The geometry and topology of the region in which a director field is embedded impose limitations on kind supported orientational order. These manifest as compatibility conditions that relate quantities describing to embedding space. For example, two dimensions (2D) splay bend fields suffice determine uniquely (up rigid motions) must comply with one relation linear Gaussian curvature manifold. I...

An efficient compression algorithm for multi-view video sequences, which are captured by two-dimensional (2D) camera arrays, is proposed in this work. First, we propose a novel prediction structure, called three-dimensional hierarchical B prediction (3DHBP), which can efficiently reduce horizontal inter-view redundancies, vertical inter-view redundancies, and temporal redundancies in multi-view...

Oversampled filter banks can be used to enhance resilience to erasures in communication systems in much the same way that finite-dimensional frames have previously been applied. This paper extends previous finite dimensional treatments to frames and signals in l2(Z) with frame expansions that can be implemented efficiently with filter banks. It is shown that tight frames attain best performance...

Gabor frames have been extensively studied in time-frequency analysis over the last 30 years. They are commonly used in science and engineering to synthesize signals from, or to decompose signals into, building blocks which are localized in time and frequency. This chapter contains a basic and self-contained introduction to Gabor frames on finite-dimensional complex vector spaces. In this setti...

Grassmannian frames are frames satisfying a minmax correlation criterion. We translate a geometrically intuitive approach for two and three dimensional Euclidean space (R and R ) into a new analytic method which is used to classify many Grassmannian frames in this setting. The method and associated algorithm decrease the maximum frame correlation, and hence give rise to the construction of spec...

The primary goal of this paper is to develop fast algorithms for signal reconstruction from magnitudes of frame coefficients. This problem is important to several areas of research in signal processing, especially speech recognition technology, as well as state tomography in quantum theory. We present linear reconstruction algorithms for tight frames associated with projective 2-designs in fini...

the generalization of p-frame in banach spaces is considered in this paper. the concepts of an $tilde{x}$-frame and a system conjugate to $tilde{x}$-frame were introduced. analogues of the results on the existence of conjugate system were obtained. the stability of $tilde{x}$-frame having a conjugate system is studied.