Related papers: Sparsity and spectral properties of dual frames
There are two notions of sparsity associated to a frame $\Psi=(\psi_i)_{i\in I}$: Analysis sparsity of $f$ means that the analysis coefficients $(\langle f,\psi_i\rangle)_i$ are sparse, while synthesis sparsity means that $f=\sum_i…
Spectral tetris is a fexible and elementary method to construct unit norm frames with a given frame operator, having all of its eigenvalues greater than or equal to two. One important application of spectral tetris is the construction of…
In this survey paper we review classical results and recent progress about a certain topic in the spectral theory of two-dimensional canonical systems. Namely, we consider the questions whether the spectrum $\sigma$ is discrete, and if it…
Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, coupling for each microring…
We develop the theory of frames and Parseval frames for finite-dimensional vector spaces over the binary numbers. This includes characterizations which are similar to frames and Parseval frames for real or complex Hilbert spaces, and the…
The spectral densities of ensembles of non-Hermitian sparse random matrices are analysed using the cavity method. We present a set of equations from which the spectral density of a given ensemble can be efficiently and exactly calculated.…
Many emerging applications involve sparse signals, and their processing is a subject of active research. We desire a large class of sensing matrices which allow the user to discern important properties of the measured sparse signal. Of…
This paper investigates regularity properties of two non-negative sparsity sets: non-negative sparse vectors, and low-rank positive semi-definite matrices. Novel formulae for their Mordukhovich normal cones are given and used to formulate…
A discrete frame for $L^2({\mathbb R}^d)$ is a countable sequence $\{e_j\}_{j\in J}$ in $L^2({\mathbb R}^d)$ together with real constants $0<A\leq B< \infty$ such that $$ A\|f\|_2^2 \leq \sum_{j\in J}|\langle f,e_j \rangle |^2 \leq…
We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…
Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low…
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.…
A large number of image super resolution algorithms based on the sparse coding are proposed, and some algorithms realize the multi-frame super resolution. In multi-frame super resolution based on the sparse coding, both accurate image…
We present a deep model that can accurately produce dense depth maps given an RGB image with known depth at a very sparse set of pixels. The model works simultaneously for both indoor/outdoor scenes and produces state-of-the-art dense depth…
Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…
Spectral variability is one of the major issue when conducting hyperspectral unmixing. Within a given image composed of some elementary materials (herein referred to as endmember classes), the spectral signature characterizing these classes…
We introduce and analyze the concept of space-spectrum uncertainty for certain commonly-used designs for spectrally programmable cameras. Our key finding states that, it is impossible to simultaneously capture high-resolution spatial images…
The purpose of this note is to establish a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for compressed sensing. For fulfilling D-RIP, the constant $\delta_k$ is used in the definition: $(1…
We study a uniform version of the strong diameter two property. In particular, we find a characterisation that does not involve ultrafilters and we use it to provide some examples of spaces with this uniform property that do not follow from…
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…