Error correction with frames: the Burt-Laplacian pyramid

The study of multiresolution representations of images led to the development of the pyramid and wavelet representations. The redundancy in the pyramid representation bestows on it the properties of an error-correcting code. The error-correcting properties of the pyramids studied are a property of the representation itself and not a result of making any assumptions about the original images. The article extends the error-reduction properties of frames to an error-correcting routine. It leads to complete noise removal for sparse noise for a class of frames. The results for images using Laplacian pyramids show an additional 10-dB improvement over the previously demonstrated noise reduction for frames.