Algorithmic solutions toward applications of compressed sensing for optical imaging

Abstract : In the past few years, the mathematical theory of compressed sensing (CS) has emerged as a new tool in the image processing field, leading to some progress in surpassing the limits stated by the Nyquist sampling theory. In particular, the CS theory establishes that a signal (image, video, etc.) can be reconstructed from a relatively small subset of non-adaptive linear random measurements, assuming that it presents a sparse structure. As this hypothesis actually holds for a large number of natural images, several imaging applications have already benefited from this theory in various aspects. The goal of the present PhD work is to investigate how the CS theory - and more generally the ideas and methods developed in relation with sparse signal reconstruction problematics - can be used to design efficient optical sensing devices with high spatial and temporal resolution for biological imaging applications. We first investigate some practical issues related to the post-processing stage required by CS acquisition schemes, and to the selection of sampling parameters. We then examine how CS can benefit to video sampling applications. Finally, with the application of CS methods for denoising tasks in mind, we focus on the error estimation issue in image denoising problems for low-light microscopy applications.
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Yoann Le Montagner. Algorithmic solutions toward applications of compressed sensing for optical imaging. Signal and Image processing. Télécom ParisTech, 2013. English. ⟨NNT : 2013ENST0065⟩. ⟨tel-00950365v2⟩

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