Spread-spectrum watermarking, in which random noise is added to transform coefficients and detected with a correlation operator, has become a preferred paradigm for many watermarking applications. This paper analyzes the performance of such a watermarking system when the underlying transform is a tight frame rather than a traditional orthonormal expansion. The analysis indicates that a tight fr...

We provide a new method for constructing equiangular tight frames (ETFs). This method is valid in both the real and complex settings, and shows that many of the few previously-known examples of ETFs are but the first representatives of infinite families of such frames. The construction is extremely simple: a tensor-like combination of a Steiner system and a regular simplex. It provides great fr...

A [semi-]continuous real function of a frame (locale) L has up to now been understood as a frame homomorphism from the frame L(R) of reals into L [as a frame homomorphism (modulo some conditions) from certain subframes of L(R) into L]. Thus, these continuities involve different domains. It would be desirable if all these continuities were to have L(R) as a common domain. This paper demonstrates...

Sets of neuronal tuning curves, which describe the responses of neurons as functions of a stimulus, can serve as a basis for approximating other functions of stimulus parameters. In a function-approximating network, synaptic weights determined by a correlation-based Hebbian rule are closely related to the coefficients that result when a function is expanded in an orthogonal basis. Although neur...

This paper presents a simplified approach for the design of semi-continuous composite beams in braced frames, where specific attention is given to the effect of joint rotational stiffness. A simple composite beam model is proposed incorporating the effects of semi-rigid end connections and the non-prismatic properties of a 'cracked' steel-concrete beam. This beam model is extended to a sub-fram...

Motivated by the idea of J-frame for a Krein space K , introduced by Giribet et al. (J. I. Giribet, A. Maestripieri, F. Martnez Peŕıa, P. G. Massey, On frames for Krein spaces, J. Math. Anal. Appl. (1), 393 (2012), 122–137.), we introduce the notion of ζ − J-tight frame for a Krein space K . In this paper we characterize J-orthonormal basis for K in terms of ζ−J-Parseval frame. We show that a K...

In this paper, we obtain symmetric C∞ real-valued tight wavelet frames in L2(R) with compact support and the spectral frame approximation order. Furthermore, we present a family of symmetric compactly supported C∞ orthonormal complex wavelets in L2(R). A complete analysis of nonstationary tight wavelet frames and orthonormal wavelet bases in L2(R) is given.

We proved that for any matrix dilation and for any positive integer n, there exists a compactly supported tight wavelet frame with approximation order n. Explicit methods for construction of dual and tight wavelet frames with a given number of vanishing moments are suggested.

We show that RIP frames, tight frames satisfying the restricted isometry property, give rise to nearly tight fusion frames which are nearly orthogonal and hence are nearly equi-isoclinic. We also show how to replace parts of the RIP frame with orthonormal sets while maintaining the restricted isometry property.

Though finite tight frames arise in many applications, they have often proved difficult to understand and construct. We investigate the nonlinear problem of finding a tight frame for which the lengths of the frame elements have been prescribed in advance. Borrowing several ideas from Classical Mechanics, we show that this problem has a natural, intuitive interpretation. In particular, we show t...