Non-orthogonal Fusion Frames and the Sparsity of Fusion Frame Operators

作者：Cahill Jameson; Casazza Peter G; Li Shidong^*

来源：Journal of Fourier Analysis and Applications, 2012, 18(2): 287-308.

DOI：10.1007/s00041-011-9200-7

• Frames
• Fusion frames
• Sparsity of the fusion frame operator
• Sensor network
• Data fusion
• Distributed processing
• Parallel processing

Fusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the efficiency of the end fusion process. This in turn is reflected in the efficiency of the inversion of the fusion frame operator S-W, which in turn is heavily dependent on the sparsity of S-W. We will show that sparsity of the fusion frame operator naturally exists by introducing a notion of non-orthogonal fusion frames. We show that for a fusion frame {W-i, v(i)}(i is an element of I), if dim(W-i) = k(i), then the matrix of the non-orthogonal fusion frame operator SW has in its corresponding location at most a k(i) x k(i) block matrix. We provide necessary and sufficient conditions for which the new fusion frame operator S-W is diagonal and/or a multiple of an identity. A set of other critical questions are also addressed. A scheme of multiple fusion frames whose corresponding fusion frame operator becomes an diagonal operator is also examined.

• 出版日期2012-4