基于样条小波框架方法的散乱数据重构

A B-spline wavelet frame based scattered data reconstruction

B样条小波框架能够有效的表示光滑和局部震荡函数,并同时提供时间和频率域局部化,因此在信号和图像处理等领域应用广泛,例如图像恢复。针对从混合或未知类型噪音的散乱数据中重构原始信号这一问题,本文提出了一个基于B样条小波框架的变分模型,并应用增广拉格朗日乘子法和加速近端梯度下降方法求解该模型,进一步给出了模型解的Lp范数(1≤p≤+∞)误差分析,最后通过对噪音数据重构进行数值实验并与其它的变分模型结果作比较,从而说明了本文方法的有效性。

B- spline wavelet frames are very popular in signal and image processing,such as image restoration,since they are able to represent both smooth and locally bumpy functions in an efficient way and provide time and frequency localization. This paper presents a B-spline wavelet frame based model for recovering signals from scattered data with mixed or unknown noises,and applies the augmented Lagrangian multiplier method and accelerated proximal gradient method to solve the model. Furthermore, an Lp-norm[(1≤p≤+∞)] error analysis of the solution is established. In the end,numerical experimentsfor noisy data reconstruction are performed and compared with other variational methods to demonstrate the advantages of our approach.