Orthogonal Least Absolute Value for Sparse Spike Deconvolution


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.

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Data Availability Statement

The generated data and the codes of the proposed work are available from the corresponding author on reasonable request.


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Had, A., Sabri, K. Orthogonal Least Absolute Value for Sparse Spike Deconvolution. Circuits Syst Signal Process (2021). https://doi.org/10.1007/s00034-021-01667-z

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  • Sparsity
  • Random impulses
  • Deconvolution
  • Greedy algorithm
  • Phonocardiogram signal