Deconvolution of sparse spike trains accounting for wavelet phase shifts and colored noise

The problem of the restoration of spiky sequences when the usual convolution model is corrupted by nonstationary wavelet phase-shifts is addressed. To this end, an extended convolution model driven by a Bernoulli-Gaussian (BG)-like process is introduced. This setting lends itself to easy extension of algorithms designed for BG deconvolution. A comparison of practical results obtained with this new method and BG deconvolution is provided. Numerical experiments indicate an increased robustness compared with standard BG methods.<>