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arXiv · 1604.03499

Noisy 1-Bit Compressed Sensing Embeddings Enjoy a Restricted Isometry Property

Scott Spencer
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Abstract

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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Scott Spencer. 2016-04-12. Noisy 1-Bit Compressed Sensing Embeddings Enjoy a Restricted Isometry Property. https://arxiv.org/abs/1604.03499

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