Abstract
We consider the problem of reconstructing a function from linear binary measurements. That is, the samples of the function are given by inner products with functions taking only the values 0 and 1. We consider three particular methods for this problem, the parameterized-background data-weak (PBDW) method, generalized sampling and infinite-dimensional compressed sensing. The first two methods are dependent on knowing the stable sampling rate when considering samples by Walsh function and wavelet reconstruction. We establish linearity of the stable sampling rate, which is sharp, allowing for optimal use of these methods. In addition, we provide recovery guaranties for infinite-dimensional compressed sensing with Walsh functions and wavelets.
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