Related papers: Balanced frames: a useful tool in signal processin…
We introduce and develop the concept of oblique duality for fusion frames. This concept provides a mathematical framework to deal with problems in distributed signal processing where the signals, considered as elements in a Hilbert space…
The sparse signal processing literature often uses random sensing matrices to obtain performance guarantees. Unfortunately, in the real world, sensing matrices do not always come from random processes. It is therefore desirable to evaluate…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
Frames play an important role in various practical problems related to signal and image processing. In this paper, we define computable frames in computable Hilbert spaces and obtain computable versions of some of their characterizations.…
Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We…
In information fusion, one is often confronted with the following problem: given a preexisting set of measurements about an unknown quantity, what new measurements should one collect in order to accomplish a given fusion task with optimal…
Recently, frame multipliers, pair frames, and controlled frames have been investigated to improve the numerical efficiency of iterative algorithms for inverting the frame operator and other applications of frames. In this paper, the concept…
Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded…
Operator-valued frames are natural generalization of frames that have been used in quantum computing, packets encoding, etc. In this paper, we focus on developing the theory about operator-valued frames for finite Hilbert spaces. Some…
In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly…
Weaving Hilbert space frames have been introduced recently by Bemrose et al. to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle, so we obtain new…
Finite unit norm tight frames provide Parseval-like decompositions of vectors in terms of redundant components of equal weight. They are known to be exceptionally robust against additive noise and erasures, and as such, have great potential…
We consider existence and uniqueness of symmetric approximation of frames by normalized tight frames and of symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces H . More precisely, we determine whether a given frame…
Fusion frames are extensively studied due to their effectiveness in recovering signals from large-scale data. They are applicable in distributed processing, wireless sensor networks, and packet encoding systems due to their robustness and…
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
Equiangular tight frames (ETFs) have found significant applications in signal processing and coding theory due to their robustness to noise and transmission losses. ETFs are characterized by the fact that the coherence between any two…
A frame is an overcomplete set that can represent vectors(signals) faithfully and stably. Two frames are equivalent if signals can be essentially represented in the same way, which means two frames differ by a permutation, sign change or…
Nonstationary Gabor frames, recently introduced in adaptive signal analysis, represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. Due to the lack of a…
A new notion in frame theory, so called weaving frames has been recently introduced to deal with some problems in signal processing and wireless sensor networks. Also, fusion frames are an important extension of frames, used in many areas…