Olivier Leblanc

The emerging generation of radio-interferometric (RI) arrays are set to form images of the sky with a new regime of sensitivity and resolution. This implies a significant increase in visibility data volumes, which for single-frequency observations will scale as \( \mathcal O(Q^2B) \)for \(Q \)antennas and \(B \)short-time integration intervals (or batches), calling for efficient data dimensionality reduction techniques. This paper proposes a new approach to data compression during acquisition, coined \emphmodulated rank-one projection (MROP). MROP compresses the \(Q\times Q \)batchwise covariance matrix into a smaller number \(P \)of random rank-one projections and compresses across time by trading \(B \)for a smaller number \(M \)of random modulations of the ROP measurement vectors. Firstly, we introduce a dual perspective on the MROP acquisition, which can either be understood as random beamforming, or as a post-correlation compression. Secondly, we analyse the noise statistics of MROPs and demonstrate that the random projections induce a uniform noise level across measurements independently of the visibility-weighting scheme used. Thirdly, we propose a detailed analysis of the memory and computational cost requirements across the data acquisition and image reconstruction stages, with comparison to state-of-the-art dimensionality reduction approaches. Finally, the MROP model is validated for monochromatic intensity imaging both in simulation and from real data, with comparison to the classical and \emphbaseline-dependent averaging (BDA) models, and using the uSARA optimisation algorithm for image formation. Our results suggest that the data size necessary to preserve imaging quality using MROPs is reduced to the order of image size, well below the original and BDA data sizes.

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.