Noisy 1-Bit Compressed Sensing Embeddings Enjoy a Restricted Isometry   Property
  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. 
Scott Spencer
math.CA cs.IT math.IT