and efficiency. However, signal reconstruction is considered as one of the biggest challenge faced by the CS method. Therefore in this paper, we aim to address this challenge by proposing an Adaptive Iterative Forward–Backward Greedy Algorithm (AFB). AFB algorithm is different from all other reconstruction algorithms, as it depends on solving the least squares problem in the forward phase, which increases the probability of selecting the correct columns better than other reconstruction algorithms. In addition, AFB improves the selection process by removing the incorrect columns selected in the previous step. To evaluate the AFB’s reconstruction performance, we used two types of data: computer-generated data and real data set (Intel Berkeley data set). The simulation results show that AFB outperforms Forward–Backward Pursuit, Subspace Pursuit, Orthogonal Matching Pursuit, and Regularized OMP in terms of reducing reconstruction error. Keywords IoT · WSNs · Compressive sensing · Reconstruction algorithms · Greedy algorithms
* Ahmed Aziz [email protected] Walid Osamy [email protected] Ahmed M. Khedr [email protected] 1
Computer Science Department, Faculty of Computers and Artificial Intelligence, University of Benha, Benha, Egypt
2
Tashkent State University of Economic, Tashkent, Uzbekistan
3
Department of Applied Natural Science, College of Community in Unaizah, Qassim University, Qassim, Kingdom of Saudi Arabia
4
Computer Science Department, University of Sharjah, Sharjah 27272, UAE
5
Faculty of Science, Zagazig University, Zagazig, Egypt
13
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A. Aziz et al.
1 Introduction Compressive sensing (CS) [1–5] method has been proposed as a novel data reduction method for reducing the size of data transmitted through the IoT network. According to CS method, the base station (BS) needs only M ≥ K log N∕K , where M is the size of compressed samples, K is the sparsity level and N is the signal dimension, to recover the original signal x ∈ RN from only y ∈ RM measurements such that y = 𝛷x and 𝛷 is CS matrix. On the other hand, the CS reconstruction process aims to recover N samples from only M measurements, where M ≪ N , which makes it NP-hard problem [6]. The CS reconstruction problem can be expressed as follows:
minx ∥ x ∥0 s.t. y = 𝛷x
(1)
In Eq. 1, the CS reconstruction process aims to recover the sparsity level of the original signal x such that the CS matrix 𝛷 and the measurements vector y are given. A lot of algorithms have been proposed to address this problem such as convex relaxation and greedy algorithm. In convex relaxation algorithms, the problem in (1) is relaxed by replacing L0 to L1 [7] as follo
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