We construct Shannon-like Parseval frame wavelets on a class of non commutative two-step nilpotent Lie groups. Our work was inspired by a construction given by Azita Mayeli on the Heisenberg group. The tools used here are representation theoretic. However, a great deal of Gabor theory is used for the construction of the wavelets. The construction obtained here is very explicit, and we are even ...

A reproducing system is a countable collection of functions {φj : j ∈ J } such that a general function f can be decomposed as f = ∑ j∈J cj(f) φj , with some control on the analyzing coefficients cj(f). Several such systems have been introduced very successfully in mathematics and its applications. We present a unified viewpoint to the study of reproducing systems on locally compact abelian grou...

This paper presents a new low computational power compression/decompression algorithm for very low bit-rate video-stream integrated on a standard architecture for domotic sensor network based on the IEEE 1451 standards. The proposed method uses frame theory elements and the greedy Matching Pursuit algorithm in order to identify a 2D Gabor sub-dictionary able to compress information included in ...

We study the efficient numerical solution of infinite matrix equations Au = f for a matrix A in the Jaffard algebra. These matrices appear naturally via frame discretizations in many applications such as Gabor analysis, sampling theory, and quasi-diagonalization of pseudo-differential operators in the weighted Sjöstrand class. The proposed algorithm has two main features: firstly, it converges ...

  Introduction: The process of discriminating among benign and malignant hyperplasia begun with subjective methods using light microscopy and is now being continued with computerized morphometrical analysis requiring some features. One of the main features called Volume Percentage of Stroma (VPS) is obtained by calculating the percentage of stroma texture. Currently, this feature is calculated ...

Abstract In this work, we analyze Gabor frames for the Weyl--Heisenberg group and wavelet extended affine group. Firstly, give necessary sufficient conditions existence of nonstationary translates. Using these conditions, prove from We present a representation functions in closure linear span frame sequence terms Fourier transform window functions. show that canonical dual translates has same s...

Recognizing places using Lidar in large-scale environments is challenging due to the sparse nature of point cloud data. In this letter we present BVMatch, a Lidar-based frame-to-frame place recognition framework, that capable estimating 2D relative poses. Based on assumption ground area can be approximated as plane, uniformly discretize into grids and project 3D scans bird's-eye view (BV) image...

In this paper, we first prove the metric approximation property for weighted mixed-norm L (p1,...,pn) w spaces. Using Gabor frame representation, this implies that the same property holds in weighted modulation and Wiener amalgam spaces. As a consequence, Grothendieck’s theory becomes applicable, and we give criteria for nuclearity and r-nuclearity for operators acting on these spaces as well a...

We give a program describing the pervasiveness of the short-time Fourier transform (STFT) in a host of topics including the following: waveform design and optimal ambiguity function behavior for radar and communications applications; vector-valued ambiguity function theory for multi-sensor environments; finite Gabor frames for deterministic compressive sensing and as a background for the HRT co...