Recently, it has been shown that interior tomography problems in x-ray CT can be uniquely determined if tiny subregions inside of the region of interest are known. The solution can be obtained by the projection onto c...
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ISBN:
(纸本)9781467364553
Recently, it has been shown that interior tomography problems in x-ray CT can be uniquely determined if tiny subregions inside of the region of interest are known. The solution can be obtained by the projection onto convex sets (POCS) combined with the back projection filtration algorithm. However, it is well-known that the convergence speed of POCS is slow;hence, to overcome the limitation, this paper employs a parallel proximal algorithm (PPXA) to simultaneously consider multiple convex constraints rather than projecting on each of them sequentially as in POCS. Our simulation results show that the solution for the interior tomography problem can be accurately obtained using PPXA with a much smaller number of iterations than POCS.
Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding ...
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Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding (CSC), has been recently reintroduced and extensively studied. CSC brings a natural remedy to the limitation of typical sparse enforcing approaches of handling global and high-dimensional signals by local, patch-based, processing. While the classic field of sparse representations has been able to cater for the diverse challenges of different signal processing tasks by considering a wide range of problem formulations, almost all available algorithms that deploy the CSC model consider the same problem form. As we argue in this paper, this CSC pursuit formulation is also too restrictive as it fails to explicitly exploit some local characteristics of the signal. This work expands the range of formulations for the CSC model by proposing two convex alternatives that merge global norms with local penalties and constraints. The main contribution of this work is the derivation of efficient and provably converging algorithms to solve these new sparse coding formulations.
Stereo matching is an active area of research in image processing. In a recent work, a convex programming approach was developed in order to generate a dense disparity field. In this paper, we address the same estimat...
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ISBN:
(纸本)9781457705397
Stereo matching is an active area of research in image processing. In a recent work, a convex programming approach was developed in order to generate a dense disparity field. In this paper, we address the same estimation problem and propose to solve it in a more general convex optimization framework based on proximal methods. More precisely, unlike previous works where the criterion must satisfy some restrictive conditions in order to be able to numerically solve the minimization problem, this work offers a great flexibility in the choice of the involved criterion. The method is validated in a stereo image coding framework, and the results demonstrate the good performance of the proposed parallel proximal algorithm.
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