32 citations · 145 across the 28 of their papers we have counts for
7 papers · 1 filter
A Wavelet Plancherel Theory with Application to Multipliers and Sparse Approximations
Ron Levie, Nir Sochen
We introduce an extension of continuous wavelet theory that enables an efficient implementation of multiplicative operators in the coefficient space. In the new theory, the signal…
Uncertainty principles and optimally sparse wavelet transforms
Ron Levie, Nir Sochen
In this paper we introduce a new localization framework for wavelet transforms, such as the 1D wavelet transform and the Shearlet transform. Our goal is to design nonadaptive windo…
Group representation design of digital signals and sequences
Shamgar Gurevich, Ronny Hadani, Nir Sochen
In this survey a novel system, called the oscillator system, consisting of order of p^3 functions (signals) on the finite field F_{p}, is described and studied. The new functions a…
The discrete Fourier transform: A canonical basis of eigenfunctions
Shamgar Gurevich, Ronny Hadani, Nir Sochen
The discrete Fourier transform (DFT) is an important operator which acts on the Hilbert space of complex valued functions on the ring Z/NZ. In the case where N=p is an odd prime nu…
The finite harmonic oscillator and its applications to sequences, communication and radar
Shamgar Gurevich, Ronny Hadani, Nir Sochen
A novel system, called the oscillator system, consisting of order of p^3 functions (signals) on the finite field F_p; with p an odd prime, is described and studied. The new functio…
The finite harmonic oscillator and its associated sequences
Shamgar Gurevich, Ronny Hadani, Nir Sochen
A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication…
On some deterministic dictionaries supporting sparsity
Shamgar Gurevich, Ronny Hadani, Nir Sochen
We describe a new construction of an incoherent dictionary, referred to as the oscillator dictionary, which is based on considerations in the representation theory of finite groups…