Several phenomena encountered in nature are characterized by very localized events occurring randomly at given times. Random pulses are an appropriate modelling tool for such events. Usually, the impulses are hidden in the noise due to unwanted convolution. In some cases, the problem is more complex because of the short time lag between the pulses. Considering these problems, the resulting signal is unclear and can lead to an erroneous analysis. Hence the need for deconvolution to restore the pulsed signal in order to obtain a more accurate diagnosis. The main objective of this study is to propose a new algorithm called orthogonal least absolute value. The particularity of this algorithm lies in its selection criterion. The algorithm iteratively selects the atom minimizing the absolute value of the approximation error. This allows the proposed algorithm to outperform classical greedy algorithms when the peaks are very close to each other. Numerical and experimental simulations are performed to study the proposed algorithm and compare its behavior to other greedy algorithms in deconvolution framework. Simulations results prove the performance of the proposed algorithm, especially when the impulses are very close to each other.

自然界中遇到的几种现象的特征是在给定时间随机发生的非常局部化的事件。随机脉冲是此类事件的合适建模工具。通常，由于不需要的卷积，脉冲被隐藏在噪声中。在某些情况下，由于脉冲之间的时间间隔较短，因此问题更加复杂。考虑到这些问题，所产生的信号尚不清楚，并可能导致错误的分析。因此，需要进行去卷积以恢复脉冲信号以获得更准确的诊断。这项研究的主要目的是提出一种称为正交最小绝对值的新算法。该算法的特殊性在于其选择标准。该算法迭代地选择最小化逼近误差绝对值的原子。当峰值彼此非常接近时，这使得所提出的算法能够胜过经典的贪婪算法。进行了数值和实验仿真，以研究该算法并将其与反卷积框架中其他贪婪算法的行为进行比较。仿真结果证明了所提算法的性能，特别是当脉冲非常接近时。