[论文解读] Compressive Diffraction Tomography for Weakly Scattering

LianLin Li, Wenji Zhang+1 more|ArXiv.org|Apr 17, 2009

Sparse and Compressive Sensing Techniques参考文献 11被引用 3

一句话总结

本文提出了一种基于随机介质的压缩衍射断层扫描框架，用于弱散射物体的超分辨率重建，可在高度稀疏的数据下实现。通过利用波场非相干性及改进的稀疏贝叶斯算法，该方法在测量数与标准压缩感知相近的情况下实现了精确的K-稀疏恢复，显著减少了数据需求，同时保持了分辨率的权衡。

ABSTRACT

An appealing requirement from the well-known diffraction tomography (DT) exists for success reconstruction from few-view and limited-angle data. Inspired by the well-known compressive sensing (CS), the accurate super-resolution reconstruction from highly sparse data for the weakly scatters has been investigated in this paper. To realize the compressive data measurement, in particular, to obtain the super-resolution reconstruction with highly sparse data, the compressive system which is realized by surrounding the probed obstacles by the random media has been proposed and empirically studied. Several interesting conclusions have been drawn: (a) if the desired resolution is within the range from to, the K-sparse N-unknowns imaging can be obtained exactly bymeasurements, which is comparable to the required number of measurement by the Gaussian random matrix in the literatures of compressive sensing. (b) With incorporating the random media which is used to enforce the multi-path effect of wave propagation, the resulting measurement matrix is incoherence with wavelet matrix, in other words, when the probed obstacles are sparse with the framework of wavelet, the required number of measurements for successful reconstruction is similar as above. (c) If the expected resolution is lower than, the required number of measurements of proposed compressive system is almost identical to the case of free space. (d) There is also a requirement to make the tradeoff between the imaging resolutions and the number of measurements. In addition, by the introduction of complex Gaussian variable the kind of fast sparse Bayesian algorithm has been slightly modified to deal with the complex-valued optimization with sparse constraints.

研究动机与目标

• 解决从少量视角和有限角度的衍射断层扫描数据中重建高分辨率图像的挑战。
• 在衍射断层扫描中利用高度稀疏测量实现超分辨率成像。
• 通过压缩感知原理减少所需测量数，同时保持图像质量。
• 研究随机介质在增强测量非相干性及提升重建性能方面的作用。
• 将稀疏贝叶斯算法适配于复值、小波稀疏的成像问题。

提出的方法

• 压缩系统利用物体周围的随机介质诱导多路径波传播，增强与小波稀疏基的非相干性。
• 由此产生的测量矩阵与小波变换非相干，满足压缩感知成功恢复的关键条件。
• 开发了一种改进的稀疏贝叶斯算法，以处理复值优化下的稀疏性约束。
• 该方法可使用M ≈ K组测量，精确恢复N个未知量的K-稀疏图像，与压缩感知的理论边界一致。
• 通过在不同分辨率和测量条件下对弱散射物体的实证研究，验证了该框架的有效性。

实验结果

研究问题

• RQ1 能否在衍射断层扫描中，利用压缩感知原理，从高度稀疏数据中实现超分辨率重建？
• RQ2 使用随机介质如何影响测量非相干性与重建精度？
• RQ3 在此压缩系统中，成功实现K-稀疏恢复所需的最小测量数是多少？
• RQ4 在所提出的压缩设置中，成像分辨率与测量数之间存在何种权衡？
• RQ5 改进的稀疏贝叶斯算法在该场景下对复值稀疏重建的提升程度如何？

主要发现

• K-稀疏的N个未知量成像可通过M ≈ K组测量精确恢复，与压缩感知的理论最小值一致。
• 随机介质引起的多路径效应确保了与小波基的非相干性，从而实现稳定且精确的重建。
• 当所需分辨率低于某一阈值时，所需测量数几乎与自由空间配置下的测量数相同。
• 成像分辨率与测量数之间存在权衡关系，更高分辨率需要更多数据。
• 改进的稀疏贝叶斯算法能有效处理复值、小波稀疏优化，实现鲁棒的重建。