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Assume that an unknown integral operator living in some known subspace is observed indirectly, by evaluating its action on a discrete measure containing a few isolated Dirac masses at an unknown location. Is this information enough to recover the impulse response location and the operator with a sub-pixel accuracy? We study this question and bring to light key geometrical quantities for exact and stable recovery. We also propose an in-depth study of the presence of additive white Gaussian noise. We illustrate the well-foundedness of this theory on the challenging optical imaging problem of blind deconvolution and blind deblurring with non-stationary operators. [ABSTRACT FROM AUTHOR]

Measuring attenuation coefficients is a fundamental problem that can be solved with diverse techniques such as X-ray or optical tomography and lidar. We propose a novel approach based on the observation of a sample from a few different angles. This principle can be used in existing devices such as lidar or various types of fluorescence microscopes. It is based on the resolution of a nonlinear inverse problem. We propose a specific computational approach to solve it and show the well-foundedness of the approach on simulated data. Some of the tools developed are of independent interest. In particular, we propose an efficient method to correct attenuation defects, new robust solvers for the lidar equation as well as new efficient algorithms to compute the proximal operator of the logsumexp function in dimension 2. [ABSTRACT FROM AUTHOR]

The Graetz problem is a convection-diffusion equation in a pipe invariant along a direction. The contribution of the present work is to propose a mathematical analysis of the Neumann, Robin, and periodic boundary condition on the boundary of a semi-infinite pipe. The solution in the 3D space of the original problem is reduced to eigenproblems in the 2D section of the pipe. The set of solutions is described, its structure depending on the type of boundary condition and on the sign of the total flow of the fluid. This analysis is the cornerstone of numerical methods to solve the Graetz problem in finite pipes, semi-infinite pipes, and exchangers of arbitrary cross-section. Numerical test cases illustrate the capabilities of these methods to provide solutions in various configurations. [ABSTRACT FROM AUTHOR]