Sparse deconvolution in one and two dimensions: applications in endocrinology and single-molecule fluorescence imaging.

Deconvolution of noisy signals is an important task in analytical chemistry, examples being spectral deconvolution or deconvolution in microscopy. When the number of spectral peaks or single emitters in imaging is limited, the solution of the deconvolution is required to be sparse, and desirable results are obtained using a penalized estimation techniques. We impose sparseness by using penalized regression with a penalty based on the L0-norm, as discussed in earlier work. Several extensions to this approach are presented. Results are demonstrated on pulse identification in endocrine data where the aim is to model the secretion pattern as a sparse series of spikes. An application in single-molecule fluorescence imaging demonstrates the algorithm when applied to two-dimensional data.