用于简化图像分割的高效的基于梯度的$\ell^0$超分辨率
Efficient $\ell^0$ gradient-based Super Resolution for simplified image segmentation
摘要：
在目标图像梯度稀疏的假设下，考虑了一种单图像超分辨率的变分模型。我们通过考虑结合二次数据保真度的图像梯度上的各向同性和各向异性$\ell^0$正则化来执行此假设，类似于[1]中针对一般信号恢复问题所研究的。对于该模型的数值实现，我们提出了一种新的高效ADMM分裂算法，其子步骤的解决方案计算效率高的硬阈值和标准的共轭梯度求解器。我们在高度退化的合成和真实世界数据上测试了我们的模型，并将我们的结果与几种变分方法以及最先进的深度学习技术进行了定量比较。我们的实验表明，$\ell^0$梯度正则化的超分辨率图像可以有效地用于提高标准分割算法的准确性时，适用于QR和细胞检测，和土地覆盖分类问题，在通过其他方法实现的结果相比。
英文摘要：
We consider a variational model for single-image super-resolution based on the assumption that the gradient of the target image is sparse. We enforce this assumption by considering both an isotropic and an anisotropic $\ell^0$ regularisation on the image gradient combined with a quadratic data fidelity, similarly as studied in [1] for general signal recovery problems. For the numerical realisation of the model, we propose a novel efficient ADMM splitting algorithm whose substeps solutions are computed efficiently by means of hard-thresholding and standard conjugate-gradient solvers. We test our model on highly-degraded synthetic and real-world data and quantitatively compare our results with several variational approaches as well as with state-of-the-art deep-learning techniques. Our experiments show that $\ell^0$ gradient-regularised super-resolved images can be effectively used to improve the accuracy of standard segmentation algorithms when applied to QR and cell detection, and landcover classification problems, in comparison to the results achieved by other approaches.
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