Applications of Gröbner bases to signal and image processing: a survey

DOI10.1016/j.laa.2004.01.008zbMath1070.94002OpenAlexW2099890072MaRDI QIDQ1888344

Zhiping Lin, Li Xu, Qinghe Wu

Publication date: 23 November 2004

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2004.01.008

zbMATH Keywords

Gröbner basesmultivariate polynomialFIR filterIIR filtermultidimensional waveletsmultidimensional filter banks

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items (10)

Multidimensional perfect reconstruction filter banks: An approach of algebraic geometry ⋮ On the reduction of multivariate quadratic systems to best rank-1 approximation of three-way tensors ⋮ The Steinberg group of a monoid ring, nilpotence, and algorithms ⋮ Exact linear modeling with polynomial coefficients ⋮ The Number of Gröbner Bases in Finite Fields (Research) ⋮ Small Gröbner fans of ideals of points ⋮ nD methods for 1D parameter-dependent systems ⋮ Common eigenvector approach to exact order reduction for Roesser state-space models of multidimensional systems ⋮ A short history of algebraic statistics ⋮ Smooth supersaturated models

Uses Software

• CoCoA
• Macaulay2
• Mathematica
• SINGULAR

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gröbner bases and multidimensional FIR multirate systems
• On explicit solutions to the Bezout equation
• New constructive methods in classical ideal theory
• Über B. Buchbergers Verfahren, Systeme algebraischer Gleichungen zu lösen
• Output feedback stabilizability and stabilization algorithms for 2D systems
• Multi-channel multi-variate equalizer design
• An algorithmic proof of Suslin's stability theorem for polynomial rings
• Notes on \(n\)-\(D\) polynomial matrix factorizations
• Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
• Multidimensional FIR filter bank design using Grobner bases
• Balanced multiwavelet bases based on symmetric FIR filters
• Feedback stabilization of multivariable two-dimensional linear systems
• Notes on n-Dimensional System Theory
• Stability and margin of stability tests for multidimensional filters
• Polynomial matrix primitive factorization over arbitrary coefficient field and related results
• SINGULAR
• Multidimensional causal, stable, perfect reconstruction filter banks
• Optimal design of synthesis filters in multidimensional perfect reconstruction FIR filter banks using Grobner bases
• On syzygy modules for polynomial matrices
• Gröbner bases and systems theory
• A constructive approach to stabilizability and stabilization of a class of \(n\)D systems
• Parametrized family of 2-D non-factorable FIR lossless systems and Gröbner bases
• Gröbner bases for problem solving in multidimensional systems
• Multi-dimensional filter banks and wavelets -- a system theoretic perspective

This page was built for publication: Applications of Gröbner bases to signal and image processing: a survey