A compressed sensing approach to low-radiation CT reconstruction

Abstract

This paper is on reduction of x-ray radiation dosage in computerized tomography (CT) examinations without compromising the image quality by compressed sensing (CS). For this purpose, the smoothness of the sinogram data set and the sparsity of its frequency transformation are exploited which, in corporation with a randomly projected x-ray radiation scheme, can result in a randomly undersampled partial Fourier matrix as the sensing matrix for CS reconstruction. The formulation of this CT data acquisition and reconstruction scheme satisfies the incoherence and sparsity properties required by CS theory. Based on this scheme, a weighted ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularized optimization algorithm is proposed for computing the CS image reconstruction. Its reconstruction performance and advantages over other known CT reconstruction methods are demonstrated by simulated phantom and CT images.