Error correction in images using overcomplete pyramid representations
Subrata Rakshit, Charles H. Anderson · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
The Burt pyramid was developed as a means of decomposing images into multiscale representations. Unlike the wavelet transforms, which are complete orthonormal transformations, the pyramid transforms are overcomplete like frames. In addition, the Burt pyramid has an exact reconstruction rule. This paper first examines the consequences of that redundancy and exact reconstruction. Even though the pyramids are not strictly frames, the pyramids are characterized in much the same way as frames. The issue of error detection is addressed next, followed by the development of an error correction algorithm. This leads to a 10 dB noise reduction in addition to the reduction inherent to reconstruction of frames. Examples are given to show the performance for different types of noise.