The Wiener filter is analyzed for stationary complex Gaussian signals from an information-theoretic point of view. A dual-port analysis of the Wiener filter leads to a decomposition based on orthogonal projections and results in a new multistage method for implementing the Wiener filter using a nested chain of scalar Wiener filters. This new representation of the Wiener filter provides the capa...

Wiener filter is widely used for image denoising and restoration. It is alternatively known as the minimum mean square error filter or the least square error filter, since the objective function used in Wiener filter is an age-old benchmark called the Mean Square Error (MSE). Wiener filter tries to approximate the degraded image so that its objective function is optimized. Although MSE is consi...

Wiener would have been extremely gratified had he known that the American Mathematical Society would honor him in death with an issue of the Bulletin. He had had a failing heart for many years and death had come to hold no fear for him, but the possibility of lack of esteem by his colleagues was most painful to him. Unfortunately Wiener did have grave doubts all of his professional life as to w...

the padmakar-ivan (pi) index is a first-generation topological index (ti) based on sums overall edges between numbers of edges closer to one endpoint and numbers of edges closer to theother endpoint. edges at equal distances from the two endpoints are ignored. an analogousdefinition is valid for the wiener index w, with the difference that sums are replaced byproducts. a few other tis are discu...

Drugs and other chemical compounds are often modeled as polygonal shapes, where each vertex represents an atom of the molecule, and covalent bonds between atoms are represented by edges between the corresponding vertices. This polygonal shape derived from a chemical compound is often called its molecular graph, and can be a path, a tree, or in general a graph. An indicator defined over this mol...

Robust Implementations of the Multistage Wiener Filter By John David Hiemstra The research in this dissertation addresses reduced rank adaptive signal processing, with specific emphasis on the multistage Wiener filter (MWF). The MWF is a generalization of the classical Wiener filter that performs a stage-by-stage decomposition based on orthogonal projections. Truncation of this decomposition pr...

The Padmakar-Ivan (PI) index is a first-generation topological index (TI) based on sums over all edges between numbers of edges closer to one endpoint and numbers of edges closer to the other endpoint. Edges at equal distances from the two endpoints are ignored. An analogous definition is valid for the Wiener index W, with the difference that sums are replaced by products. A few other TIs are d...

It is well known that the vertices of any graph can be put in a linear preorder so that for random walk on the graph vertices appearing earlier in the preorder are “easier to reach but more difficult to get out of”. We exhibit further such preorders corresponding to various functions related to random walk and study their relationships. These preorders coincide when the graph is a tree, but not...

In this paper, we give solutions for the two conjectures on the inverse problem of the Wiener index of peptoids proposed by Goldman et al. We give the first conjecture a positive proof and the second conjecture a negative answer.

The Wiener index of a connected graph is the sum of all pairwise distances of vertices of the graph. In this paper, we consider the Wiener indices of trees with perfect matchings, characterizing the eight trees with smallest Wiener indices among all trees of order 2 ( 11) m m with perfect matchings.