Compressed sensing in noisy imaging environments

Compressive Sampling, or Compressed Sensing, has recently generated a tremendous amount of excitement in the image processing community. Compressive Sampling involves taking a relatively small number of non-traditional samples in the form of projections of the signal onto random basis elements or random vectors (random projections). Recent results show that such observations can contain most of the salient information in the signal. It follows that if a signal is compressible in some basis, then a very accurate reconstruction can be obtained from these observations. In many cases this reconstruction is much more accurate than is possible using an equivalent number of conventional point samples. This paper motivates the use of Compressive Sampling for imaging, presents theory predicting reconstruction error rates, and demonstrates its performance in electronic imaging with an example.