Deep Inertia $L_p$ Half-Quadratic Splitting Unrolling Network for Sparse View CT Reconstruction

TL;DR

This paper introduces a novel deep unrolling network for sparse view CT reconstruction that combines $L_p$-norm regularization, inertial steps, and deep learning initialization, achieving superior results with theoretical convergence guarantees.

Contribution

It proposes a new inertial $L_p$-norm half-quadratic splitting algorithm with proven convergence, integrating deep learning for improved sparse view CT reconstruction.

Findings

Outperforms existing methods in fewer view scenarios

Handles complex noise effectively

Provides theoretical convergence guarantees

Abstract

Sparse view computed tomography (CT) reconstruction poses a challenging ill-posed inverse problem, necessitating effective regularization techniques. In this letter, we employ $L_p$-norm ($0<p<1$) regularization to induce sparsity and introduce inertial steps, leading to the development of the inertial $L_p$-norm half-quadratic splitting algorithm. We rigorously prove the convergence of this algorithm. Furthermore, we leverage deep learning to initialize the conjugate gradient method, resulting in a deep unrolling network with theoretical guarantees. Our extensive numerical experiments demonstrate that our proposed algorithm surpasses existing methods, particularly excelling in fewer scanned views and complex noise conditions.