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Linear reconstructions and the analysis of the stable sampling rate

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High quality reconstruction from a small amount of measurements is of high interest in a lot of applications, as medical imaging, lensless cameras and fluorescence microscopy. This is now feasible due to approaches as Generalized sampling and the Projected Backward Data Weak method. Both methods have in common that their performance depends highly on the angle between the sampling and the reconstruction space. In this talk we will look at the reconstruction from binary measurements modeled with Walsh functions. We will show that the relation between the dimension of the sampling and the reconstruction space only needs to be linear for the reconstruction with boundary wavelets. Additionally, we will show that for Haar wavelets we even get a sharp bound.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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