An eigen approach to stable multichannel blind deconvolution under an FIR subspace model

Multichannel blind deconvolution is a bilinear inverse problem that recovers an unknown signal observed as convolutions with multiple unknown filters. We are particularly interested in the case where the unknown filters are known to be short-length finite impulse response (FIR) filters a priori. Under this FIR prior, classical methods based on the commutativity of the convolution were proposed and analyzed in 1990s. However, these classical methods are sensitive to additive noise when working with finitely many observations. In certain applications, domain-specific knowledge provides a subspace prior on the FIR coefficients. Leveraging this additional prior, we propose a modification of the classical methods to alleviates the sensitivity and derive its nonasymptotic analysis. Numerical results show that this modified method improves the classical method significantly and outperforms other competing methods for multichannel blind deconvolution.