Sparse matrices in frame theory

作者：Krahmer Felix; Kutyniok Gitta^*; Lemvig Jakob

来源：Computational Statistics, 2014, 29(3-4): 547-568.

DOI：10.1007/s00180-013-0446-1

• Dual frames
• Frames
• Redundancy
• Signal processing
• Tight frames

Frame theory is closely intertwined with signal processing through a canon of methodologies for the analysis of signals using (redundant) linear measurements. The canonical dual frame associated with a frame provides a means for reconstruction by a least squares approach, but other dual frames yield alternative reconstruction procedures. The novel paradigm of sparsity has recently entered the area of frame theory in various ways. Of those different sparsity perspectives, we will focus on the situations where frames and (not necessarily canonical) dual frames can be written as sparse matrices. The objective for this approach is to ensure not only low-complexity computations, but also high compressibility. We will discuss both existence results and explicit constructions.

• 出版日期2014-6