Noisy 1-bit Compressed Sensing Embeddings Enjoy A Restricted Isometry Property

Spencer Scott. Arxiv 2016

[Paper]    
ARXIV Quantisation

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.

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