Discrete Uncertainty Principles and Sparse Signal Processing

作者：Bandeira, Afonso S.; Lewis, Megan E.; Mixon, Dustin G.^*

来源：Journal of Fourier Analysis and Applications, 2018, 24(4): 935-956.

DOI：10.1007/s00041-017-9550-x

• Uncertainty principle
• Sparsity
• Compressed sensing

We develop new discrete uncertainty principles in terms of numerical sparsity, which is a continuous proxy for the 0-norm. Unlike traditional sparsity, the continuity of numerical sparsity naturally accommodates functions which are nearly sparse. After studying these principles and the functions that achieve exact or near equality in them, we identify certain consequences in a number of sparse signal processing applications.

• 出版日期2018-8