33,840 research outputs found
Cell Detection by Functional Inverse Diffusion and Non-negative Group SparsityPart I: Modeling and Inverse Problems
In this two-part paper, we present a novel framework and methodology to
analyze data from certain image-based biochemical assays, e.g., ELISPOT and
Fluorospot assays. In this first part, we start by presenting a physical
partial differential equations (PDE) model up to image acquisition for these
biochemical assays. Then, we use the PDEs' Green function to derive a novel
parametrization of the acquired images. This parametrization allows us to
propose a functional optimization problem to address inverse diffusion. In
particular, we propose a non-negative group-sparsity regularized optimization
problem with the goal of localizing and characterizing the biological cells
involved in the said assays. We continue by proposing a suitable discretization
scheme that enables both the generation of synthetic data and implementable
algorithms to address inverse diffusion. We end Part I by providing a
preliminary comparison between the results of our methodology and an expert
human labeler on real data. Part II is devoted to providing an accelerated
proximal gradient algorithm to solve the proposed problem and to the empirical
validation of our methodology.Comment: published, 15 page
Jump-sparse and sparse recovery using Potts functionals
We recover jump-sparse and sparse signals from blurred incomplete data
corrupted by (possibly non-Gaussian) noise using inverse Potts energy
functionals. We obtain analytical results (existence of minimizers, complexity)
on inverse Potts functionals and provide relations to sparsity problems. We
then propose a new optimization method for these functionals which is based on
dynamic programming and the alternating direction method of multipliers (ADMM).
A series of experiments shows that the proposed method yields very satisfactory
jump-sparse and sparse reconstructions, respectively. We highlight the
capability of the method by comparing it with classical and recent approaches
such as TV minimization (jump-sparse signals), orthogonal matching pursuit,
iterative hard thresholding, and iteratively reweighted minimization
(sparse signals)
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