Pseudoframes for subspaces have been recently introduced by S. Li and H. Ogawa as a tool to analyze lower dimensional data with arbitrary flexibility of both the analyzing and the dual sequence. In this paper we study Gabor pseudoframes for affine subspaces by focusing on geometrical properties of their associated sets of parameters. We first introduce a new notion of Beurling dimension for dis...

This paper presents GRASTA (Grassmannian Robust Adaptive Subspace Tracking Algorithm), an efficient and robust online algorithm for tracking subspaces from highly incomplete information. The algorithm uses a robust l-norm cost function in order to estimate and track non-stationary subspaces when the streaming data vectors are corrupted with outliers. We apply GRASTA to the problems of robust ma...

‎in this paper‎, ‎first we develop the duality concept for $g$-bessel sequences‎ ‎and bessel fusion sequences in hilbert spaces‎. ‎we obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎we also expand every $g$-bessel ‎sequence to a frame by summing some elements‎. ‎we define the restricted isometry property for ‎$g$-frames and generalize some resu...

We study closed subspaces of L(X ), where (X , μ) is a σ-finite measure space, that are invariant under the unitary representation associated to a measurable action of a discrete countable LCA group Γ on X . We provide a complete description for these spaces in terms of range functions and a suitable generalized Zak transform. As an application of our main result, we prove a characterization of...

Sensorineural systems often use groups of redundant neurons to represent stimulus information both during transduction and population coding of features. This redundancy makes the system more robust to corruption in the representation. We approximate neural coding as a projection of the stimulus onto a set of vectors, with the result encoded by spike trains. We use the formalism of frame theory...

This paper proposes the kernel orthogonal mutual subspace method (KOMSM) for 3D object recognition. KOMSM is a kernel-based method for classifying sets of patterns such as video frames or multi-view images. It classifies objects based on the canonical angles between the nonlinear subspaces, which are generated from the image patterns of each object class by kernel PCA. This methodology has been...

In this paper we study the fusion frame potential, that is a generalization of the BenedettoFickus (vectorial) frame potential to the finite-dimensional fusion frame setting. Local and global minimizers of this potential are studied, when we restrict it to a suitable set of fusion frames. These minimizers are related to tight fusion frames as in the classical vector frame case. Still, tight fus...

In this paper we study the fusion frame potential, that is a generalization of the BenedettoFickus (vectorial) frame potential to the finite-dimensional fusion frame setting. The structure of local and global minimizers of this potential is studied, when we restrict the frame potential to suitable sets of fusion frames. These minimizers are related to tight fusion frames as in the classical vec...

We study structures called d-frames which were developed by the last two authors for a bitopological treatment of Stone duality. These structures consist of a pair of frames thought of as the opens of two topologies, together with two relations which serve as abstractions of disjointness and covering of the space. With these relations, the topological separation axioms regularity and normality ...

We present a Dynamic Data Driven Application System (DDDAS) to track 2D shapes across large pose variations by learning non-linear shape manifold as overlapping, piecewise linear subspaces. The learned subspaces adaptively adjust to the subject by tracking the shapes independently using Kanade Lucas Tomasi(KLT) point tracker. The novelty of our approach is that the tracking of feature points is...