Compressed sensing-based image reconstruction for discrete tomography with sparse view and limited angle geometries

This paper addresses the image reconstruction problem in discrete tomography, particularly under challenging imaging conditions such as sparse-view and limited-angle geometries commonly encountered in computed tomography (CT). These conditions often result in low-quality reconstructions due to insufficient projection data and incomplete angular coverage. To overcome these limitations, we propose a novel reconstruction framework that integrates compressed sensing (CS) with a parametric level set (PLS) method tailored for discrete images. The proposed approach leverages prior knowledge of discrete gray-level values and employs a parametric level set function to represent boundaries in both binary and multi-gray-level images. Unlike previous methods, our PLS is constructed using a dictionary of basis functions composed of single-scale or multiscale Gaussian functions. Reconstruction is formulated as 𝚤1-norm minimization of Gaussian coefficients, promoting sparsity. We assess the method's robustness by introducing varying levels of Gaussian noise into the projection data under both sparse-view and limited-angle conditions. Quantitative evaluations using PSNR, SSIM, and Dice coefficients demonstrate that the proposed method preserves boundary sharpness and accurately reconstructs discrete intensity levels, even in highly undersampled and noisy scenarios. Simulations and experiments on both synthetic and real CT data confirm that the proposed approach consistently outperforms conventional methods in terms of reconstruction quality, boundary accuracy, and noise robustness.