Protecting wavelet lifting transforms

Wavelet transforms are the central to many applications in image processing and data compression. They have banks of multirate filters that are difficult to protect from computer-induced numerical errors. An efficient algorithm-based fault tolerance approach is proposed for detecting arithmetic errors in the output data. Concurrent weighted parity values are designed to detect the effects of a single numerical error within the transform structure. The parity calculations use weighted sums of data, where the input parity weighting is related to the weighting used on the output data. Each parity computation is properly viewed as an inner product between weighting values and the data motivating the use of dual space functionals related to the error gain matrices that describe error propagations to the output. The parity weighting values are defined by a combination of dual space functionals. An iterative procedure for evaluating the design of the parity weights has been incorporated in Matlab code.