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In this paper, we propose a low-rank matrix completion and cellular automaton model to effectively exploit the nonlocal inter-pixel correlation for image interpolation and enhancement applications. Different from tasks such as image denoising, in image interpolation and colour demosaicking, the many visually unpleasant artefacts (for example, ringing effects and zipper artefacts) are generally fine scale structures and lead to small singular values of the data matrix, and therefore, we propose to use L0-norm, instead of the relaxed L1-norm, to regularise the singular values so that the fine scale artefacts can be effectively removed without affecting the large-scale image edges. The entire framework can be applied for extended matrix arrangement. We also incorporate a cellular automaton model with inter-pixel correlations and extend it for image interpolation. Experimental results show that the proposed method produces reasonably good results as compared with state-of-the-arts in terms of both peak signalto-noise ratio measure and subjective visual quality.

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To understand the quantile regression model, research on a statistical analysis of advanced mathematics teaching quality evaluation was proposed. In the research, based on the test bank and questionnaires, statistical analysis was applied to examine the quality of the test bank and investigate the factors affecting the teaching quality, to understand the students’ scores, find the main factors affecting the teaching quality and use them to analyze the students’ learning status and learning quality. This will help teachers understand and grasp the students’ learning process and improve their teaching ability. And it can provide a theoretical basis for qualitative and quantitative analysis to further improve the high quality.