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Adaptive optics (AO) system which is widely used in astronomical observations can improve the image quality by the real-time measurement and correction of the wave-front. One of the main problems in the AO system is the poor quality of the image because of the system noises. The noises in AO system are additive noises. The main sources of the noises are the background noise, the photon noise, and the readout noise of charge-coupled device. The background noise is distributed evenly and is easy to process. The photon noise is dependent on the characteristics of the spot itself. Readout noise, which is Gaussian distribution with the mean value of 0 and the variance of 2, is the main noise source in AO system. In this paper, we focus on the readout noise and propose a new regularization model to remove additive noises from the AO system. In this model, the regularization parameters can be adaptively changed. A nonconvex regularization term is used to make the homogeneous region of the image smooth efficiently, while the integrity of the spot can be well restored. The properties of the regularization proposed are shown below. 1) The proposed nonconvex regularization term can act as the L0 norm which is sparser than L1 norm. 2) The proposed model can protect the edge of the spot from over smoothing. To prevent the edges from over smoothing, the regularization parameter must be an increasing function. Moreover, it converges to a constant so that it cannot affect the strong gradient of the image. 3) The regularization term proposed is nonconvex which is more sensible to the minor change of the image. Therefore, the edges of the image can be better preserved. Though the proposed model can well preserve the edges of the spot, it is difficult to resolve by traditional methods because of the nonconvexity. Split Bregman algorithm and augmented Lagrangian duality algorithm are used to solve this problem. We can obtain a denoised spot image as well as an edge indicator by using the proposed model. The visual and quantitative evaluations are used to value the restored images. The evaluating indicators are the peak signal-to-noise ratio and centroid detecting error which includes the root mean square and the peak valley value of the centroid deviation. The simulation and experimental results show the efficiency of this model in removing the additive noises from the AO system.

Strong front wall clutter has serious impacts on the target detection and imaging in the through-wall radar (TWR) system. A method of robust wall clutter suppression based on the entropy of an expanded antenna source for ultra-wide-band through-wall radar is presented in this paper. The model of TWR scenario consists of four layers. Assume that the first and the third layers are air space, while the second and the fourth layers are composed of uniform flat concrete wall. The circular target, assumed to be a perfect electric conductor, is located in the third layer. Along the measurement line which is parallel to the front wall, the transceiver antenna scans uniformly. The echo signals that come from the target and walls are processed into discrete data at first, so that the calculation of probability space is subsequently implemented and the discrete data are expanded as well. And then the entropy of the expanded data that contain robust wall clutter and echo of target is calculated. Taking into consideration the amplitude of target signal varying in each scan, while that of clutter signal is not, it is evident that the entropy can be utilized to discriminate the signals between the target and wall. According to the difference between the entropy of the wall clutter and that of the target, a certain threshold can be set and the optimum tolerance threshold is adaptively selected on the basis of target-to-clutter ratio. With the optimum tolerance threshold, process of clutter suppression is conducted. Finally, back projection is employed for imaging of target. In this paper, data of through-wall radar for simulation are provided by GprMax2D/3D, based on the finite difference-time domain methsd. The clutter suppression and imaging are separately conducted by the method based on data entropy and the method proposed in this paper. Comparing the results of simulations, it is shown that the gain of target-to-clutter ratio for the former is 15.51 dB, and that for the latter is 19.74 dB. It is obvious that the proposed method can provide imaging with higher quality for the same measurement, and it requires fewer scans with the same quality of imaging as well. Computational complexity of the proposed method and the method based on entropy can be expressed as O(M NL) and O(M N) , respectively