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In image inpainting, it is crucial that the identification and inpainting of local detail features and the preservation of global features. The models based on fractional-order partial differential equations were characterized by rich evolutionary behaviors, which allow image details to be effectively understood and a certain sharpening effect to be exhibited in image inpainting. However, issues such as inaccurate identification of large-scale features and over-sharpening are prone to be encountered. An optimal control model was proposed and the objective function was defined by the total variation energy of image global features and the constraint was formulated by a spatial fractional-order vector-valued Cahn-Hilliard equation, aiming to achieve a balanced effect between local detail restoration and preservation of global features. L2 gradient flow, H-1 gradient flow, and convex splitting were applied to design a numerical scheme for non-convex constraint conditions. And then the split bregman method was used to optimize the objective function with a dynamic grayscale adjustment strategy was introduced to maintain grayscale discrimination capability while enhancing computational efficiency. The numerical experiments demonstrate that the new model achieves an improvement on peak signal to noise ratio(PSNR) ranging from 0.371 8 dB to 9.935 2 dB compared to other methods, exhibiting strong competitiveness in terms of structural similarity(SSIM) and greater effectiveness on images with fragmental damages. Moreover, compared to traditional fractional-order equation models, the computational time is reduced by a factor of 49.50% to 52.91%.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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