Compressed Sensing Based 3D Tomographic Reconstruction for Rotational Angiography

Abstract

In this paper, we address three-dimensional tomographic reconstruction of rotational angiography acquisitions. In clinical routine, angular subsampling commonly occurs, due to the technical limitations of C-arm systems or possible improper injection. Standard methods such as filtered backprojection yield a reconstruction that is deteriorated by sampling artifacts, which potentially hampers medical interpretation. Recent developments of compressed sensing have demonstrated that it is possible to significantly improve reconstruction of subsampled datasets by generating sparse approximations through 1-penalized minimization. Based on these results, we present an extension of the iterative filtered backprojection that includes a sparsity constraint called soft background subtraction. This approach is shown to provide sampling artifact reduction when reconstructing sparse objects, and more interestingly, when reconstructing sparse objects over a non-sparse background. The relevance of our approach is evaluated in cone-beam geometry on real clinical data.

Compressed‐sensing‐based content‐driven hierarchical reconstruction: Theory and application to C‐arm cone‐beam tomography

“…If we consider a weighted sum of any of the above constraints, we would need to find the proximal operator that simultaneously enforces them all. For instance, we previously associated the positivity constraint and the ℓ 1 -norm 16…”

“…Vessels being naturally sparse, one can achieve subsampling artifact reduction using constrained ℓ 1 -norm, non-TV, and minimization. 16 The scheme uses homotopy, 17 a mean to accelerate convergence, and is inspired by compressed sensing, but it can be interpreted in different terms and has led us to a more generic approach that we shall call content-driven hierarchical tomographic reconstruction.…”

“…We describe several hierarchical schemes aiming at streak artifacts reduction that are applicable to C-arm CBCT: the empirical orthogonal matching pursuit (OMP) approach with the ℓ 0 pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the ℓ 1 -norm constraint of compressed sensing, that is amenable to reconstructing sparse vessels over a nonsparse background; homotopy with total variation; and a novel empirical extension of homotopy to nonlinear diffusion (NLD). 18 In order to supplement the results we obtained in the context of C-arm vascular imaging, 16,19 we here focus on TVconstrained reconstructions of C-arm CBCT for soft tissues. We provide results on simulated CT data and real C-arm CBCT data showing the interest of TV-based homotopy in terms of image quality improvement, speed of convergence, and ease of parameterization.…”

Exponential Wavelet Iterative Shrinkage Thresholding Algorithm for compressed sensing magnetic resonance imaging

“…This theorem states that a band-limited analog signal can be perfectly reconstructed from a finite sequence of samples if the sampling rate exceeds 2B, where B is the highest frequency of the original signal [23]. When the rate of sampling is lower than the Nyquist frequency, the high frequency portion of signals will be aliased or folded over into the lower frequency portion of the signal [50].…”

Cardiac C‐arm computed tomography using a 3D + time ROI reconstruction method with spatial and temporal regularization

“…As such, it allows the reconstruction algorithm to better exploit the data. A 4Dregularized reconstruction method, based on temporal nonlocal means (TNLM), was proposed by Jia et al 17 Langet et al have proposed a 3D + time reconstruction algorithm for injected arteries, 18 which is a specific problem leading to specialized algorithms. Momey et al proposed a 2D + time reconstruction method based on total variation (short TV) regularization, 19 and later extended it to 3D + time.…”