压缩感知的域分解方法
Domain decomposition methods for compressed sensing
AI总结：
提出用于最小化含数据保真项和全变分约束泛函的序贯与并行域分解算法，分析收敛性，并通过数值实验展示在插值/修复及压缩感知问题中恢复分段常数医学图像的有效性。
摘要：
我们提出了几种域分解算法，用于序贯和并行最小化由数据保真项和全变分约束构成的泛函。分析了算法的收敛性质。我们提供了几个数值实验，展示了算法在插值/修复问题中分别恢复一维和二维信号的成功应用，以及在压缩感知问题中从部分傅里叶系数组恢复分段常数医学图像的成功应用。
英文摘要：
We present several domain decomposition algorithms for sequential and parallel minimization of functionals formed by a discrepancy term with respect to data and total variation constraints. The convergence properties of the algorithms are analyzed. We provide several numerical experiments, showing the successful application of the algorithms for the restoration 1D and 2D signals in interpolation/inpainting problems respectively, and in a compressed sensing problem, for recovering piecewise constant medical-type images from partial Fourier ensembles.
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