Complex-valued data are encountered in many application areas of signal and image processing. In the context of optimization of functions of real variables, subspacealgorithms have recently attracted much interest, d...
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ISBN:
(纸本)9781479936878
Complex-valued data are encountered in many application areas of signal and image processing. In the context of optimization of functions of real variables, subspacealgorithms have recently attracted much interest, due to their efficiency in solving large-size problems while simultaneously offering theoretical convergence guarantees. The goal of this paper is to show how some of these methods can be successfully extended to the complex case. More precisely, we investigate the properties of the proposed complex-valued Majorize- Minimize Memory Gradient (3MG) algorithm. An important practical application of these results arises for image reconstruction in Parallel Magnetic Resonance Imaging (PMRI). Comparisons with existing optimization methods confirm the good performance of our approach for PMRI reconstruction.
Stochastic optimization plays an important role in solving many problems encountered in machine learning or adaptive processing. In this context, the second-order statistics of the data are often unknown a priori or t...
详细信息
ISBN:
(纸本)9781479946037
Stochastic optimization plays an important role in solving many problems encountered in machine learning or adaptive processing. In this context, the second-order statistics of the data are often unknown a priori or their direct computation is too intensive, and they have to be estimated on-line from the related signals. In the context of batch optimization of an objective function being the sum of a data fidelity term and a penalization (e.g. a sparsity promoting function), Majorize-Minimize (MM) subspace methods have recently attracted much interest since they are fast, highly flexible and effective in ensuring convergence. The goal of this paper is to show how these methods can be successfully extended to the case when the cost function is replaced by a sequence of stochastic approximations of it. Simulation results illustrate the good practical performance of the proposed MM Memory Gradient (3MG) algorithm when applied to 2D filter identification.
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