Space-Variant Total Variation boosted by learning techniques in few-view tomographic imaging

TL;DR

This paper introduces a novel space-variant TV regularization model enhanced by neural network-based gradient approximation, improving medical image reconstruction quality from limited noisy tomographic data.

Contribution

It develops a new regularization approach combining neural networks and space-variant TV, with theoretical analysis and a tailored optimization algorithm for better image reconstruction.

Findings

Enhanced reconstruction quality from few-view data

Effective denoising while preserving details

Theoretical proof of solution uniqueness

Abstract

This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary objective of the proposed optimization model is to achieve a good balance between denoising and the preservation of fine details and edges, overcoming the performance of the popular and largely used Total Variation (TV) regularization through the application of appropriate pixel-dependent weights. The proposed strategy leverages the role of gradient approximations for the computation of the space-variant TV weights. For this reason, a convolutional neural network is designed, to approximate both the ground truth image and its gradient using an elastic loss function in its training. Additionally, the paper provides a theoretical analysis of the proposed model, showing the uniqueness of its solution, and illustrates a Chambolle-Pock algorithm tailored to address the specific problem at hand. This comprehensive framework integrates innovative regularization techniques with advanced neural network capabilities, demonstrating promising results in achieving high-quality reconstructions from low-sampled tomographic data.