Deep Inertia $L_{p}$ Half-Quadratic Splitting Unrolling Network for Sparse View CT Reconstruction

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.