Image Reconstruction in Compressive Sensing Using the Level 3 Reverse Biorthogonal 4.4 (rbio4.4) Discrete Wavelet Transform and SP, CoSaMP and ALISTA Algorithm

This paper presents an efficient image reconstruction method based on Compressive Sensing (CS) theory, leveraging the level-3 Reverse Biorthogonal 4.4 (rbio4.4) discrete wavelet transform in combination with three reconstruction algorithms: Subspace Pursuit (SP), Compressive Sampling Matched Pursuit (CoSaMP), and the Analytic Learned Iterative Shrinkage Thresholding Algorithm (ALISTA). The approach exploits the sparsity of images in a suitable wavelet basis, enabling compressed acquisition from a reduced number of random linear measurements. The process consists of four stages: (1) decomposition of the original image using the rbio4.4 wavelet transform to obtain sparse coefficients, (2) compressed sampling via a random measurement matrix, (3) reconstruction of the sparse signal using SP, CoSaMP, or ALISTA, and (4) final image reconstruction through the inverse wavelet transform. Experimental evaluation was conducted on the classic Lena image (200 × 200 pixels), comparing the three algorithms in terms of reconstruction quality measured by the Structural Similarity Index (SSIM) and computational cost (reconstruction time in minutes) across sampling rates ranging from 10% to 60%. Results show that all three algorithms achieve nearly identical reconstruction quality (virtually indistinguishable SSIM values at each sampling rate), confirming their effectiveness within the CS. However, ALISTA stands out significantly due to its exceptional speed, exhibiting substantially lower reconstruction times thanks to its learned nature, which replaces iterative procedures with fixed, optimized operations. In contrast, CoSaMP demonstrates higher and sometimes unpredictable computational times depending on the sampling rate. These findings highlight ALISTA’s strong potential for real-time or embedded applications.