Transmitted data may be corrupted by both noise and data loss. Grassmannian frames are in some sense optimal representations of data transmitted over a noisy channel that may lose some of the transmitted coefficients. Fusion frame (or frame of subspaces) theory is a new area that has potential to be applied to problems in such fields as distributed sensing and parallel processing. Grassmannian ...

This paper studies the design of data fusion algorithm for asynchronous system with integer times sampling. Firstly, the multisensor asynchronous samplings is mapped to the basic axis, accordingly a sampling sequence of single sensor can be taken. Secondly, aiming at the sensor with the densest sampling points, the modified parallel filtering is given. Afterwards, the sequential filtering fusio...

Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Given a spectrum for a desired fusion frame operator and dimensions for subspaces, one existing method for creating unitweight fusion frames with these properties is the flexible a...

Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from a fusion frame. We use a block sparsity model for fusion frames and then show that sparse signals under this model can be compressively sampled and reconstr...

David Kroetsch Master of Applied Science University of Waterloo September 2007 Multi-frame Measurement Fusion for State Estimation Simultaneous Localization and Mapping (SLAM) is a technique used by robots and autonomous vehicles to build up a map while operating in an unknown environment, while at the same time keeping track of a current position estimate. This process is not as straightforwar...

Glutamic acid decarboxylase (GAD;E.C. 4.1.1.15) catalyzes the production of GABA, the major inhibitory neurotransmitter in the mammalian brain. We recently isolated a lambda gt-11 recombinant, lambda-GAD, that contains the cDNA for GAD from feline brain (Kaufman et al., 1986). Interestingly, the beta-galactosidase-GAD fusion protein encoded by lambda GAD is enzymatically active, catalyzing the ...

This paper addresses continuous fusion frames and fusion pairs which are extensions of discrete fusion frames and continuous frames. The study of equalities and inequalities for various frames has seen great achievements. In this paper, using operator methods we establish some new inequalities for continuous fusion frames and fusion pairs. Our results extend and improve ones obtained by Balan, ...

We characterize when a coherent state or continuous frame for a Hilbert space may be sampled to obtain a frame, which solves the discretization problem for continuous frames. In particular, we prove that every bounded continuous frame for a Hilbert space may be sampled to obtain a frame.

Recently fusion frame was considered as a generalization of frame in Hilbert spaces. In this paper, we establish several new inequalities for fusion frames with a scalar in Hilbert spaces. It is shown that the results we obtained can immediately lead to the existing corresponding results when we choose suitable scalars. Mathematics subject classification (2010): 42C15, 47B40.