Seminar Details
2023-02-21 (14h) : Interferometric Lensless Imaging: Rank-one Projections of Image Frequencies with Speckle Illuminations
At Euler building(room a.002)
Organized by Mathematical Engineering
Speaker :
Leblanc, Olivier
Abstract :
Lensless endoscopy with multicore fibers (MCF) is a technology that enables fluorescent imaging of biological samples at cellular scale.
In this talk, I will show that under a common far-field approximation, the corresponding speckle imaging process is tantamount to collecting multiple symmetric rank-one projections (SROP) of an Hermitian interferometric matrix---a matrix encoding a subsampling of the Fourier transform of the sample image. Specifically, each SROP of this matrix is achieved with the complex vector shaping the incident wavefront using a spatial light modulator (SLM), and, for specific MCF core arrangements, the interferometric matrix collects as many image frequencies as the square of the core number. Configuring the SLM randomly allows us to characterize the sample complexity of the system through a two-component sensing perspective.
In particular, by inspecting the separate dimensional conditions ensuring the specific restricted isometry properties of the two composing sensing models in the observation of sparse images, we show that a basis pursuit denoising (BPDN) program associated with an L1-fidelity cost provably provides a stable and robust image estimate. In parallel, numerical and experimental reconstruction results demonstrate the effectiveness of this imaging procedure for a TV-penalized formulation of the inverse problem.