基于稀疏优化的图像压缩感知重建算法

Compressive Sensing Image Reconstruction Algorithm Based on Optimized Sparse Representation

摘要:

在信号的稀疏表示方法中,传统的基于变换基的稀疏逼近不能自适应性地提取图像的纹理特征,而基于过完备字典的稀疏逼近算法复杂度过高。针对该问题,文章提出了一种基于小波变换稀疏字典优化的图像稀疏表示方法。该算法在图像小波变换的基础上构建图像过完备字典,利用同一场景图像的小波变换在纹理上具有内部和外部相似的属性,对过完备字典进行灰色关联度的分类,有效提高了图像表示的稀疏性。将该新算法应用于图像信号进行稀疏表示,以及基于压缩感知理论的图像采样和重建实验,结果表明新算法总体上提升了重建图像的峰值信噪比与结构相似度,并能有效缩短图像重建时间。

Abstract:

In the signal sparse representation methods, the traditional sparse approximation based on transform basis cannot extract the texture features of image adaptively, and the sparse approximation algorithm based on the over-complete dictionary is too complex. To solve this problem, a sparse representation method based on sparse dictionary optimization of wavelet transform is proposed. Based on the wavelet transform of image, this algorithm constructs over-complete dictionaries, and makes use of the similar attributes in interior and exterior on the texture in wavelet transform of images in the same scene, and classifies the over-complete dictionary with grey correlation degree, which improves the effectiveness of sparse representation. The new algorithm is applied in image signal sparse representation and image sampling and reconstruction experiments based on compressive sensing theory. The results show that the new algorithm improves the peak signal to noise ratio (PSNR) and structural similarity (SSIM) of reconstructed images as a whole, and can shorten the time of image reconstruction effectively.