Recently published research shows that Lomax distribution exhibits compressibility in Lorentz curves. In this paper, we address the problem of signal reconstruction in the high noise level and phase error environments in a Bayesian framework of Lomax prior distribution. Furthermore, from the perspective of improving sparsity and compressibility of the signal constraints, a novel reconstruction model deducted from Lomax-prior-based Bayesian compressed sensing (LomaxCS) is proposed. The LomaxCS improves the accuracy of existing Bayesian compressed sensing signal reconstruction methods and enhances the robustness against Gauss noise and phase errors. Compared with the conventional models, the proposed LomaxCS model still reveals the general profile of the signal in the worst conditions. The experimental results demonstrate that the proposed algorithm can achieve substantial improvements in terms of recovering signal quality and robustness; meanwhile, it brings an evident application prospect.

中文翻译：

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基于 Lomax 先验的使用贝叶斯压缩感知的鲁棒信号恢复

最近发表的研究表明 Lomax 分布在洛伦兹曲线中表现出可压缩性。在本文中，我们在 Lomax 先验分布的贝叶斯框架中解决了在高噪声水平和相位误差环境中的信号重建问题。此外，从提高信号约束的稀疏性和可压缩性的角度出发，提出了一种从基于Lomax-prior的贝叶斯压缩感知(LomaxCS)推导出的新型重构模型。LomaxCS 提高了现有贝叶斯压缩感知信号重建方法的准确性，并增强了对高斯噪声和相位误差的鲁棒性。与传统模型相比，所提出的 LomaxCS 模型仍然揭示了信号在最坏条件下的一般轮廓。实验结果表明，该算法在恢复信号质量和鲁棒性方面取得了实质性的提升；同时，也带来了明显的应用前景。