基于自适应加权压缩感知的图像超分辨率重建

压缩感知理论被广泛应用于从少量随机观测中精确地重构原始信号，基于压缩感知理论来实现图像的超分辨率重建，在利用图像的局部稀疏性先验的基础上，采取了以下两项措施：一是通过对图像降质模型的估计，采用K-奇异值分解(K-singular value decomposition, K-SVD)算法构建过完备字典对，依据同一图像高低分辨率观测在对应字典下稀疏表示系数相似的特点，将字典对所表示的高低分辨率图像间的映射关系带入目标函数中，避免了降采样和模糊算子难以抽象为矩阵形式对求解造成的影响；二是在待超分辨率图像稀疏编码时提出一种自适应加权的梯度投影稀疏重构(adaptive weighting gradient projection for sparse reconstruction, AWGPSR)算法，克服了传统正交匹配追踪(orthogonal matching pursuit, OMP)算法在这一步需要固定稀疏度的缺陷，可获得更加精确的稀疏表示系数。结合得到的稀疏表示系数与高分辨率字典可以重建出图像的高频分量，将重建的高频分量与低频部分融合可以得到最终的图像超分辨率重建结果。实验结果表明，...

Image super-resolution reconstruction via adaptive weighted compressed sensing

Compressed sensing theory is widely used to accurately reconstruct the original signal from a small number of random observations. In this paper, based on compressed sensing theory to achieve super-resolution reconstruction of images, the following two measures are taken on the basis of using the local sparsity prior of images: (1) By estimating the image degradation model, the K-SVD algorithm is used to construct the over-complete dictionary pair, and based on the similarity of high and low resolution observations of the same image in the corresponding dictionary, the mapping relationship between high and low resolution images represented by the dictionary pair is brought into the objective function, avoiding the impact of downsampling and the difficulty of abstracting the fuzzy operator into matrix form on the solution; (2) An adaptive weighted AWGPSR algorithm is proposed in the sparse coding of the super-resolution image to be sparse, which overcomes the traditional OMP algorithm that requires a fixed sparsity in this step deficiency in this step of the traditional OMP algorithm, and can obtain more accurate sparse representation coefficients. The high-frequency component of the image can be reconstructed by combining the obtained sparse representation coefficients with the high-resolution dictionary, and the final image super-resolution reconstruction result can be obtained by fusing the reconstructed high-frequency component with the low-frequency part. The experimental results show that the proposed algorithm outperforms other related methods both in terms of subjective visual and objective evaluation indexes.