This paper introduces a new sparse Bayesian learning (SBL) algorithm that jointly recovers a temporal sequence of edge maps from noisy and under-sampled Fourier data. The new method is cast in a Bayesian framework and uses a prior that simultaneously incorporates intra-image information to promote sparsity in each individual edge map with inter-image information to promote similarities in any unchanged regions. By treating both the edges as well as the similarity between adjacent images as random variables, there is no need to separately form regions of change. Thus we avoid both additional computational cost as well as any information loss resulting from pre-processing the image. Our numerical examples demonstrate that our new method compares favorably with more standard SBL approaches.

翻译：本文提出一种新的稀疏贝叶斯学习算法，用于从含噪且欠采样的傅里叶数据中联合恢复时间序列边缘图。该方法基于贝叶斯框架，采用一种先验模型，该模型同时整合了图像内部信息以促进每个边缘图的稀疏性，以及图像间信息以保持未变化区域的相似性。通过将边缘及相邻图像间的相似性均视为随机变量，无需单独划分变化区域，从而避免了预处理带来的额外计算开销和信息损失。数值实验表明，与标准稀疏贝叶斯学习方法相比，本文方法具有更优的性能。