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

Area of Science:

• Medical Imaging
• Image Reconstruction
• Computational Imaging

Background:

• Computed tomography (CT) imaging often faces challenges with sparse-view and limited-angle data acquisition.
• These conditions lead to low-quality image reconstructions due to insufficient projection data and incomplete angular sampling.
• Existing reconstruction methods struggle to maintain accuracy and sharpness under such challenging conditions.

Purpose of the Study:

• To develop a novel image reconstruction framework for discrete tomography.
• To address limitations in sparse-view and limited-angle CT imaging.
• To improve the accuracy and robustness of image reconstruction in challenging scenarios.

Main Methods:

• Integration of compressed sensing (CS) with a parametric level set (PLS) method for discrete images.
• Utilizing prior knowledge of discrete gray-level values and representing boundaries with a PLS function.
• Formulating reconstruction as 𝚤1-norm minimization of Gaussian coefficients for sparsity, using single- or multiscale Gaussian basis functions.

Main Results:

• The proposed method demonstrates robustness against varying levels of Gaussian noise in projection data.
• Quantitative evaluations (PSNR, SSIM, Dice) show preserved boundary sharpness and accurate reconstruction of discrete intensity levels.
• The approach consistently outperforms conventional methods in reconstruction quality, boundary accuracy, and noise robustness in simulations and real data.

Conclusions:

• The novel CS-PL S framework effectively reconstructs discrete images from undersampled and noisy projection data.
• This method offers superior performance in preserving image details and accuracy compared to traditional techniques.
• The findings are significant for improving CT image quality in challenging acquisition geometries.