稀疏间隙：与维度成比例的不确定性原理
The Sparsity Gap: Uncertainty Principles Proportional to Dimension
摘要：
在非相干字典中，大多数允许稀疏表示的信号都允许唯一的稀疏表示。换句话说，如果不严格使用更多的原子，就没有办法表达信号。这项工作表明，稀疏信号通常享有更高的特权：信号的每个非最佳表示需要比稀疏表示更多的原子，除非它包含许多相同的原子作为稀疏表示。这一发现的一个影响是赋予出现在稀疏表示中的特定原子一定程度的合法性。这个结果也可以看作是随机稀疏信号在非相干字典上的不确定性原理。
英文摘要：
In an incoherent dictionary, most signals that admit a sparse representation admit a unique sparse representation. In other words, there is no way to express the signal without using strictly more atoms. This work demonstrates that sparse signals typically enjoy a higher privilege: each nonoptimal representation of the signal requires far more atoms than the sparsest representation-unless it contains many of the same atoms as the sparsest representation. One impact of this finding is to confer a certain degree of legitimacy on the particular atoms that appear in a sparse representation. This result can also be viewed as an uncertainty principle for random sparse signals over an incoherent dictionary.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
