论文标题
具有全球Optima保证的InVex正规化器改进成像
Improved Imaging by Invex Regularizers with Global Optima Guarantees
论文作者
论文摘要
图像重建通过正规化器增强，例如，在图像上执行稀疏性，低等级或平滑性先验，在视觉任务中有许多成功的应用，例如计算机摄影，生物医学和光谱成像。人们已经很高兴的是，在重建质量方面，非凸正规化器通常比凸的正规化器表现更好。但是，他们的收敛分析仅被确定为关键点，而不是全球最佳选择。为了减轻全球最佳选择的保证损失，我们建议应用\ textit {invexity}的概念，并提供第一个证明的INVEX正规化器的列表，以改善图像重建。此外，在通过这种invex正则化改进后，我们为各种先进的图像重建技术建立了融合保证，可为全局最佳选择。据我们所知，这是使用INVEX正则化以通过全球最佳保证来改善成像的第一项实用工作。为了证明INVEX正则化的有效性，使用基准数据集进行了数值实验，以实现各种成像任务。
Image reconstruction enhanced by regularizers, e.g., to enforce sparsity, low rank or smoothness priors on images, has many successful applications in vision tasks such as computer photography, biomedical and spectral imaging. It has been well accepted that non-convex regularizers normally perform better than convex ones in terms of the reconstruction quality. But their convergence analysis is only established to a critical point, rather than the global optima. To mitigate the loss of guarantees for global optima, we propose to apply the concept of \textit{invexity} and provide the first list of proved invex regularizers for improving image reconstruction. Moreover, we establish convergence guarantees to global optima for various advanced image reconstruction techniques after being improved by such invex regularization. To the best of our knowledge, this is the first practical work applying invex regularization to improve imaging with global optima guarantees. To demonstrate the effectiveness of invex regularization, numerical experiments are conducted for various imaging tasks using benchmark datasets.
