单帧数字图像分辨率改善的频域正则化方法

现有多帧序列频域分辨率改善方法主要基于柯西-高斯先验模型，对单帧图像处理效果不理想。在分析频谱混叠公式的基础上，研究了单帧图像分辨率改善的频域方法。提出了基于柯西-高斯先验模型的正则化方法，由于柯西-高斯先验模型具有较好的信号稀疏表示能力，因此能有效地改善图像的分辨率。设计了迭代求解算法，给出了迭代初值的稳健算法，并将二维计算问题转化为一维计算问题，实现了方法的快速计算，同时大大地减少了存储量。文中给出了一维信号和遥感图像两个算例，计算结果表明，方法可以有效地改善图像的分辨率。

Frequency Domain Regularization for Single Frame Image Resolution Improvement

In this paper, the resolution improving method in frequency domain based on spectral aliasing equation is put forward for a single frame image. But the current algorithms, which are effective for multi-frames of low-resolution images, cannot be simply applied to only one frame low-resolution image. The main reason is that they are all based on the quadratic distribution of the spectral amplitudes. The application of Cauchy prior model is generalized into the domain of optical images resolution improvement. Since it has fairly good ability in signal sparse expression, the model can improve the resolution effectively. We describe the procedure that gives an iterative nonlinear estimation for the cost function, a robust algorithm with iterated initial solutions is discussed and it is converted into another matrix that is less sensitive to the initial value of the spectral amplitudes. We transfer the two-dimension problem into one dimension problem, so the algorithm is faster and effectively reduces the memory. The one dimension signal and a remote sensing image are compared in the end, and the results show the effectiveness of this algorithm.