Wiener Filter on Meet/Join Lattices

Recent work introduced a framework for signal processing (SP) on meet/join lattices. Such a lattice is partially ordered and supports a meet (or join) operation that returns the greatest lower bound and the smallest upper bound of two elements, respectively. Lattices appear in various domains and can be used, for example, to express rankings in social choice theory or multisets in combinatorial auctions. Discrete lattice SP (DLSP) uses the meet operation as shift and derives associated notions of convolution and Fourier transform for signals indexed by lattices. In this paper we extend DLSP with Wiener filtering for denoising and demonstrate it on two prototypical applications.