Heterogeneous questionnaires and Rényi's entropy
In this paper, we explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.
In this paper, a new class of Hierarchical Residue Number Systems (HRNSs) is proposed, where the numbers are represented as a set of residues modulo factors of 2k ± 1 and modulo 2k . The converters between the proposed HRNS and the positional binary number system can be built as 2-level structures using efficient circuits designed for the RNS (2k-1, 2k, 2k+1). This approach allows using many small moduli in arithmetic channels without large conversion overhead. The advantages resulting from the...
In finite sets with n elements, every similarity relation (or fuzzy equivalence) can be represented by an n x n-matrix S = (sij), sij ∈ [0,1], such that sii = 1 (1 ≤ i ≤ n), sij = sji for any i,j and S o S = S, where o denotes the max-min product of matrices. These matrices represent also dendograms and sets of closed balls of a finite ultrametric space (vid. [1], [2], [3]).
Every unit in the ring of the residual classes mod induces canonically an automorphism of the algebra . Let be a cyclic code, i.e. an ideal. If the numbers and are relatively prime then there exists a well-known characterization of the code . We extend this characterization to the general case.
As is known, color images are represented as multiple, channels, i.e. integer-valued functions on a discrete rectangle, corresponding to pixels on the screen. Thus, image compression, can be reduced to investigating suitable properties of such, functions. Each channel is compressed independently. We are, representing each such function by means of multi-dimensional, Haar and diamond bases so that the functions can be remembered, by their basis coefficients without loss of information. For, each...
We discuss possible algorithms for interpolating data given in a set of curves and/or points in the plane. We propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations. The Absolute Minimal Lipschitz Extension model (AMLE) is singled out and studied in more detail. We show experiments suggesting a possible application, the restoration of images with poor dynamic range. We...
Old movies suffer from various types of degradation: severe noise, blurred edges of objects (low contrast), scratches, spots, etc. Finding an efficient denoising method is one of the most important and one of the oldest problems in image sequence processing. The crucial thing in image sequences is motion. If the motion is insignificant, then any motion noncompensated method of filtering can be applied. However, if the noise is significant, then this approach gives most often unsatisfactory results....