In this paper, we formally connect between vector median lters, morphological operators, and geometric partial diierential equations. Considering a lexicographic order, which permits to deene an order between vectors in IR N , we rst show that the vector median lter of a vector-valued image is equivalent to a collection of innmum-supremum morphological operations. We then proceed and study the ...

Assuming an auto regressive (AR) lter model driven by a non-Gaussian white noise we formulate a general parameter estimation problem. A maximum likelihood solution gives an AR estimate of the l-ter and the probability distribution function parameters for non-Gaussian input. The proposed method is optimal in the information theoretic sense, giving the most probable model for the source and lter ...

This paper presents a V olterra function based lter as the receiver for a direct-sequence-code-division-multiplex-access (DS-CDMA) system. The envisaged application would be cellular telephony, where the receiver will be required to be adaptive due to channel eeects. The results obtained from the V olterra l-ter are compared against the linear minimum-mean-square-error (MMSE) lter and the nonli...

We study the lter L (A) of computably enumerable supersets (modulo nite sets) of an r-maximal set A and show that, for some such set A, the property of being co nite in L (A) is still 0 3 -complete. This implies that for this A, there is no uniformly computably enumerable \tower" of sets exhausting exactly the coin nite sets in L (A).

This tutorial reviews the theory, structure and design methods for M-channel perfect-reconstruction (PR) lter banks. Some of the lter banks being considered here are the two-channel orthogonal lter bank; biorthogonal linear-phase lter banks; M-channel cosine-modulated lter banks and M-channel linear-phase lter banks. The connection with wavelet transform will be elaborated on the case of discre...

This paper puts forth the notion that explicitly speciied transition bands have been introduced in the lter design literature in part as an indirect approach for dealing with discontinu-ities in the desired frequency response. We suggest that the use of explicitly speciied transition bands is sometimes inappropriate because, to satisfy a meaningful optimality criterion, their use implicitly ass...

Abduction is an inference mechanism where given a knowledge base and some observations , the reasoner tries to nd hypotheses which together with the knowledge base explain the observations. A reasoning based on such an inference mechanism is referred to as abductive reasoning. Given a theory and some observations, by l-tering the theory with the observations, we mean selecting only those models...

In multirate digital signal processing, we often encounter decimators, interpolators and complicated interconnections of these with LTI lters. We also encounter cyclo-wide-sense stationary (CWSS) processes and linear periodically time-varying (LPTV) systems. It is often necessary to understand the effects of multirate systems on the statistical properties of their input signals. Some of these i...

Roger L. Claypoole, Jr. and Richard G. Baraniuk, Rice University Summary We introduce and discuss biorthogonal wavelet transforms using the lifting construction. The lifting construction exploits a spatial{domain, prediction{error interpretation of the wavelet transform and provides a powerful framework for designing customized transforms. We discuss the application of lifting to adaptive and n...