Construction of Regularized Parametric Projection Filters

泛函分析-图像恢复问题的理论发展进行了，并提出了许多滤波器族，如投影滤波器族和参数投影滤波器族。在实际应用中，由于复原图像对原图像的保真度取决于所用复原滤波器的稳定性，因此增强其鲁棒性是非常重要的，本文针对计算量小、保真度高的参数投影滤波器族，提出了一种新的对退化过程扰动具有鲁棒性的滤波器族。在为期两年的项目中，我们提出了正则化参数投影滤波器族、M-N范数参数投影滤波器族和信号自适应参数投影滤波器族，并通过数值仿真验证了它们的有效性，同时还提出了扰动、参数和正则化参数的选择准则。该准则在一定程度上使参数投影滤波器族的参数选择成为可能，从而使复原图像具有更高的保真度。

Functional Analysis-Theoretical developments of Image Restoration Problems carried on, and many filter-families such as Projection Filter- and Parametric Projection Filter-families were proposed. In practice, since the fidelity of restored images to original images depends on the stability of used restoration filters, it is very important to strengthen their robustness.The study is to introduce a new filter-family that is robust against the perturbation of degraded processes for the parametric projection filter-family with less calculations and high fidelity. In the two-years term of project, we proposed the following three restoration filter-families and confirmed their effectiveness by numerical simulations :Regularized Parametric Projection Filter-Family, M-N-Norm Parametric Projection Filter-Family, and Signal Adaptive Parametric Projection Filter-Family.Moreover, we introduced a criterion to choose perturbation, parametric and regularized parameters. The criterion makes us possible to choose the optimal, parameter of Parametric Projection Filter-family in a sense, and it results in the higher fidelity of restored images.