249 research outputs found
Restoration of images based on subspace optimization accelerating augmented Lagrangian approach
AbstractWe propose a new fast algorithm for solving a TV-based image restoration problem. Our approach is based on merging subspace optimization methods into an augmented Lagrangian method. The proposed algorithm can be seen as a variant of the ALM (Augmented Lagrangian Method), and the convergence properties are analyzed from a DRS (Douglas–Rachford splitting) viewpoint. Experiments on a set of image restoration benchmark problems show that the proposed algorithm is a strong contender for the current state of the art methods
Optimization Methods for Inverse Problems
Optimization plays an important role in solving many inverse problems.
Indeed, the task of inversion often either involves or is fully cast as a
solution of an optimization problem. In this light, the mere non-linear,
non-convex, and large-scale nature of many of these inversions gives rise to
some very challenging optimization problems. The inverse problem community has
long been developing various techniques for solving such optimization tasks.
However, other, seemingly disjoint communities, such as that of machine
learning, have developed, almost in parallel, interesting alternative methods
which might have stayed under the radar of the inverse problem community. In
this survey, we aim to change that. In doing so, we first discuss current
state-of-the-art optimization methods widely used in inverse problems. We then
survey recent related advances in addressing similar challenges in problems
faced by the machine learning community, and discuss their potential advantages
for solving inverse problems. By highlighting the similarities among the
optimization challenges faced by the inverse problem and the machine learning
communities, we hope that this survey can serve as a bridge in bringing
together these two communities and encourage cross fertilization of ideas.Comment: 13 page
Accelerated Cardiac Diffusion Tensor Imaging Using Joint Low-Rank and Sparsity Constraints
Objective: The purpose of this manuscript is to accelerate cardiac diffusion
tensor imaging (CDTI) by integrating low-rankness and compressed sensing.
Methods: Diffusion-weighted images exhibit both transform sparsity and
low-rankness. These properties can jointly be exploited to accelerate CDTI,
especially when a phase map is applied to correct for the phase inconsistency
across diffusion directions, thereby enhancing low-rankness. The proposed
method is evaluated both ex vivo and in vivo, and is compared to methods using
either a low-rank or sparsity constraint alone. Results: Compared to using a
low-rank or sparsity constraint alone, the proposed method preserves more
accurate helix angle features, the transmural continuum across the myocardium
wall, and mean diffusivity at higher acceleration, while yielding significantly
lower bias and higher intraclass correlation coefficient. Conclusion:
Low-rankness and compressed sensing together facilitate acceleration for both
ex vivo and in vivo CDTI, improving reconstruction accuracy compared to
employing either constraint alone. Significance: Compared to previous methods
for accelerating CDTI, the proposed method has the potential to reach higher
acceleration while preserving myofiber architecture features which may allow
more spatial coverage, higher spatial resolution and shorter temporal footprint
in the future.Comment: 11 pages, 16 figures, published on IEEE Transactions on Biomedical
Engineerin
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