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Parameter estimation using sparse reconstruction with dynamic dictionaries

We consider the problem of parameter estimation for signals characterized by sums of parameterized functions. We present a dynamic dictionary subset selection approach to parameter estimation where we iteratively select a small number of dictionary elements and then alter the parameters of these dictionary elements to achieve better signal model fit. The proposed approach avoids the use of highly oversampled (and highly correlated) dictionary elements, which are needed in fixed dictionary approaches to reduce parameter bias associated with dictionary quantization. We demonstrate estimation performance on a sinusoidal signal estimation example.