Improved total variation-based CT image reconstruction applied to clinical data

Abstract

In computed tomography there are different situations where reconstruction has to be performed with limited raw data. In the past few years it has been shown that algorithms which are based on compressed sensing theory are able to handle incomplete datasets quite well. As a cost function these algorithms use the ℓ(1)-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 past few years. The most popular way is optimizing the raw data and sparsity cost functions separately in an alternating manner. In this paper we will follow this strategy and present a new method to adapt these optimization steps. Compared to existing methods which perform similarly, the proposed method needs no a priori knowledge about the raw data consistency. It is ensured that the algorithm converges to the lowest possible value of the raw data cost function, while holding the sparsity constraint at a low value. This is achieved by transferring the step-size determination of both optimization procedures into the raw data 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 step-size adaption in a different way. Additional prior information as proposed by the PICCS algorithm can be incorporated easily into the optimization process.

The rotate-plus-shift C-arm trajectory. Part I. Complete data with less than 180° rotation

“…In these cases, the rotate-plus-shift trajectory may be combined with reconstruction algorithms dedicated to avoid limited angle artifacts. 6,8 The proposed trajectory allows for the acquisition of a fully sampled data set with a mobile C-arm system mechanically limited to a rotation range of at least 180…”

“…[7][8][9] These techniques, however, do not achieve image quality or size of the reconstructed volume comparable to the short scan reference.…”

A Review on Image Reconstruction through MRI k-Space Data

“…The minimization technique is used to bring down the number of missing coefficients. They discussed two models of Alternating Minimization algorithm such that one model follows the sparsity and other one follows Total Variation [77]. This algorithm is applied for MRI reconstruction which was then a comparatively latest imaging technology that is capable of resolving the image using spatial and temporal atomic scale.…”

Iterative denoising algorithms for perfusion C-arm CT with a rapid scanning protocol

“…First, we investigate the iTV approach [6], where the regularization term is the total variation norm R TV (x) = x TV . In this case operator T is given by an iterative gradient descent procedure with automatic adaption of the TV gradient step size to assure improved data consistency after one iteration of Algorithm 1.…”

“…For the rapid scanning protocol we recently applied an iterative tight frame (TF) wavelet-based reconstruction algorithm [3] in a brain perfusion phantom study [4] to increase CNR in the tissue TACs, which showed promising results to improve the perfusion maps compared to FDK [5] reconstruction. In this work, we compare the latter approach to the JBF and the improved total variation (iTV) [6] regularization techniques. However, all these approaches are based on ART [7] and thus computationally expensive.…”