Implementation of sparse image reconstruction strategies using compressive sensing: optimization algorithms and neural networks

Abstract

Compressive sensing (CS) theory allows for the recovery of signals at a sampling rate lower than that required by the Nyquist-Shannon theorem. This theory has led to the development of single-pixel imaging (SPI) systems, which enable the acquisition of 2D images with one-dimensional sensors using a set of light samples through coded apertures and the appropriate CS optimization algorithm. This work describes the procedure for reconstructing images from a CS-SPI system using conventional optimization algorithms as well as neural network-based algorithms. Their performance is demonstrated for different sampling matrices using the Python programming language and the test image, cameraman, which was adjusted to the inputs required by each algorithm. Five conventional algorithms are presented: OMP, CoSaMP, IRLS, Lasso, and BP, as well as five neural network-based algorithms: DR2, HSCNN-R, AMP-Net, Recon-Net, and IstaxRecon. The performance of these algorithms is presented to guide the selection of the method according to the needs of each CS-SPI application and the characteristics of each algorithm. The results showed that for conventional algorithms, LASSO demonstrated good performance in terms of execution time, and in the case of neural network-based algorithms, the HSCNN-R and IstaxRecon models showed high performance at different sampling rates.