  We investigate the sign-linear embeddings of 1-bit compressed sensing given
by Gaussian measurements. One can give short arguments concerning a Restricted
Isometry Property of such maps using Vapnik-Chervonenkis dimension of sparse
hemispheres. This approach has a natural extension to the presence of additive
white noise prior to quantization. Noisy one-bit mappings are shown to satisfy
an RIP when the metric on the sphere is given by the noise.
