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 ℓ1norm of the image after it has been transformed by a sparsifying transformation. This yields to an inequalityconstrained 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 eld 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 rawdata are mostly removed without introducing new eects like staircasing. All scenarios are compared to an existing implementation of the ASDPOCS algorithm, which realizes the stepsize adaption in a dierent way. Additional prior information as proposed by the PICCS algorithm can be incorporated easily into the optimization process.

Image artefact propagation in motion estimation and reconstruction in interventional cardiac C-arm CT

“…The weighting parameter α for the PICCS algorithm was set to 0.5, which is the upper bound of the optimal range from 0.4–0.5 (Theriault-Lauzier et al 2012). The relaxation parameter β for the iTV optimization was set to 0.8 and the iTV parameter ω to 0.8 as in the original paper (Ritschl et al 2010). A number of 4 data consistency and 10 objective function iterations were set.…”

4-D motion field estimation by Combined Multiple Heart Phase Registration (CMHPR) for cardiac C-arm data

“…The reference volume needs to provide a low artifact level with minor streak artifacts, but needs to represent sharp edges of the endocardial wall. As a first attempt, the prior image constrained compressed sensing (PICCS) and the improved total variation (iTV) algorithm are used [10], [15], [16]. As prior volume for the PICCS reconstruction, a FBP reconstruction with data from a whole short-scan is used.…”

“…The objective function is minimized in an alternating manner, the raw data constraint is minimized and in the second step the sparsity cost function is optimized. In order to ensure that the raw data cost function converges to the best possible value and simultaneously ensure that the sparsity constraint converges to a low value, the improved total variation (iTV) was introduced by Ritschl et al [15], [16]. Additionally, a bilateral filter is applied to the reconstructed volume at every iteration step in order to suppress apparent noise.…”