Journal ArticleDOI
Reducible polynomials in more than one variable
Monson H. Hayes,James H. McClellan +1 more
- Vol. 70, Iss: 2, pp 197-198
Reads0
Chats0
TLDR
In this paper, it was shown that the set of factorable multi-dimensional polynomials is extremely small in the sense that almost all polynomials in two or more variables are irreducible.Abstract:
Polynomials in more than one variable arise frequently in multidimensional signal processing applications. Unlike polynomials in a single variable, multidimensional polynomials cannot, in general, be factored. In this note, it is shown that the set of factorable multi-dimensional polynomials is extremely small in the sense that almost all polynomials in two or more variables are irreducible.read more
Citations
More filters
Proceedings ArticleDOI
Compressive phase retrieval
TL;DR: A new algorithm is developed for the phase retrieval problem that exploits a signal's compressibility rather than its support to recover it from Fourier transform magnitude measurements.
Proceedings ArticleDOI
Recovery of sparse 1-D signals from the magnitudes of their Fourier transform
TL;DR: This work gives conditions, which when satisfied, allow unique recovery from the autocorrelation with very high probability, for one-dimensional signals, and develops two non-iterative recovery algorithms for sparse signals.
Journal ArticleDOI
STFT Phase Retrieval: Uniqueness Guarantees and Recovery Algorithms
TL;DR: This work first develops conditions under, under which the short-time Fourier transform magnitude is an almost surely unique signal representation, then considers a semidefinite relaxation-based algorithm (STliFT) and provides recovery guarantees.
Book ChapterDOI
Fourier Phase Retrieval: Uniqueness and Algorithms
TL;DR: This chapter surveys methods to guarantee uniqueness in Fourier phase retrieval and presents different algorithmic approaches to retrieve the signal in practice, and outlines some of the main open questions in this field.
Journal ArticleDOI
Sparse Phase Retrieval: Uniqueness Guarantees and Recovery Algorithms
TL;DR: It is shown that TSPR can provably recover most discrete-time sparse signals and the recovery is robust in the presence of measurement noise, and these recovery guarantees are asymptotic in nature.
References
More filters
Journal ArticleDOI
The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform
TL;DR: In this article, the phase or magnitude information alone is not sufficient, in general, to uniquely specify a sequence, however, a large class of sequences are shown to be recoverable from their phases or magnitudes.
Journal ArticleDOI
Problems and progress in multidimensional systems theory
TL;DR: The troubles and trends of research in multidimensional system theory are presented, with special emphasis in the areas of multivariable network analysis and synthesis, and multiddimensional digital filters.