多通道反卷积模型在信号处理、图像恢复等领域有着广泛应用。小波基具有多尺度结构及刻画函数空间等特性，因而在反卷积模型的函数估计中取得了良好效果。基于此，本项目将利用小波方法研究高维多通道反卷积模型。. 本项目针对普通光滑、超光滑和box-car三类卷积算子展开讨论。假定待估函数具有各向异性结构，利用各向异性小波基研究上述模型。在带标准布朗运动噪声的情形下，通过阈值方法构造自适应的小波估计器，并给出其在各向异性Besov空间中的Lp风险上界。鉴于分数次布朗运动可以描述大范围相依误差，进一步研究带分数次布朗运动噪声的多通道反卷积模型，给出自适应小波估计器的Lp风险上界，并分析通道数目和分数次布朗运动噪声对收敛阶的影响。

Multichannel deconvolution model is widely applied to signal processing, picture recovery and so on. Since the wavelet basis has the property of multiresolution structure and characterization for functional spaces, it performs well in estimating the unknown function of deconvolution model. Hence, this program will apply wavelet methods to study the multichannel deconvolution model for high dimension spaces.. This program will discuss the multichannel deconvolution model under three different convolution operators, i.e. ordinary smoothness, super smoothness and box-car convolution operator. Assuming that the estimated function is anisotropic, we will apply the anisotropic wavelet basis to study the model. When the errors follow standard Brownian motions, we will construct the adaptive wavelet estimators by thresholding method, and provide their upper bounds on convergence rates in the Lp-risk. Since the fractional Brownian motions can describe the long-range dependence errors, we will study the multichannel deconvolution model with the errors following fractional Brownian motions, prove the upper bounds on convergence rates in the Lp-risk as well as analyzing the effects of both the fractional Brownian motion errors and the number of channels.