结合自适应稀疏表示和全变分约束的图像重建

Adaptive sparse representation and total variation constraint based image reconstruction

针对以二维小波变换和离散余弦变换为代表的固定正交基在图像压缩感知高分辨率重建中的局限性,提出了一种新的自适应冗余字典稀疏表示结合全变分约束的图像高分辨率重建算法.该算法以迭代过程的中间图像作为训练样本,通过自适应学习获得适合样本特征的冗余字典,它充分利用了字典原子与待重建图像的相关性,获得了待重建图像的理想完备稀疏表示,从而降低了采样率,提高了图像重建质量.最后,以全变分作为正则化条件,采用交替迭代算法求解稀疏优化问题.仿真结果表明,该算法可以在低采样率下重建出高质量的图像.

In view of the limitation of fixed complete orthogonal transformation, represented by two- dimensional wavelet transform and discrete cosine transform in compressed sensing high-resolution image reconstruction, this paper proposes a new method for high-resolution image reconstruction based on adaptive redundant dictionary sparse representation with the total variation constraint. The algorithm takes the intermediate image in the process of iteration as the training sample to get a redundant dictionary suitable for sample characteristics by adaptive learning. It makes full use of the correlation between dictionary atoms and the image to get an ideal complete sparse representation, thus reducing the sampling rate and improving the quality of image reconstruction. Finally, the algorithm takes the total variation as a constraint and uses the split Bregman iterative method to solve the sparse optimization problem. Simulation shows that the proposed method can reconstruct high quality images under a low sampling rate.