Truncation of Wavelet Matrices: Edge Effects and the Reduction of Topological Control
📜 Abstract
The abstract could not be reliably extracted. The supplied Elsevier PDF was inaccessible to the document reader, and the bibliographic records and indexed references located during verification did not reproduce the paper’s abstract. I have therefore not substituted a reconstructed or paraphrased abstract.
✨ Summary
The paper studies the boundary and edge effects introduced when wavelet matrices or transforms defined on unbounded or periodic domains are truncated to finite intervals or finite matrices. Its central contribution is the treatment of truncation as a problem involving the topology of the underlying domain, rather than merely as the removal of small matrix entries. The work is associated with methods for reducing boundary artifacts while preserving useful structural properties of wavelet representations.
Subsequent research cites the paper in connection with finite-interval wavelet constructions, including interval wavelets that avoid endpoint restrictions associated with periodic wavelets. It has also been cited in work on wavelet-based matrix sparsification and in technical patents addressing border artifacts in wavelet image compression. Later quantum-computing research references the paper as part of the literature on discrete and continuous wavelet transformations. These citations indicate influence primarily on boundary handling, finite-domain wavelet analysis, sparse matrix representations, and wavelet-based compression; the available evidence does not establish a specific commercial product directly derived from the paper. (ftp.math.utah.edu)