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.

本文关注从有限数量的线性测量中重建无限维信号的问题。特别是，我们表明，对于二进制测量（使用Walsh函数和Hadamard矩阵建模）和小波重构，稳定的采样率是线性的。这意味着当使用小波作为重构空间时，二进制测量与傅立叶采样一样有效。强大的重构技术包括广义采样及其压缩版本，以及基于数据同化的最新方法。这些方法的共同点在于，重建质量在很大程度上取决于采样和重建空间之间的子空间角度，这取决于稳定的采样率。根据本文提供的理论，