A novel sparse reconstruction method based on multi-objective Artificial Bee Colony algorithm

doi:10.1016/j.sigpro.2021.108283

Signal Processing

Volume 189, December 2021, 108283

https://doi.org/10.1016/j.sigpro.2021.108283 Get rights and content

Highlights

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A sparse reconstruction method based on multi-objective artificial Bee colony algorithm is proposed.
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The proposed method is called MOABC-SR.
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The effectiveness of the MOABC-SR is demonstrated on various test signals.
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The reconstruction performance of MOABC-SR is better than the compared algorithms.

Abstract

Compressed sensing is a signal processing method that performs the compressing and sensing processes at the same time. Sparse signal reconstruction is one of the most important issues of compressed sensing. The developments in sparse signal reconstruction methods directly affect the performance of the compressed sensing process. Many sparse signal reconstruction methods have been proposed in the literature. In general, these algorithms are classified as convex optimization, non-convex optimization, and greedy algorithms. In addition, multi-objective optimization algorithms have started to be used in sparse signal reconstruction lately. A sparse signal reconstruction method based on a Multi-objective Artificial Bee Colony algorithm is proposed in this study. The proposed algorithm optimizes the sparsity and measurement error at the same time. Furthermore, it uses the iterative half thresholding algorithm to improve the convergence acceleration of the method. The proposed method was evaluated by using various test signals. Additionally, it was compared with other sparse signal reconstruction algorithms. According to the obtained results, the proposed method has some superiority over the compared algorithms.

Section snippets

1. Introduction

Compressed sensing (CS) is a signal processing technique that can recover a sparse signal by using a low number of measurements [1], [2], [3], [4]. A signal needs to be sparse for the implementation of CS reconstruction. A signal $x \in R^{N}$ can be represented as the linear combination of basis vectors as (1). $x = \sum_{i = 1}^{N} (s_{i} ψ_{i}) or x = ψ s$

The vector s is another representation of the signal x in a transform domain. The signal x is called k-sparse if only k numbers of s_i coefficients in (1) are non-zero and the

2. Proposed Multi-Objective Method for Sparse Reconstruction

In this study, a novel sparse reconstruction method based on MOABC is proposed. Firstly, the general principles of the ABC algorithm are mentioned in this part of the study. Then, the details of the MOABC-SR algorithm designed for sparse signal reconstruction are explained in Algorithm 1. Moreover, the algorithm steps of the local search method used to improve the convergence of the proposed method are mentioned in Algorithm 2. Finally, the method used for selecting a final solution from the PF

3. Results and Discussions

In this section of the study, the reconstruction performance of MOABC-SR is tested by using various test problems. These test problems are artificially generated, SOTF [39], and image signals. They are suitable for practical systems and span a wide range of test properties like signal length, sparsity level, and measurement numbers. In addition, SOTF test signals shown in Table 2 have been used to test the other proposed MOSR methods in the literature [26,28,37]. Also, the MOABC-SR algorithm

4. Computational Complexity

The main parts of the proposed method are composed of the main loop of ABC, the local search method, and the final solution selection method. Therefore, the computational complexity of MOABC-SR is mainly dominated by the number of foods of ABC (N_f), the iteration number of the local search method (N_ls), and the iteration number of the final solution selection method. The local search method is used twice in the main loop of ABC and the final solution selection method is used only once outside

5. Conclusion

This study proposes a method based on a multi-objective artificial bee colony algorithm for sparse signal reconstruction problems. MOABC-SR optimizes the objectives of sparsity and measurement error simultaneously. The method has very few control parameters and is efficient. Furthermore, IHT is integrated into the MOABC algorithm as the local search method. The selection of the final solution is done by a designed method based on the pseudo-inverse of the obtained non-dominated solutions.

CRediT authorship contribution statement

Murat Emre Erkoc: Conceptualization, Methodology, Software, Writing – original draft, Writing – review & editing. Nurhan Karaboga: Supervision, Formal analysis, Visualization, Validation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work has been supported by Erciyes University Scientific Research Projects Coordination Unit under grant number FDK-2021-10946.

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View full text

A novel sparse reconstruction method based on multi-objective Artificial Bee Colony algorithm

Highlights

Abstract

Section snippets

1. Introduction

2. Proposed Multi-Objective Method for Sparse Reconstruction

3. Results and Discussions

4. Computational Complexity

5. Conclusion

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgements

CR Math

Appl Comput Harmon Anal

Appl Comput Harmon Anal

Appl Soft Comput

Inform Sci

Inform Sci

Appl Soft Comput

J Franklin Institute-Eng Appl Math

Swarm Evol Comput

Eng Sci Technol Int J-Jestech

Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information

IEEE Trans Inf Theory

Compressed sensing

IEEE Trans Inf Theory

An introduction to compressive sampling

IEEE Signal Process Mag

Compressive sensing

IEEE Signal Process Mag

Matching pursuits with time-frequency dictionaries

IEEE Trans Signal Process

Signal recovery from random measurements via orthogonal matching pursuit

IEEE Trans Inf Theory

Atomic decomposition by basis pursuit

Siam J Sci Comput

Fast Solution of l(1)-Norm Minimization Problems When the Solution May Be Sparse

IEEE Trans Inf Theory

Regression shrinkage and selection via the Lasso

J R Stat Soc Ser B-Methodol

Least angle regression

Ann Stat

An iterative thresholding algorithm for linear inverse problems with a sparsity constraint

Commun Pure Appl Math

Evolutionary algorithms for sparse signal reconstruction

Sig Image Video Process

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IEEE Trans Evol Comput

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