Blind calibration of multi-channel samplers using sparse recovery

We propose an algorithm for blind calibration of multi-channel samplers in the presence of unknown gains and offsets, which is useful in many applications such as multi-channel analog-to-digital converters, image super-resolution, and sensor networks. Using a subspace-based rank condition developed by Vandewalle et al., we obtain a set of linear equations with respect to complex harmonics whose frequencies are determined by the offsets, and the coefficients of each harmonic are determined by the discrete-time Fourier transforms of outputs of each of the channels. By discretizing the offsets over a fine grid, this becomes a sparse recovery problem where the signal of interest is sparse with an additional structure, that in each block there is only one nonzero entry. We propose a modified CoSaMP algorithm that takes this structure into account to estimate the offsets. Our algorithm is scalable to large numbers of channels and can also be extended to multi-dimensional signals. Numerical experiments demonstrate the effectiveness of the proposed algorithm.