Two features desired in a three-dimensional (3D) optical tomographic image reconstruction algorithm are the ability to reduce imaging artifacts and to do fast processing of large data volumes. Traditional iterative inversion algorithms are impractical in this context due to their heavy computational and memory requirements. We propose and experimentally validate a novel scalable iterative mini-batch algorithm (SIMBA) for fast and high-quality optical tomographic imaging. SIMBA enables highquality imaging by combining two complementary information sources: the physics of the imaging system characterized by its forward model and the imaging prior characterized by a denoising deep neural net. SIMBA easily scales to very large 3D tomographic datasets by processing only a small subset of measurements at each iteration. We establish the theoretical fixedpoint convergence of SIMBA under nonexpansive denoisers for convex data-fidelity terms. We validate SIMBA on both simulated and experimentally collected intensity diffraction tomography (IDT) datasets. Our results show that SIMBA can significantly reduce the computational burden of 3D image formation without sacrificing the imaging quality.

Plug-and-play priors (PnP) is a broadly applicable methodology for solving inverse problems by exploiting statistical priors specified as denoisers. Recent work has reported the stateof-the-art performance of PnP algorithms using pre-trained deep neural nets as denoisers in a number of imaging applications. However, current PnP algorithms are impractical in large-scale settings due to their heavy computational and memory requirements. This work addresses this issue by proposing an incremental variant of the widely used PnP-ADMM algorithm, making it scalable to large-scale datasets. We theoretically analyze the convergence of the algorithm under a set of explicit assumptions, extending recent theoretical results in the area. Additionally, we show the effectiveness of our algorithm with nonsmooth datafidelity terms and deep neural net priors, its fast convergence compared to existing PnP algorithms, and its scalability in terms of speed and memory.

Regularization by denoising (RED) is a powerful framework for solving imaging inverse problems. Most RED algorithms are iterative batch procedures, which limits their applicability to very large datasets. In this paper, we address this limitation by introducing a novel online RED (On-RED) algorithm, which processes a small subset of the data at a time. We establish the theoretical convergence of On-RED in convex settings and empirically discuss its effectiveness in non-convex ones by illustrating its applicability to phase retrieval. Our results suggest that On-RED is an effective alternative to the traditional RED algorithms when dealing with large datasets.

Plug-and-play priors (PnP) is a broadly applicable methodology for solving inverse problems by exploiting statistical priors specified as denoisers. Recent work has reported the state-of-the-art performance of PnP algorithms using pre-trained deep neural nets as denoisers in a number of imaging applications. However, current PnP algorithms are impractical in large-scale settings due to their heavy computational and memory requirements. This work addresses this issue by proposing an incremental variant of the widely used PnP-ADMM algorithm, making it scalable to large-scale datasets. We theoretically analyze the convergence of the algorithm under a set of explicit assumptions, extending recent theoretical results in the area. Additionally, we show the effectiveness of our algorithm with nonsmooth data-fidelity terms and deep neural net priors, its fast convergence compared to existing PnP algorithms, and its scalability in terms of speed and memory.Preprint. Under review.

This paper investigates the estimate of motion parameters from 3D hand joint positions. We formulate the issue as an inverse kinematics problem with biomechanical constraints and propose a fast and robust iterative approach to address the constrained optimization. It elaborately designs a coordinate descent algorithm to decompose the problem into a sequence of decisions on the transformation around each kinematic node (i.e., joint), while the decision for each node is equivalent to a point matching problem. Addressing the whole optimization then amounts to considering all nodes of the kinematic tree from its root to leaves one by one. This not only accelerates the process but also improves the accuracy of the solution of the inverse kinematic optimization. Experiments show that our approach is able to yield results comparable to and even better than those by the state-of-the-art methods.