The iterations of many sparse estimation algorithms are comprised of a fixed linear filter cascaded with a thresholding nonlinearity, which collectively resemble a typical neural network layer. Consequently, a lengthy sequence of algorithm iterations can be viewed as a deep network with shared, hand-crafted layer weights. It is therefore quite natural to examine the degree to which a learned network model might act as a viable surrogate for traditional sparse estimation in domains where ample training data is available. While the possibility of a reduced computational budget is readily apparent when a ceiling is imposed on the number of layers, our work primarily focuses on estimation accuracy. In particular, it is well-known that when a signal dictionary has coherent columns, as quantified by a large RIP constant, then most tractable iterative algorithms are unable to find maximally sparse representations. In contrast, we demonstrate both theoretically and empirically the potential for a trained deep network to recover minimal `0-norm representations in regimes where existing methods fail. The resulting system is deployed on a practical photometric stereo estimation problem, where the goal is to remove sparse outliers that can disrupt the estimation of surface normals from a 3D scene.
[1] Bo Xin, Yizhou Wang, Wen Gao and David Wipf. Maximal Sparsity with Deep Networks?, accepted by Neural Information Processing Systems (NIPS 2016), 2016.
Bo Xin is currently an associate researcher in Visual Computing Group at Microsoft Research Asia (MSRA). Before joining MSRA in Jul. 2016, he received his Ph.D. from Peking University. He worked with Prof. Yizhou Wang and Prof. Wen Gao, and did a joint PhD program at University of California, Los Angeles, supervised by Prof. Alan L. Yuille. His research interests include mathematical optimization (including convex, submodular, Bayesian and non-convex optimization) and their applications in machine learning and computer vision. |

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