Wavelet Estimation via Sparse Multichannel Blind Deconvolution

We introduce a Sparse Multichannel Blind Deconvolution (SMBD) method. The method is a modification of Euclid’s blind deconvolution where the multichannel impulse response is estimated by solving an homogeneous system of equations. SMBD can tolerate moderate levels of noise and does not require knowing the source duration. SMBD solves the homogeneous system of equations arising in Euclid deconvolution by imposing sparsity on the multichannel impulse response. To avoid the trivial solution, the sparse reflectivity is constrained to have unit norm. The latter results in non- convex optimization that is solved via a constrained steepest descent technique.