Faster PET reconstruction with a stochastic primal-dual hybrid gradient method

Abstract

Image reconstruction in positron emission tomography (PET) is computationally challenging due to Poisson noise, constraints and potentially non-smooth priors-let alone the sheer size of the problem. An algorithm that can cope well with the first three of the aforementioned challenges is the primal-dual hybrid gradient algorithm (PDHG) studied by Chambolle and Pock in 2011. However, PDHG updates all variables in parallel and is therefore computationally demanding on the large problem sizes encountered with modern PET scanners where the number of dual variables easily exceeds 100 million. In this work, we numerically study the usage of SPDHG-a stochastic extension of PDHG-but is still guaranteed to converge to a solution of the deterministic optimization problem with similar rates as PDHG. Numerical results on a clinical data set show that by introducing randomization into PDHG, similar results as the deterministic algorithm can be achieved using only around 10 % of operator evaluations. Thus, making significant progress towards the feasibility of sophisticated mathematical models in a clinical setting.

Block-Coordinate Proximal Algorithms for Scale-Free Texture Segmentation

“…Two algorithms are considered: the forward-backward algorithm [13] applied on the dual formulation of (2), and the primal-dual algorithm (cf. [15], [23], [2]). In this context, such algorithms are efficient for medium size images and for small values of the regularization parameter λ.…”

“…Block dual forward-backward. Proposed in [19], it leads to Algorithm 1 when customized to Problem (2). Convergence of the sequence (h [k] ) k∈N towards the unique solution to (2) is secured if…”

“…2). A local estimation hn is conducted as in Section 2.1, using scales 2 2 ≤ 2 j ≤ 2 4 , followed by a TV-denoising estimation h, as proposed in (2). Performances reported here are obtained as averages across 10 independent realizations.…”

“…Scale-free and total variation based texture segmentation. Texture segmentation constitutes a major challenge in image processing, medical imaging being a prominent example, e.g., for tumor localization [1] or for macroscopic brain functional connectivity assessment [2]. Biological tissues being complicated organic structures, medical images often consists of complex textures, the segmentation of which requires the use of advanced image processing tools.…”

“…[16,17]), which remains a hot topic. In the same time, some block-coordinate strategies were devised for solving generic convex problems, both for forward-backward iterations [12,18,19] and primal-dual algorithms [18,20,21,22,23,2]. In [19], an accelerated forward-backward algorithm based on deterministic block activation is proposed and applied to the joint deconvolution and deinterlacing of video sequences.…”