Qing Qu
A Nonconvex Approach for Exact and Efficient Multichannel Sparse Blind Deconvolution
Qing Qu, Xiao Li, Zhihui Zhu
We formulate the task as a nonconvex optimization problem over the sphere.
Convolutional Phase Retrieval
Qing Qu, Yuqian Zhang, Yonina Eldar, John Wright
Neural Information Processing Systems http://nips.cc/
A Nonconvex Approach for Exact and Efficient Multichannel Sparse Blind Deconvolution
Qing Qu, Xiao Li, Zhihui Zhu
Neural Information Processing Systems http://nips.cc/
Convolutional Phase Retrieval
Qing Qu, Yuqian Zhang, Yonina Eldar, John Wright
This model is motivated by applications to channel estimation, optics, and underwater acoustic communication, where the signal of interest is acted on by a given channel/filter, and phase information is difficult or impossible to acquire. We show that when a is random and m is sufficiently large, x can be efficiently recovered up to a global phase using a combination of spectral initialization and generalized gradient descent. The main challenge is coping with dependencies in the measurement operator; we overcome this challenge by using ideas from decoupling theory, suprema of chaos processes and the restricted isometry property of random circulant matrices, and recent analysis for alternating minimizing methods.