Generalized sparse Bayesian learning and application to image reconstruction
Generalized sparse Bayesian learning and application to image reconstruction
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DOI：
10.1137/22m147236x
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发表时间：
2022-01
期刊：
影响因子：
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通讯作者：
J. Glaubitz;Anne Gelb;Guohui Song
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文献类型：
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作者：
J. Glaubitz;Anne Gelb;Guohui Song
基于间接、噪声或不完整数据的图像重建仍然是一项重要但具有挑战性的任务。虽然诸如压缩感测的方法已经在各种设置中展示了高分辨率图像恢复，但是由于参数调整，仍然存在鲁棒性问题。此外，由于恢复仅限于点估计，因此不可能量化不确定性，而这通常是可取的。由于这些固有的限制，稀疏贝叶斯学习方法有时被采用来恢复未知的后验分布。稀疏贝叶斯学习假设未知数的某些线性变换是稀疏的。然而，大多数开发的方法是针对特定的问题，特定的前向模型和先验。在这里，我们提出了一种广义的稀疏贝叶斯学习方法。它的优点是可以用于各种类型的数据采集和先验信息。图像重建/恢复的一些初步结果表明，其潜在的使用去噪，去模糊，和磁共振成像。
Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues of robustness due to parameter tuning. Moreover, since the recovery is limited to a point estimate, it is impossible to quantify the uncertainty, which is often desirable. Due to these inherent limitations, a sparse Bayesian learning approach is sometimes adopted to recover a posterior distribution of the unknown. Sparse Bayesian learning assumes that some linear transformation of the unknown is sparse. However, most of the methods developed are tailored to specific problems, with particular forward models and priors. Here, we present a generalized approach to sparse Bayesian learning. It has the advantage that it can be used for various types of data acquisitions and prior information. Some preliminary results on image reconstruction/recovery indicate its potential use for denoising, deblurring, and magnetic resonance imaging.