Fast spatially variant deconvolution for optical microscopy via iterative shrinkage thresholding

Deconvolution offers an effective way to improve the resolution of optical microscopy data. While fast algorithms are available when the point spread function (PSF) is shift-invariant (SI), they are not directly applicable in thick samples, where the problem is shift-variant (SV). Here, we propose a fast iterative shrinkage/thresholding 3D deconvolution method that uses different PSFs at every depth. This is realized by modeling the imaging system as a multi-rate filter-bank, with each channel corresponding to a distinct 3D PSF dependent on the position along the optical axis. The complexity associated with the thresholded Landweber update in each iteration of our SV algorithm is equivalent to that of an iteration in an SI algorithm, multiplied by the number of channels in the filter-bank. We simulated images of a set of beads embedded in an aqueous gel, using varying PSFs along the optical axis, to illustrate the effectiveness of our algorithm.