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Abstract: The Grassmannian manifold \(G(k, n)\) serves as a fundamental tool in signal processing, computer vision, and machine learning, where problems often involve classifying, clustering, or comparing subspaces. In this work, we propose a sketching-based approach to approximate Grassmannian kernels using random projections.

Abstract: Representing and processing data in spherical domains presents unique challenges, primarily due to the curvature of the domain, which complicates the application of classical Euclidean techniques. Implicit neural representations (INRs) have emerged as a promising alternative for high-fidelity data representation; however, to effectively handle spherical domains, these methods must be adapted to the inherent geometry of the sphere to maintain both accuracy and stability.

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: Recently, many self-supervised learning methods for image reconstruction have been proposed that can learn from noisy data alone, bypassing the need for ground-truth references. Most existing methods cluster around two classes: i) Noise2Self and similar cross-validation methods that require very mild knowledge about the noise distribution, and ii) Stein’s Unbiased Risk Estimator (SURE) and similar approaches that assume full knowledge of the distribution.

Abstract: Dithering techniques, through the addition of a (random) signal before the Analog to Digital Converter (ADC), are widely used in acquisition chain designs for their ability to shape the quantization noise, e.

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.