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Abstract: In numerous inverse problems, state-of-the-art solving strategies involve training neural networks from ground truth and associated measurement datasets that, however, may be expensive or impossible to collect. Recently, self-supervised learning techniques have emerged, with the major advantage of no longer requiring ground truth data.

Abstract: Random embedding techniques, such as random Fourier features, are widely used to sketch initial data to a new, kernelised feature space. In this work, we leverage a specific property of random rank-one projection operators, the sign product embedding, to approximate a quadratic polynomial kernel using the scalar product of a pair asymmetric vector embeddings, with one taking only binary values.

Abstract: Lensless illumination single-pixel imaging with a multicore fiber (MCF) is a computational imaging technique that enables potential endoscopic observations of biological samples at cellular scale. In this work, we show that this technique is tantamount to collecting multiple symmetric rank-one projections (SROP) of a Hermitian interferometric matrix – a matrix encoding the spectral content of the sample image.

Abstract: Random data sketching (or projection) is now a classical technique enabling, for instance, approximate numerical linear algebra and machine learning algorithms with reduced computational complexity and memory. In this context, the possibility of performing data processing (such as pattern detection or classification) directly in the sketched domain without accessing the original data was previously achieved for linear random sketching methods and compressive sensing.

Abstract: We propose a direct imaging method for the detection of exoplanets based on a combined low-rank plus structured sparse model. For this task, we develop a dictionary of possible effective circular trajectories a planet can take during the observation time, elements of which can be efficiently computed using rotation and convolution operation.

Abstract: Random data sketching (or projection) is now a classical technique enabling, for instance, approximate numerical linear algebra and machine learning algorithms with reduced computational complexity and memory. In this context, the possibility of performing data processing (such as pattern detection or classification) directly in the sketched domain without accessing the original data was previously achieved for linear random sketching methods and compressive sensing.

Abstract: Rank-one projections (ROP) of matrices and quadratic random sketching of signals support several data processing and machine learning methods, as well as recent imaging applications, such as phase retrieval or optical processing units.

Abstract: Lensless endoscopy (LE) with multicore fibers (MCF) enables fluorescent imaging of biological samples at cellular scale. In this work, we show that the corresponding imaging process is tantamount to collecting multiple rank-one projections (ROP) of an Hermitian interferometric matrix—a matrix encoding a subsampling of the Fourier transform of the sample image.

Abstract: Neural networks (NNs) with random weights appear in a variety of machine learning applications, perhaps most prominently as initialization of many deep learning algorithms. We take one step closer to their theoretical foundation by addressing the following data separation problem: Under what conditions can a random NN make two classes \(\mathcal X^{-}, \mathcal X^{\plus} \subset \mathbb R^{d}\) (with positive distance) linearly separable?