Designing structured tight frames via an alternating projection method

By Joel A. Tropp, Inderjit S. Dhillon, Robert W. Heath, Thomas Strohmer. IEEE Transactions on Information Theory, 2005

503 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/2309802f896a7b0a66641cd247e611e211367da1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

The Undecimated Wavelet Decomposition and its Reconstruction (2007, methodology): “The alternating projection method [33] is a known technique for consistent reconstruction with frames, frame design and more generally for inverse eigenvalue problems (see survey in [34]).”
Spatially Sparse Precoding in Millimeter Wave MIMO Systems (2013, background): “Unfortunately, the complex non-convex nature of the feasible set FRF makes finding such a projection both analytically (in closed form) and algorithmically intractable [69]–[72].”
Designing Unimodular Sequence Sets With Good Correlations—Including an Application to MIMO Radar (2009, methodology): “In Section V, we present an algorithm named CAD (CA-direct) which is a more direct approach to sequence design than the CA algorithm in [9] (see also [13] and [23]).”
On the existence of equiangular tight frames (2007, background): “The symbol I indicates an identity matrix whose dimensions are determined by context.”
Optimized Projections for Compressed Sensing (2007, methodology): “This algorithm is inspired by a similar approach adopted in [ 16 ] for the design of Grassmanian frames that minimize the mutual coherence of a desired dictionary.”
THE SCHUR-HORN THEOREM FOR OPERATORS AND FRAMES WITH PRESCRIBED NORMS AND FRAME OPERATOR. (2005, background): “It is known (see [5], [19]) that, in the finite dimensional case, there is a connection between frame admissibility and the theory of majorization, in particular, the Schur-Horn theorem.”
Steiner equiangular tight frames (2010, unknown): “Other approaches are given in [11, 25, 29].”
New Algorithms for Designing Unimodular Sequences With Good Correlation Properties (2009, background): “2 and [20]), which we call CA-pruned (CAP).”
Frequency Selective Hybrid Precoding for Limited Feedback Millimeter Wave Systems (2015, background): “Indeed, this observation can also be related to the structure of the solutions of the nearest matrix and nearest tight frame problems [67], [68].”
Signal Synthesis and Receiver Design for MIMO Radar Imaging (2008, background): “In fact, because is singular in such a case, it follows that the maximum magnitude of its off-diagonal elements must be of the order or larger; consequently, the ratio between and is of the order but not smaller.”
An Introduction to Frames (2008, background): “The redundant counterpart of a basis is called a frame.1 It is generally acknowledged2 that frames were born in 1952 in the work of Duffin and Schaeffer [78].”