Reconstruction of Sparse-View Tomography via Banded Matrices

Abstract

Computed Tomography (CT) is one of the significant research areas in medical image analysis. One of the main aspects of CT that researchers remain focused, is on reducing the dosage as X-rays are generally harmful to human bodies. In order to reduce radiation dosage, compressed sensing (CS) based methodologies appear to be promising. The basic premise is that medical images have inherent sparsity in some transformation domain. As a result, CS provides the possibility of recovering a high quality image from fewer projection data. In general, the sensing matrix in CT is generated from Radon projections by appropriately sampling the radial and angular parameters. In our work, by restricting the number of such parameters, we generate an under-determined linear system involving projection (Radon) data and a sparse sensing matrix, bringing thereby the problem into CS framework.

Among various recent solvers, the Split-Bregman iterative scheme has of late become popular due to its suitability for solving a wide variety of optimization problems. Intending to exploit the underlying structure of sensing matrix, the present work analyzes its properties and finds a banded structure for an associated intermediate matrix. Using this observation, we simplify the Split-Bregman solver, proposing thereby a CT-specific solver of low complexity. We also provide the efficacy of proposed method empirically.