Occam filters for stochastic sources with application to digital images

An Occam filter employs lossy data compression to separate signal from noise. Previously it was shown that Occam filters are useful for filtering random noise from discrete samples of a deterministic and continuous signal. In this paper, we show that Occam filters can also be used to separate two stochastic sources, with the effectiveness of the separation depending on their relative compressibility. We then construct an Occam filter based on singular value decomposition (SVD) and apply it to digital images corrupted with Gaussian noise. We observe that the SVD-based Occam filter outperforms the wavelet-based denoising method of Donoho and Johnstone (1994) and DeVore and Lucier (1992)