scholarly journals Compactly Supported Curvelet-Type Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Kenneth N. Rasmussen ◽  
Morten Nielsen
Keyword(s):  
Sparse Representation ◽  
Compact Support ◽  
Type Systems ◽  
Linear Combinations ◽  
Smooth Functions ◽  
Constructive Description ◽  
Compactly Supported ◽  
Single Function ◽  
Type Spaces ◽  
Finite Linear

We study a flexible method for constructing curvelet-type frames. These curvelet-type systems have the same sparse representation properties as curvelets for appropriate classes of smooth functions, and the flexibility of the method allows us to give a constructive description of how to construct curvelet-type systems with a prescribed nature such as compact support in direct space. The method consists of using the machinery of almost diagonal matrices to show that a system of curvelet molecules which is sufficiently close to curvelets constitutes a frame for curvelet-type spaces. Such a system of curvelet molecules can then be constructed using finite linear combinations of shifts and dilates of a single function with sufficient smoothness and decay.

Study on Over-Complete Dictionaries for Sparse Representations of Signals

2012 ◽  
Vol 157-158 ◽  
pp. 796-799
Author(s):  
Guang Chun Gao ◽  
Kai Xiong ◽  
Li Na Shang ◽  
Sheng Ying Zhao ◽  
Cui Zhang
Keyword(s):  
Inverse Problems ◽  
Compressed Sensing ◽  
Sparse Representation ◽  
Sparse Representations ◽  
Experimental Results ◽  
Decomposition Algorithm ◽  
Linear Combinations ◽  
Design Algorithm ◽  
Sparse Decomposition

In recent years there has been a growing interest in the study of sparse representation of signals. The redundancy of over-complete dictionary can make it effectively capture the characteristics of the signals. Using an over-complete dictionary that contains prototype signal-atoms, signals are described as linear combinations of a few of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, Compressed Sensing (CS), and more. Recent activities in this field concentrate mainly on the study of sparse decomposition algorithm and dictionary design algorithm. In this paper, we discuss the advantages of sparse dictionaries, and present the implicit dictionaries for signal sparse presents. The overcomplete dictionaries which combined the different orthonormal transform bases can be used for the compressed sensing. Experimental results demonstrate the effectivity for sparse presents of signals.

Multi-particle Spaces

2020 ◽  
pp. 187-200
Author(s):  
Daniel Canarutto
Keyword(s):  
Operator Algebra ◽  
Particle Physics ◽  
Arbitrary Number ◽  
Exterior Algebra ◽  
Linear Combinations ◽  
Absorption And Emission ◽  
Dirac Type ◽  
Natural Generalisation ◽  
Finite Linear ◽  
Number Of Particles

The fundamental algebraic notions needed in many-particle physics are exposed. Spaces of free states containing an arbitrary number of particles of many types are introduced. The operator algebra generated by absorption and emission operators is studied as a natural generalisation of standard exterior algebra. The link between the discrete and the distributional formalisms is provided by the spaces of finite linear combinations of semi-densities of Dirac type.

scholarly journals Generalized weighted Besov spaces on the Bessel hypergroup

2006 ◽  
Vol 4 (1) ◽  
pp. 91-111
Author(s):  
Miloud Assal ◽  
Hacen Ben Abdallah
Keyword(s):  
Besov Spaces ◽  
Generalized Convolution ◽  
Smooth Functions ◽  
General Properties ◽  
Generalized Translation ◽  
Discrete Norm ◽  
Type Spaces ◽  
Translation Operators ◽  
Weighted Besov Spaces ◽  
Besov Type Spaces

In this paper we study generalized weighted Besov type spaces on the Bessel-Kingman hypergroup. We give different characterizations of these spaces in terms of generalized convolution with a kind of smooth functions and by means of generalized translation operators. Also a discrete norm is given to obtain more general properties on these spaces.

Fractional derivatives of multidimensional Colombeau generalized stochastic processes

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Danijela Rajter-Ćirić ◽  
Mirjana Stojanović
Keyword(s):  
Stochastic Process ◽  
Fractional Derivative ◽  
Stochastic Processes ◽  
Compact Support ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
One Dimensional ◽  
Compactly Supported ◽  
Derivatives Of ◽  
Do So

AbstractWe consider fractional derivatives of a Colombeau generalized stochastic process G defined on ℝn. We first introduce the Caputo fractional derivative of a one-dimensional Colombeau generalized stochastic process and then generalize the procedure to the Caputo partial fractional derivatives of a multidimensional Colombeau generalized stochastic process. To do so, the Colombeau generalized stochastic process G has to have a compact support. We prove that an arbitrary Caputo partial fractional derivative of a compactly supported Colombeau generalized stochastic process is a Colombeau generalized stochastic process itself, but not necessarily with a compact support.

scholarly journals On the weakly-* dense subsets in $L^{\infty}(\Omega)$

2021 ◽  
Vol 16 ◽  
pp. 149
Author(s):  
P.I. Kogut ◽  
T.N. Rudyanova
Keyword(s):  
Weak Convergence ◽  
Density Property ◽  
Smooth Functions ◽  
Compactly Supported

In this paper we study the density property of the compactly supported smooth functions in the space $L^{\infty}(\Omega)$. We show that this set is dense with respect to the weak-* convergence in variable spaces.

scholarly journals Stefan–Sussmann singular foliations, singular subalgebroids and their associated sheaves

2016 ◽  
Vol 13 (Supp. 1) ◽  
pp. 1641001 ◽  
Author(s):  
Iakovos Androulidakis ◽  
Marco Zambon
Keyword(s):  
Compact Support ◽  
Tangent Bundle ◽  
Explicit Description ◽  
Lie Algebroid ◽  
Support Condition ◽  
Singular Foliation ◽  
Compactly Supported ◽  
Singular Foliations ◽  
Equivalent Characterization

We explain and motivate Stefan–Sussmann singular foliations, and by replacing the tangent bundle of a manifold with an arbitrary Lie algebroid, we introduce singular subalgebroids. Both notions are defined using compactly supported sections. The main results of this note are an equivalent characterization, in which the compact support condition is removed, and an explicit description of the sheaf associated to any Stefan–Sussmann singular foliation or singular subalgebroid.

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