SPITFIR(e): A supermaneuverable algorithm for restoring 2D-3D fluorescence images and videos,and background subtraction

While fluorescent microscopy imaging has become the spearhead of modern biology as it is able to generate long-term videos depicting 4D nanoscale cell behaviors, it is still limited by the optical aberrations and the photon budget available in the specimen and to some extend to photo-toxicity. A direct consequence is the necessity to develop flexible and "off-road" algorithms in order to recover structural details and improve spatial resolution, which is critical when pushing the illumination to the low levels in order to limit photo-damages. Moreover, as the processing of very large temporal series of images considerably slows down the analysis, special attention must be paid to the feasibility and scalability of the developed restoration algorithms. To address these specifications, we present a very flexible method designed to restore 2D-3D+Time fluorescent images and subtract undesirable out-of-focus background. We assume that the images are sparse and piece-wise smooth, and are corrupted by mixed Poisson-Gaussian noise. To recover the unknown image, we consider a novel convex and non-quadratic regularizer Sparse Hessian Variation) defined as the mixed norms which gathers image intensity and spatial second-order derivatives. This resulting restoration algorithm named SPITFIR(e) (SParse fIT for Fluorescence Image Restoration) utilizes the primal-dual optimization principle for energy minimization and can be used to process large images acquired with varied fluorescence microscopy modalities. It is nearly parameter-free as the practitioner needs only to specify the amount of desired sparsity (weak, moderate, high). Experimental results in lattice light sheet, stimulated emission depletion, multifocus microscopy, spinning disk confocal, and wide-field microscopy demonstrate the generic ability of the SPITFIR(e) algorithm to efficiently reduce noise and blur, and to subtract undesirable fluorescent background, while avoiding the emergence of deconvolution artifacts.