Blind Deconvolution From Multiple Sparse Inputs

Blind deconvolution is an inverse problem when both the input signal and the convolution kernel are unknown. We propose a convex algorithm based on $1-minimization to solve the blind deconvolution problem, given multiple observations from sparse input signals. The proposed method is related to other problems such as blind calibration and finding sparse vectors in a subspace. Sufficient conditions for exact and stable recovery using the proposed method are developed that shed light on the sample complexity. Finally, numerical examples are provided to showcase the performance of the proposed method.