  This paper is concerned with the problem of reconstructing an
infinite-dimensional signal from a limited number of linear measurements. In
particular, we show that for binary measurements (modelled with Walsh functions
and Hadamard matrices) and wavelet reconstruction the stable sampling rate is
linear. This implies that binary measurements are as efficient as Fourier
samples when using wavelets as the reconstruction space. Powerful techniques
for reconstructions include generalized sampling and its compressed versions,
as well as recent methods based on data assimilation. Common to these methods
is that the reconstruction quality depends highly on the subspace angle between
the sampling and the reconstruction space, which is dictated by the stable
sampling rate. As a result of the theory provided in this paper, these methods
can now easily use binary measurements and wavelet reconstruction bases.
