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- Radu Balan, Pete Casazza, Dan Edidin
- 2006

We will construct new classes of Parseval frames for a Hilbert space which allow signal reconstruction from the absolute value of the frame coefficients. As a consequence, signal reconstruction can be done without using phase or its estimation. This verifies a longstanding conjecture of the speech processing community.

The primary goal of this paper is to develop fast algorithms for signal reconstruction from magnitudes of frame coefficients. This problem is important to several areas of research in signal processing, especially speech recognition technology, as well as state tomography in quantum theory. We present linear reconstruction algorithms for tight frames… (More)

A complex frame is a collection of vectors that span C M and define measurements , called intensity measurements, on vectors in C M. In purely mathematical terms, the problem of phase retrieval is to recover a complex vector from its intensity measurements, namely the modulus of its inner product with these frame vectors. We show that any vector is uniquely… (More)

— The purpose of this note is to prove, for real frames, that signal reconstruction from the absolute value of the frame coefficients is equivalent to solution of a sparse signal optimization problem, namely a minimum p (quasi)norm over a linear constraint. This linear constraint reflects the coefficients relationship within the range of the analysis… (More)

We derive fast algorithms for doing signal reconstruction without phase. This type of problem is important in signal processing, especially speech recognition technology, and has relevance for state tomography in quantum theory. We show that a generic frame gives reconstruction from the absolute value of the frame coefficients in polynomial time. An… (More)

— The objective of this paper is the linear reconstruction of a vector, up to a unimodular constant, when all phase information is lost, meaning only the magnitudes of frame coefficients are known. Reconstruction algorithms of this type are relevant for several areas of signal communications, including wireless and fiber-optical transmissions. The… (More)

We show that there is no way to define degrees of 0-cycles on Artin stacks with proper good moduli spaces so that (i) the degree of an ordinary point is non-zero, and (ii) degrees are compatible with closed immersions. The theory of algebraic cycles on stacks is well-developed [Gil84, Vis89, EG98, Kre99]. On a proper Deligne-Mumford stack, the degree of a… (More)

In this paper we establish a surprising new identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.

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