多维时间信号的最优自适应非参数去噪
Optimal Adaptive Nonparametric Denoising of Multidimensional - Time Signal
摘要：
通过多维截断Legendre展开和最优经验设计，构造了一种在平方可积函数空间L（2）的经典范数下自适应渐近最优的非参数多维时间定义信号恢复（自适应滤波、噪声抵消器）.二维情况称为图片处理、图片分析或图像处理.我们提供了两个版本的置信区域构建，也是自适应的。我们提出的估计已成功地通过了用伪随机数模拟的问题和实际数据（地震信号等）的实验检验。为此，将我们对不同信号的估计与通过核或小波估计方法获得的经典估计进行比较。本文提出的估计精度较好。我们的自适应截断也可用于信号和图像压缩。
英文摘要：
We construct an adaptive asymptotically optimal in the classical norm of the space L(2) of square integrable functions non - parametrical multidimensional time defined signal regaining (adaptive filtration, noise canceller) on the background noise via multidimensional truncated Legendre expansion and optimal experience design. The two - dimensional case is known as a picture processing, picture analysis or image processing. We offer a two version of an confidence region building, also adaptive. Our estimates proposed by us have successfully passed experimental tests on problem by simulate of modeled with the use of pseudo-random numbers as well as on real data (of seismic signals etc.) for which our estimations of the different signals were compared with classical estimates obtained by the kernel or wavelets estimations method. The precision of proposed here estimations is better. Our adaptive truncation may be used also for the signal and image compression.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
