Compressive Computed Tomography Reconstruction through Denoising Approximate Message Passing

TL;DR

This paper introduces D-GAMP-CT, a novel algorithm that applies advanced Approximate Message Passing techniques with denoising to improve sparse view CT reconstruction, reducing computational demands and enhancing image quality.

Contribution

It develops a new AMP-based framework for real-world sparse view CT imaging, integrating sophisticated denoisers and noise models for better reconstruction performance.

Findings

Outperforms traditional statistical CT solvers in simulated and real scans.

Effectively handles non-linear Poisson noise and system non-linearities.

Reduces computational complexity in sparse view CT reconstruction.

Abstract

X-ray Computed Tomography (CT) reconstruction from a sparse number of views is a useful way to reduce either the radiation dose or the acquisition time, for example in fixed-gantry CT systems, however this results in an ill-posed inverse problem whose solution is typically computationally demanding. Approximate Message Passing (AMP) techniques represent the state of the art for solving under-sampling Compressed Sensing problems with random linear measurements but there are still not clear solutions on how AMP should be modified and how it performs with real world problems. This paper investigates the question of whether we can employ an AMP framework for real sparse view CT imaging? The proposed algorithm for approximate inference in tomographic reconstruction incorporates a number of advances from within the AMP community, resulting in the Denoising Generalized Approximate Message Passing CT algorithm (D-GAMP-CT). Specifically, this exploits the use of sophisticated image denoisers to regularize the reconstruction. While in order to reduce the probability of divergence the (Radon) system and Poisson non-linear noise model are treated separately, exploiting the existence of efficient preconditioners for the former and the generalized noise modelling in GAMP for the latter. Experiments with simulated and real CT baggage scans confirm that the performance of the proposed algorithm outperforms statistical CT optimization solvers.