A mathematical framework for data representation and for noise reduction is presented in this paper. The basis of the approach lies in the use of wavelets derived from the general theory of frames to construct a subspace capable of representing the original signal excluding the noise. The representation subspace is shown to be efficient in signal modeling and noise reduction, but it may be acco...

The efficient Semantic Web, needs knowledge to be presented in a well defined form which enables people and software agents to understand it. There are many knowledge representation techniques such as rules, frames, scripts, semantic network and ontology. The purpose of this paper is to illustrate the difference between semantic network and ontology techniques for medical knowledge representati...

Localizing tactile stimuli on our body requires sensory information to be represented in multiple frames of reference along the sensory pathways. These reference frames include the representation of sensory information in skin coordinates, in which the spatial relationship of skin regions is maintained. The organization of the primary somatosensory cortex matches such somatotopic reference fram...

Finite normalized tight frames are interesting because they provide decompositions in applications and some physical interpretations. In this article, we give a recursive method for constructing them.

‎In this paper‎, ‎by using the sequence of multipliers‎, ‎we introduce frames with algebraic bounds in Hilbert pro-$ C^* $-modules‎. ‎We investigate the relations between frames and $ ast $-frames‎. ‎Some properties of $ ast $-frames in Hilbert pro-$ C^* $-modules are studied‎. ‎Also‎, ‎we show that there exist two differences between $ ast $-frames in Hilbert pro-$ C^* $-modules and Hilbert $ ...

we give some new results on sparse signal recovery in the presence of noise, forweighted spaces. traditionally, were used dictionaries that have the norm equal to 1, but, forrandom dictionaries this condition is rarely satis ed. moreover, we give better estimationsthen the ones given recently by cai, wang and xu.

In this paper we study the duality of Bessel and g-Bessel sequences in Hilbert spaces. We show that a Bessel sequence is an inner summand of a frame and the sum of any Bessel sequence with Bessel bound less than one with a Parseval frame is a frame. Next we develop this results to the g-frame situation.