基於我們近期在影像去噪和影像分割研究的成功經驗，在這個三年期的研究計畫中，我們將針對影像處理中的幾個基本問題，探索其自適應變分模型及開發有效的數值計算方法。我們主要將關注下列三個影像處理主題，這些基礎議題經常來自影像處理的眾多應用問題之中：影像對比強化、影像融合、和影像超解析度重建。(1) 影像對比強化：我們將研究自適應變分模型應用於低光度影像的對比強化，其中所期望的新影像梯度接近所給定的影像，同時減低變異數以達到不均勻照明的平衡。我們亦將證明分割的Bregman迭代法可以有效地求解該自適應變分模型。(2) 影像融合：影像融合的主要目標是整合多個來源影像，將同一場景融合變成一張更具信息性的影像。我們將研究一種基於一階和二階梯度信息的自適應變分影像融合模型。其中第一要務是探索特徵選擇的策略，然後將此策略整合進該自適應變分影像融合模型中。 (3) 影像超解析度重建：影像超解析度重建的目標是採取一組包含一個或多個低解析度的輸入影像，在沒有信噪比損失的情況下提升影像的解析度。我們將結合影像填補的變分技術，極小化某一種自適應能量泛函，以重建更高解析度的影像。本年度申請主持科技部各類研究計畫共三件(含預核)，本件優先順序為第一！ ;Based on our recent successful experiences in the study of image denoising and image segmentation, in this three-year project, we are going to explore adaptive variational models and to develop efficient numerical methods for some fundamental issues in the image processing. We will mainly focus on the following three image processing tasks which are frequently arising from numerous applications: contrast enhancement, fusion, and super-resolution reconstruction. (1) Image contrast enhancement: We will study an adaptive variational model for contrast enhancement of low-light images, in which the gradient of the desired new image is close to that of given image but with reduced variance to balance inhomogeneous illumination. We will show that this adaptive variational model can be solved efficiently by using the split Bregman iterative scheme. (2) Image fusion: The main goal of image fusion is to integrate several sources images of the same scene into a more informative image. We will study an adaptive variational image fusion model based on the first and second-order gradient information. The first task is to explore a feature selection strategy which is then integrated into the adaptive variational model for image fusion. (3) Image super-resolution reconstruction: The objective of super-resolution reconstruction is to take a set of one or more low-resolution input images of a scene to increase the spatial resolution without a loss in signal-to-noise ratio. Combining with the image inpainting techniques, we will minimize an adaptive energy functional to reconstruct a higher-resolution image.
