弱散射的压缩衍射层析成像
Compressive Diffraction Tomography for Weakly Scattering
摘要：
从著名的衍射层析成像（DT）存在一个吸引人的要求，从少数视图和有限的角度数据的成功重建。受压缩感知理论的启发，本文研究了弱散射点的高稀疏数据超分辨率精确重建问题。为了实现数据压缩测量，特别是在数据高度稀疏的情况下获得超分辨率重建，提出了一种利用随机介质包围探测障碍物的压缩系统，并进行了实验研究。（a）当所需分辨率在~范围内时，可以通过测量精确地获得K稀疏N未知数成像，这与压缩感知文献中高斯随机矩阵所需的测量次数相当。(b)由于引入了随机介质以增强波传播的多路径效应，因此得到的测量矩阵与小波矩阵不相干，换句话说，在小波框架下，当探测到的障碍物稀疏时，成功重建所需的测量数与上述相似。(c)如果期望的分辨率低于，则所提出的压缩系统所需的测量次数与自由空间的情况几乎相同。(d)还需要在成像分辨率和测量次数之间进行权衡。此外，通过引入复高斯变量，对快速稀疏贝叶斯算法进行了改进，使其能够处理稀疏约束的复值优化问题。
英文摘要：
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.
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