Related papers: Gabor fusion frames generated by difference sets
A frame is a generalization of a basis of a vector space to a redundant overspanning set whose vectors are linearly dependent. Frames find applications in signal processing and quantum information theory. We present a genetic algorithm that…
Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of…
Frame is the corner stone for designing decomposition and reconstruction operations in signal processing. Famous frames include wavelets, curvelets,and Gabor. A celebrated result indicates that if a synthesis frame is chosen for…
We propose and study the problem of distribution-preserving lossy compression. Motivated by recent advances in extreme image compression which allow to maintain artifact-free reconstructions even at very low bitrates, we propose to optimize…
In this work, we investigate the sampling and reconstruction of spectrally $s$-sparse bandlimited graph signals governed by heat diffusion processes. We propose a random space-time sampling regime, referred to as {randomized} dynamical…
Most deep learning methods that achieve high segmentation accuracy require deep network architectures that are too heavy and complex to run on embedded devices with limited storage and memory space. To address this issue, this paper…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…
Windowing a Fourier transform is a useful tool, which gives us the similarity between the signal and time frequency signal, and it allows to get sense when/where ceratin frequencies occur in the input signal, this method is introduced by…
The evolution of a complex multi-state system is often interpreted as a continuous-time Markovian process. To model the relaxation dynamics of such systems, we introduce an ensemble of random sparse matrices which can be used as generators…
We resolve a longstanding open problem by reformulating the Grassmannian fusion frames to the case of mixed dimensions and show that this satisfies the proper properties for the problem. In order to compare elements of mixed dimension, we…
For every fixed constant $\alpha > 0$, we design an algorithm for computing the $k$-sparse Walsh-Hadamard transform of an $N$-dimensional vector $x \in \mathbb{R}^N$ in time $k^{1+\alpha} (\log N)^{O(1)}$. Specifically, the algorithm is…
Rotation equivariant graph neural networks, i.e. networks designed to guarantee certain geometric relations between their inputs and outputs, yield state of the art performance on spatial deep learning tasks. They exhibit high data…
Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…
Configurations of subspaces like equichordal and equiisoclinic tight fusion frames, which are in some sense optimally spread apart and which also have reconstruction properties emulating those of orthonormal bases, are useful in various…
In this paper, we discuss the development of a sublinear sparse Fourier algorithm for high-dimensional data. In ``Adaptive Sublinear Time Fourier Algorithm" by D. Lawlor, Y. Wang and A. Christlieb (2013), an efficient algorithm with…
We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a…
The two-dimensional Gabor function is adapted to natural image statistics, leading to a tractable probabilistic generative model that can be used to model simple-cell receptive-field profiles, or generate basis functions for sparse coding…
Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in signal processing. There has been much recent work on understanding the global structure of collections of finite frames with prescribed…
This paper describes a numerical method for finding good packings in Grassmannian manifolds equipped with various metrics. This investigation also encompasses packing in projective spaces. In each case, producing a good packing is…