Necessary and sufficient conditions to perform Spectral Tetris

作者：Casazza Peter G; Heinecke Andreas; Kornelson Keri^*; Wang Yang; Zhou Zhengfang

来源：Linear Algebra and Its Applications, 2013, 438(5): 2239-2255.

DOI：10.1016/j.laa.2012.10.030

• Frames
• Tight frames
• Sparsity
• Sparse matrices
• Majorization
• Synthesis operator
• Redundancy

Spectral Tetris is a powerful tool for constructing sparse equal norm Hilbert space frames. We introduce a new form of Spectral Tetris which works for non-equal-norm frames. It is known that this method cannot construct all frames-even in the new case introduced here. Until now, it has been a mystery why Spectral Tetris sometimes works and sometimes fails. We provide a complete answer by giving necessary and sufficient conditions for Spectral Tetris to construct frames with prescribed vector norms and prescribed frame operator. We present a variety of examples and include cases where Spectral Tetris always works.

• 出版日期2013-3-1