Compressive and neural-representation strategies for inverse problems From interferometric imaging to diffraction tomography
(2024)
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- Authors
- Supervisors
- Jacques, Laurent
- Abstract
- Computational imaging has revolutionized our capabilities to sense the environment, enabling a wide range of applications in domains like medical, biological, or radio-astronomical imaging. This thesis broadens the scope of the computational imaging framework in two main directions. First, the principle of compressive imaging---i.e. capturing the image information with few linear projections data---is applied to two interferometric imaging applications, namely multicore fiber lensless imaging and radio-interferometry. In both cases, it is shown that compressive imaging is possible with random projections applied at the level of the interfering elements, resulting in a linear sensing model involving Fourier subsampling and rank-one projections. In addition to the analysis of their computational complexities, the sensing models are accompanied by uniform recovery guarantees highlighting their sample complexities---the number of interfering elements and number of measurements required for image recovery. The theoretical sample complexities are confirmed numerically, and also experimentally for multicore fiber imaging. Second, contributions are brought to the field of diffraction tomography, proposing a combination of an implicit neural representation---a continuous image representation by a neural network---and a nonlinear (multiple-scattering) sensing model. Significant efforts are made in a review of the different ways to model electromagnetic wave diffraction through inhomogeneous media, leveraging first-order optimization methods to solve the subsequent linear system of equations. The reconstruction of the 3-D image through the weights of an implicit neural representation instead of discrete voxels is proposed for this nonlinear sensing model, demonstrating the benefit of (i) the nonlinearity over linear approximations of the model, and (ii) the continuous representation for handling rotations of the object. The drawbacks of the approach are highlighted and improvements necessary for experimental use are discussed.
- Affiliations
UCLouvain SST/ICTM/INMA - Pôle en ingénierie mathématique
Citations
Leblanc, O. (2024). Compressive and neural-representation strategies for inverse problems From interferometric imaging to diffraction tomography. https://hdl.handle.net/2078.5/233544