Random Tight Frames

Ehler, Martin

doi:10.1007/s00041-011-9182-5

Cited by 31 publications

(53 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we are concerned with a different generalization of frames called probabilistic frames. Developed in a series of papers [8,10,9], probabilistic frames are an intuitive way to generalize finite frames to the space of probability measures with finite second moment. The probabilistic setting is particularly compelling, given recent interest in probabilistic approaches to optimal coding, such as [15,20].…”

Section: Probabilistic Frames In the Wasserstein Metricmentioning

confidence: 99%

Duality and geodesics for probabilistic frames

Wickman

Okoudjou

2017

Linear Algebra and its Applications

View full text Add to dashboard Cite

Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their properties. In particular, we formulate a theory of transport duals for probabilistic frames and prove certain properties of this class. We also investigate paths of probabilistic frames, identifying conditions under which geodesic paths between two such measures are themselves probabilistic frames. In the discrete case this is related to ranks of convex combinations of matrices, while in the continuous case this is related to the continuity of the optimal transport plan.

show abstract

Section: Probabilistic Frames In the Wasserstein Metricmentioning

confidence: 99%

Duality and geodesics for probabilistic frames

Wickman

Okoudjou

2017

Linear Algebra and its Applications

View full text Add to dashboard Cite

show abstract

“…Probabilistic versions of frames have been introduced in [11,12,13]. Here, we extend the concept to nonorthogonal fusion frames.…”

Section: Random Nonorthogonal Fusion Framesmentioning

confidence: 99%

Tight and random nonorthogonal fusion frames

Cahill¹,

Casazza²,

Ehler³

et al. 2015

Trends in Harmonic Analysis and Its Applications

View full text Add to dashboard Cite

Abstract. This paper continues the investigation of nonorthogonal fusion frames started in [7]. First we show that tight nonorthogonal fusion frames a relatively easy to com by. In order to do this we need to establish a classification of how to to wire a self adjoint operator as a product of (nonorthogonal) projection operators. We also discuss the link between nonorthogonal fusion frames and positive operator valued measures, we define and study a nonorthogonal fusion frame potential, and we introduce the idea of random nonorthogonal fusion frames.

show abstract

“…Benedetto and Fickus (2003) characterized the class of finite unit norm tight frames as minimizers of a certain functional, the so-called frame potential. Ehler (2011) and Ehler and Okoudjou (2011) created probabilistic versions of the frame potential, and Ehler and Galanis (2011) showed their applicability in directional statistics. In our work, we adapt a functional from Benedetto et al (2010) by introducing a weighted mean of the frame potential and a data-fitting term.…”

Section: Introductionmentioning

confidence: 99%