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首页> 外文期刊>IEEE Transactions on Information Theory >Multichannel Sparse Blind Deconvolution on the Sphere
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Multichannel Sparse Blind Deconvolution on the Sphere

机译：球面上的多通道稀疏盲反卷积

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摘要

Multichannel blind deconvolution is the problem of recovering an unknown signal f and multiple unknown channels xi from their circular convolution y(i) = x(i) circle star f (i = 1, 2,..., N). We consider the case where the x(i) 's are sparse, and convolution with f is invertible. Our nonconvex optimization formulation solves for a filter h on the unit sphere that produces sparse output y(i) circle star h. Under some technical assumptions, we show that all local minima of the objective function correspond to the inverse filter of f up to an inherent sign and shift ambiguity, and all saddle points have strictly negative curvatures. This geometric structure allows successful recovery of f and x(i) using a simple manifold gradient descent (MGD) algorithm. The same approach is also applicable to blind gain and phase calibration with a Fourier sensing matrix. Our algorithm and analysis require fewer assumptions than previous algorithms for the same problem. Our theoretical findings are complemented by numerical experiments, which demonstrate superior performance of the proposed approach over the previous methods. Empirically, our algorithm has low computation cost (converging in a small number of iterations) and low memory footprint (solving only for the inverse filter of f).
机译：多通道盲解卷积是从圆形卷积y（i）= x（i）圆星f（i = 1，2，...，N）中恢复未知信号f和多个未知通道xi的问题。我们考虑x（i）稀疏且与f的卷积可逆的情况。我们的非凸优化公式可求解单位球面上的滤波器h，该滤波器产生稀疏输出y（i）圆星h。在某些技术假设下，我们证明目标函数的所有局部极小值都对应于f的逆滤波器，直至固有符号和移位模糊度，并且所有鞍点都具有严格的负曲率。这种几何结构允许使用简单的流形梯度下降（MGD）算法成功恢复f和x（i）。相同的方法也适用于使用傅立叶传感矩阵的盲增益和相位校准。对于相同的问题，我们的算法和分析比以前的算法需要更少的假设。我们的理论发现得到了数值实验的补充，数值实验证明了所提出的方法优于以前的方法。从经验上讲，我们的算法具有较低的计算成本（收敛于少量迭代）和较低的内存占用（仅针对f的逆滤波器）。

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