In many applications (e.g., widefield microscopy), image deconvolution can be used to improve the resolution of the 2D and 3D acquisitions. This inverse problem requires some prior knowledge on the original image. In variational methods, this prior knowledge corresponds to regularization constraints that are often expressed as a total-variation (TV) functional. The TV term corresponds to the L1-norm of the gradient of the solution (integral of the gradient norm). In this project, we want to use other operators inside the same L1-norm. In particular, we wish to study the properties of L1-Laplacian regularization for 3D deconvolution, and its advantages for some class of images. Applications on biomedical data are to be considered, and the results shall be compared with state-of-the-art methods (L2 and TV regularization). A fast algorithm (e.g., using the FISTA method) will be derived and coded as an imageJ plugin. The animated picture on the right illustrates the power of 3D deconvolution; taken from: "A Fast Multilevel Algorithm for Wavelet-Regularized Image Restoration", Cédric Vonesch and Michael Unser. Requisites : courses in signal/image processing, interest for algorithmic methods and general knowledge in programming (MATLAB and/or Java).