A fast homotopy algorithm for gridless sparse recovery

In this paper, we study the solving of gridless sparse optimization problem and its application to 3D image deconvolution. Based on recent works (Denoyelle et al, 2019) introducing Sliding Frank-Wolfe algorithm solve Beurling LASSO problem, introduce an accelerated algorithm, denoted BSFW, that preserves convergence properties, while removing most costly local descents. Besides, as BLASSO still relies a regularization parameter, homotopy constrained allows use more practical parameter based residual, e.g. standard deviation. Both algorithms benefit from finite termination property, i.e. they are guaranteed find solution in number step under mild conditions. These methods then applied tomographic diffractive microscopy images, with purpose explaining by small atoms convolved images. Numerical results synthetic real images illustrates improvement provided BSFW method, method their combination.