  The theory of sampling and the reconstruction of data has a wide range of
applications and a rich collection of techniques. For many methods a core
problem is the estimation of the number of samples needed in order to secure a
stable and accurate reconstruction. This can often be controlled by the Stable
Sampling Rate (SSR). In this paper we discuss the SSR and how it is crucial for
two key linear methods in sampling theory: generalized sampling and the
recently developed Parametrized Background Data Weak (PBDW) method. Both of
these approaches rely on estimates of the SSR in order to be accurate. In many
areas of signal and image processing binary samples are crucial and such
samples, which can be modelled by Walsh functions, are the core of our
analysis. As we show, the SSR is linear when considering binary sampling with
Walsh functions and wavelet reconstruction. Moreover, for certain wavelets it
is possible to determine the SSR exactly, allowing sharp estimates for the
performance of the methods.
