rank-one projection

Abstract: Many fields of science and technology face an ever-growing accumulation of “data”, such as signals, images, video, or biomedical data volumes. As a result, many techniques and algorithms, such as principal component analysis, clustering or random projection methods, have been devised to summarize these objects in reduced representations while preserving key information in this compression.

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: 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.

Here is a new short preprint: “ROP inception: signal estimation with quadratic random sketching”, available here and on arXiv. This is the first work of Rémi Delogne, carried out in collaboration with Vincent Schellekens and me.

Abstract: Lensless endoscopy (LE) with multicore fibers (MCF) enables fluorescent imaging of biological samples at cellular scale. In this talk, we will see that under a common far-field approximation, 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: Lensless endoscopy (LE) with multicore fibers (MCF) enables fluorescent imaging of biological samples at cellular scale. In this talk, we will see that under a common far-field approximation, 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.