Frames, bases, and group representations

By Deguang Han, D. Larson. 2000

623 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/e956e4a38b4d5f2c2d0c1514b2a5746f4f475787

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

G-FRAMES AND STABILITY OF G-FRAMES IN HILBERT SPACES (2008, background): “FAROUGHI, AND ASGHAR RAHIMI Han and Larson in [10] have proved that for any Parseval frame {fi}i∈I for a Hilbert space H there is a Hilbert space H ⊆ K and an orthonormal basis {ei}i∈I for K such that Pei = fi, for all i ∈ I, where P is the orthogonal projection of K onto H.”
On signal reconstruction without phase (2006, background): “It is known that two frames are equivalent if and only if their associated analysis operators have the same range (see [2,12]).”
Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(Rd) (2004, methodology): “ characteristic function of the set is a wavelet. Wavelet sets, frame wavelet sets and methods for constructing such sets have been studied recently [BMM99], [BL99], [BL01], [BS03], [DLS97], [DLS98], [HL00] [Ola03], [OS03]. Our methods give constructions of wavelet sets with translations on irregula”
Ellipsoidal tight frames and projection decompositions of operators (2003, background): “References in the study of frames include [4], [8], and [9].”
Symmetric informationally complete quantum measurements (2003, methodology): “We note in passing that using this group to find a SIC-POVM makes P a Gabor or Weyl-Heisenberg frame, this being the definition of such a frame [24]; such a SIC-POVM P is useful in defining finite-dimensional analogs of the familiar P and Q quasidistributions of infinite dimensions.”
Operator-valued frames (2007, methodology): “Some papers dealing with infinite frames which relate directly or indirectly to this article are [15, 13, 9, 2, 10, 20, 19, 21].”
FRAME REPRESENTATIONS FOR GROUP-LIKE UNITARY OPERATOR SYSTEMS (2003, background): “We can also consider the direct sum representations of a group-like unitary system which are related to the concept of strongly disjoint frames introduced in [10] (or, equivalently, to the concept of orthogonal multiframes introduced by R.”
A module frame concept for Hilbert C*-modules (2000, methodology): “Larson in [11] and by investigations by M.”