Optimizing Sparse Adaptive Representations of Signals Using Energy-Based Algorithm Enhancements

稀疏分解算法自适应地扩展一个信号在一个过完备的一组有限支持的功能称为原子，包括一个字典。这些非线性算法的目标是找到一种既稀疏、高效、鲁棒，又具有信息量和延展性的表示。研究人员正在对各种信号的稀疏分解的能量含量进行建模，以优化性能。这项工作将导致更好的自适应原子选择策略的稀疏分解，以及字典，更一致的一类信号的内在结构。这将导致一种方法来确定稀疏表示的哪些项实际上属于信号，哪些项是分解的伪影。这项研究的应用程序，依赖于表示的波形，如地质和生物医学数据分析，内容检索，源分离，音乐声音变换等的影响。稀疏表示提供了一个有吸引力的替代标准正交展开。稀疏表示的一些算法的一个特性是创建没有物理意义的术语，而是反映算法的贪婪。研究人员将这种现象称为暗能量，因为这些项在信号重建中被取消了。虽然以前的工作解决这些虚假的条款已被视为滋扰，有证据表明，暗能量体现了有用的信息，信号和它的一致性与字典。它还可以为选择原子或学习更好的原子提供更好的策略。研究人员正在探索暗能量的性质及其对原始信号，字典和用于生成分解的策略的意义。

Sparse decomposition algorithms adaptively expand a signal in terms of an over-complete set of finite-support functions called atoms that comprise a dictionary. These nonlinear algorithms aim to find a representation that is at once sparse, efficient, and robust, as well as informative and malleable. The investigators are modeling the energy content of sparse decompositions for a variety of signals in order to optimize performance. This work will lead to better adaptive atom selection strategies for sparse decompositions, as well as dictionaries that are more coherent to the intrinsic structures of a class of signals. It will result in a way to determine which terms of a sparse representation actually belong to the signal and which are artifacts of the decomposition. This research has implications for applications that rely on representations of waveforms such as geological and biomedical data analyses, content retrieval, source separation, music sound transformation, etc.Sparse representations provide an attractive alternative to standard orthonormal expan-sions. One property of some algorithms for sparse representations is the creation of terms that are not physically meaningful, but reflect instead the greediness of the algorithm. The investigators refer to this phenomenon as dark energy because these terms are cancelled in the signal reconstruction. Although previous work addressing these spurious terms has viewed them as a nuisance, there is evidence suggesting that dark energy embodies useful information about the signal and its coherency with the dictionary. It can also provide a better strategy for choosing atoms or learning better ones. The investigators are exploring the nature of dark energy and its significance for the original signal, the dictionary, and the strategies used to generate decompositions.