Comparisons of Linear and nonlinear pyramid schemes for signal and image processing

Linear filters banks are being used extensively in image and video applications. New research results in wavelet applications for compression and de-noising are constantly appearing in the technical literature. On the other hand, non-linear filter banks are also being used regularly in image pyramid algorithms. There are some inherent advantages in using non-linear filters [1] instead of linear filters when non-Gaussian processes are present in images. However, a consistent way of comparing performance criteria between these two schemes has not been fully developed yet. In this paper a recently discovered tool, sample selection probabilities [16], is used to compare the behavior of linear and non-linear filters. In [16] the conversion from weights of order statistics (OS) filters to coefficients of the impulse response is obtained through these probabilities. However, the reverse problem: the conversion from coefficients of the impulse response to the weights of OS filters is not yet fully understood. One of the reasons for this diffculty is the highly non-linear nature of the partitions and generating function used in [16]. In the present paper the problem is posed as an optimization of integer linear programming subject to constraints directly obtained from the coefficients of the impulse response. Although the technique to be presented is not completely refined, it certainly appears to be promising. Some results will be shown.