Compressive Diffraction Tomography for Weakly Scattering

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 0.2λ to 0.4λ , the K-sparse N-unknowns imaging can be obtained exactly by ( ) ( ) log N O K K measurements, 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 than0.4λ , 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. INDEX TERMInverse scattering problem, the diffractive tomography(DT), the Born/Rytov approximation, the super-resolution imaging, the sparse Bayesian optimization, compressive sensing (CS),