  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.
