Improved sparsity-constrained image reconstruction applied to clinical CT data

Abstract

Compresssed sensing seems to be very promising for image reconstruction in computed tomography. In the last years it has been shown, that these algorithms are able to handle incomplete data sets quite well. As cost function these algorithms use the ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> — norm of the image after it has been transformed by a sparsifying transformation. This yields to an inequality — constrained convex optimization problem. Due to the large size of the optimization problem some heuristic optimization algorithms have been proposed in the last years. The most popular way is optimizing the rawdata and sparsity cost functions separately in an alternating manner. In this paper we will follow this strategy. Thereby we present a new method to adapt these optimization steps. Compared to existing methods which perform similar, the proposed method needs no a priori knowledge about the rawdata consistency. It is ensured that the algorithm converges to the best possible value of the rawdata cost function, while holding the sparsity constraint at a low value. This is achieved by transferring both optimization procedures into the rawdata domain, where they are adapted to each other. To evaluate the algorithm, we process measured clinical datasets. To cover a wide field of possible applications, we focus on the problems of angular undersampling, data lost due to metal implants, limited view angle tomography and interior tomography. In all cases the presented method reaches convergence within less than 25 iteration steps, while using a constant set of algorithm control parameters. The image artifacts caused by incomplete raw-data are mostly removed without introducing new effects like staircasing. All scenarios are compared to an existing implementation of the ASD — POCS algorithm, which realizes the stepsize adaption in a different way. Additional prior information as proposed by the PICCS algorithm can be incorporated easily into the optimization process.