A Faster and More Accurate Iterative Threshold Algorithm for Signal Reconstruction in Compressed Sensing

Jianxiang Wei; Shumin Mao; Jiming Dai; Ziren Wang; Weidong Huang; Yonghong Yu

doi:10.3390/s22114218

A Faster and More Accurate Iterative Threshold Algorithm for Signal Reconstruction in Compressed Sensing

Sensors (Basel). 2022 Jun 1;22(11):4218. doi: 10.3390/s22114218.

Authors

Jianxiang Wei¹, Shumin Mao², Jiming Dai², Ziren Wang³, Weidong Huang⁴, Yonghong Yu⁵

Affiliations

¹ School of Management, Nanjing University of Posts and Telecommunications, Nanjing 210003, China.
² School of Internet of Things, Nanjing University of Posts and Telecommunications, Nanjing 210003, China.
³ School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China.
⁴ Key Research Base of Philosophy and Social Sciences in Jiangsu-Information Industry Integration Innovation and Emergency Management Research Center, Nanjing 210003, China.
⁵ College of Tongda, Nanjing University of Posts and Telecommunications, Nanjing 210003, China.

Abstract

Fast iterative soft threshold algorithm (FISTA) is one of the algorithms for the reconstruction part of compressed sensing (CS). However, FISTA cannot meet the increasing demands for accuracy and efficiency in the signal reconstruction. Thus, an improved algorithm (FIPITA, fast iterative parametric improved threshold algorithm) based on mended threshold function, restart adjustment mechanism and parameter adjustment is proposed. The three parameters used to generate the gradient in the FISTA are carefully selected by assessing the impact of them on the performance of the algorithm. The developed threshold function is used to replace the soft threshold function to reduce the reconstruction error and a restart mechanism is added at the end of each iteration to speed up the algorithm. The simulation experiment is carried out on one-dimensional signal and the FISTA, RadaFISTA and RestartFISTA are used as the comparison objects, with the result that in one case, for example, the residual rate of FIPITA is about 6.35% lower than those three and the number of iterations required to achieve the minimum error is also about 102 less than that of FISTA.

Keywords: FISTA; compressed sensing; parameter adjustment; restart adjustment mechanism; signal reconstruction; threshold function.

Grants and funding

This research was supported in part by the Major Project of Philosophy and Social Science Research in Jiangsu Universities of China (2020SJZDA102), the Future Network Scientific Research Fund Project (FNSRFP-2021-YB-54) and Tongda College of Nanjing University of Posts and Telecommunications (XK203XZ21001).