基于AMP框架的小波域图像压缩重构

Wavelet Domain Image Compressive Reconstruction Based on AMP Framework

针对压缩感知中的图像重构问题,基于近似消息传递(AMP)框架,提出一种新的图像压缩重构算法。该算法推导AMP框架在小波域下的系数迭代公式,证明AMP中滤波函数的操作对象是图像的小波系数,通过小波变换提高处理对象的稀疏度,并引入Wiener函数降低标量函数的求导复杂度。实验结果表明,与基于梯度投影的重构算法和正交匹配追踪算法相比,该算法具有较好的视觉效果和较高的重构精度。

This paper proposes a novel image compressive reconstruction algorithm based on Approximate Message Passing（AMP）.The novel algorithm derives the formulation in wavelet domain under the AMP framework,and proves that the filter function effects are the wavelet coefficients of image.It uses the wavelet transformation to increase the sparsity of processing objects,and incorporates the Wiener function to decrease the computational complexity.Experimental results demonstrate that,compared with the reconstruction algorithm based on gradient projection and the orthogonal matching pursuit algorithm,the proposed method is realized easily and shows some advantage on both of reconstruction accuracy and visualization.