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Nonlinear image processing and filtering: A unified approach based on vertically weighted regression

Ewaryst Rafajłowicz, Mirosław Pawlak, Angsar Steland (2008)

International Journal of Applied Mathematics and Computer Science

A class of nonparametric smoothing kernel methods for image processing and filtering that possess edge-preserving properties is examined. The proposed approach is a nonlinearly modified version of the classical nonparametric regression estimates utilizing the concept of vertical weighting. The method unifies a number of known nonlinear image filtering and denoising algorithms such as bilateral and steering kernel filters. It is shown that vertically weighted filters can be realized by a structure...

Note on an Improvement of the Griesmer Bound for q-ary Linear Codes

Hamada, Noboru, Maruta, Tatsuya (2011)

Serdica Journal of Computing

Let nq(k, d) denote the smallest value of n for which an [n, k, d]q code exists for given integers k and d with k ≥ 3, 1 ≤ d ≤ q^(k−1) and a prime or a prime power q. The purpose of this note is to show that there exists a series of the functions h3,q, h4,q, ..., hk,q such that nq(k, d) can be expressed.This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 20540129.

Notion of information and independent component analysis

Una Radojičić, Klaus Nordhausen, Hannu Oja (2020)

Applications of Mathematics

Partial orderings and measures of information for continuous univariate random variables with special roles of Gaussian and uniform distributions are discussed. The information measures and measures of non-Gaussianity including the third and fourth cumulants are generally used as projection indices in the projection pursuit approach for the independent component analysis. The connections between information, non-Gaussianity and statistical independence in the context of independent component analysis...

On a complete set of operations for factorizing codes

Clelia De Felice (2006)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

It is known that the class of factorizing codes, i.e., codes satisfying the factorization conjecture formulated by Schützenberger, is closed under two operations: the classical composition of codes and substitution of codes. A natural question which arises is whether a finite set 𝒪 of operations exists such that each factorizing code can be obtained by using the operations in 𝒪 and starting with prefix or suffix codes. 𝒪 is named here a complete set of operations (for factorizing codes). We show...

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