论文标题
分段平滑信号恢复的估计和不确定性量化
Estimation and uncertainty quantification for piecewise smooth signal recovery
论文作者
论文摘要
本文提出了一种稀疏的贝叶斯学习（SBL）算法，该算法对于高阶总变化（HOTV）稀疏性的线性反问题。对于稀疏信号恢复的问题，SBL通常比最大后验估计值（包括依赖L1正则化的估计值）产生更准确的估计值。此外，SBL而不是单个信号估计，而是产生完整的后密度估计值，可用于不确定性定量。但是，SBL仅立即适用于具有直接稀疏性的问题，或者适用于可以通过合成形成的问题。本文演示了如何通过合成来提出HOTV稀疏性问题，然后开发相应的贝叶斯学习方法。这扩展了贝叶斯学习可用的问题类别，例如，涉及分段平滑功能或数据信号的逆问题。提供了数值示例来证明如何有效地采用这种新技术。
This paper presents a sparse Bayesian learning (SBL) algorithm for linear inverse problems with a high order total variation (HOTV) sparsity prior. For the problem of sparse signal recovery, SBL often produces more accurate estimates than maximum a posteriori estimates, including those that rely on l1 regularization. Moreover, rather than a single signal estimate, SBL yields a full posterior density estimate which can be used for uncertainty quantification. However, SBL is only immediately applicable to problems having a direct sparsity prior, or to those that can be formed via synthesis. This paper demonstrates how a problem with an HOTV sparsity prior can be formulated via synthesis, and then develops a corresponding Bayesian learning method. This expands the class of problems available to Bayesian learning to include, e.g., inverse problems dealing with the recovery of piecewise smooth functions or signals from data. Numerical examples are provided to demonstrate how this new technique is effectively employed.
