In various applications, the adoption of optimal energy matching pursuit with dictionary elements is common. When the dictionary elements are indexed by parameters within a bounded region, exhaustion-type algorithms can be employed. This article aims to investigate a process that converts the optimal parameter selection in unbounded regions to a bounded and closed (compact) sub-domain. Such a process provides accessibility for energy matching pursuit in a wide range of applications. The paper initially focuses on the open unit disc and the upper-half complex plane, introducing adaptive Fourier decomposition as the underlying methodology. It then extends this concept to general Hilbert spaces with a dictionary and Bochner spaces for random signals. Computational examples are included to illustrate the concepts presented.

在各种应用中，采用字典元素的最优能量匹配追求是很常见的。当字典元素由有界区域内的参数索引时，可以采用穷举型算法。本文旨在研究将无界区域中的最优参数选择转换为有界且封闭（紧凑）子域的过程。这样的过程为在广泛的应用中追求能量匹配提供了可及性。本文首先关注开单位圆盘和上半复平面，引入自适应傅里叶分解作为基础方法。然后，它将这个概念扩展到带有字典的一般希尔伯特空间和随机信号的博赫纳空间。包括计算示例来说明所提出的概念。