基于MCMC的盲伯努利-高斯反卷积的增强采样方案
Enhanced sampling schemes for MCMC based blind Bernoulli-Gaussian deconvolution
AI总结：
针对盲稀疏反卷积问题，提出并比较了两种新的MCMC采样方案：K元组吉布斯采样器和部分边缘化采样器，后者通过积分出高斯幅度提高效率，仿真验证了收敛速度优势。
摘要：
本文提出并比较了两种新的基于伯努利-高斯模型的稀疏反卷积采样方案。为了在盲和无监督背景下解决此类反卷积问题，通常采用马尔可夫链蒙特卡洛（MCMC）框架，且最常选择的采样方案是吉布斯采样器。然而，这种采样方案无法有效探索状态空间。我们的第一个替代方案，$K$元组吉布斯采样器，本质上是一种分组吉布斯采样器。第二种方案称为部分边缘化采样器，通过从目标分布中积分掉高斯幅度得到。虽然第一种方案作为吉布斯采样器的特例其数学有效性显而易见，但本文提供了更详细的分析以证明第二种方案的有效性。对于这两种方法，提出了在计算和存储成本方面的优化实现。最后，仿真结果验证了两种方案在收敛时间上均比普通吉布斯采样器更高效。基准序列仿真表明，部分边缘化采样器比$K$元组吉布斯采样器需要更少的迭代次数收敛。然而，其每次迭代的计算负载随数据长度几乎呈二次增长，而$K$元组吉布斯采样器仅呈线性增长。
英文摘要：
This paper proposes and compares two new sampling schemes for sparse deconvolution using a Bernoulli-Gaussian model. To tackle such a deconvolution problem in a blind and unsupervised context, the Markov Chain Monte Carlo (MCMC) framework is usually adopted, and the chosen sampling scheme is most often the Gibbs sampler. However, such a sampling scheme fails to explore the state space efficiently. Our first alternative, the $K$-tuple Gibbs sampler, is simply a grouped Gibbs sampler. The second one, called partially marginalized sampler, is obtained by integrating the Gaussian amplitudes out of the target distribution. While the mathematical validity of the first scheme is obvious as a particular instance of the Gibbs sampler, a more detailed analysis is provided to prove the validity of the second scheme. For both methods, optimized implementations are proposed in terms of computation and storage cost. Finally, simulation results validate both schemes as more efficient in terms of convergence time compared with the plain Gibbs sampler. Benchmark sequence simulations show that the partially marginalized sampler takes fewer iterations to converge than the $K$-tuple Gibbs sampler. However, its computation load per iteration grows almost quadratically with respect to the data length, while it only grows linearly for the $K$-tuple Gibbs sampler.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
