Following the traditional total variational denoising model in removing medical image noise with blurred image texture details, among other problems, an adaptive medical image fractional-order total variational denoising model with an improved sparrow search algorithm is proposed in this study. This algorithm combines the characteristics of fractional-order differential operators and total variational models. The model preserves the weak texture region of the image improvement based on the unique amplitude-frequency characteristics of the fractional-order differential operator. The order of the fractional-order differential operator is adaptively determined by the improved sparrow search algorithm using both the sine search strategy and the diversity variation processing strategy, which can greatly improve the denoising ability of the fractional-order differential operator. The experimental results reveal that the model not only achieves the adaptivity of fractional-order total variable differential order, but also can effectively remove noise, preserve the texture structure of the image to the maximum extent, and improve the peak signal-to-noise ratio of the image; it also displays favorable prospects for applications in medical image denoising.

The idea of stacking layers is adopted to construct a deep multivariate statistical model, hierarchical canonical correlation analysis (HCCA). Its hierarchical structure is motivated form the deep network. The proposed HCCA model has the features of low computational complexity, strong correlative feature extraction, and causal interpretability. Its correlation advantages are theoretically demonstrated, then the evaluation metrics about accuracy and complexity are presented. The HCCA-based fault monitoring method is proposed for industrial processes, and the variable contributions are analyzed based on the residual statistic. The experiment results on Tennessee Eastman and real industry wastewater treatment processes show an average fault detection rate of 87.91$\%$ and 99.49$\%$. It also decreases an average false alarm rate to 0.92$\%$ and 0.32$\%$, respectively.

The traditional fractional order total variational model has better results in denoising and maintaining texture details in infrared images. However, it is difficult to determine the order of fractional order differentiation in image processing so that the model has the best denoising effect. To solve this problem, a fractional order total variational infrared image denoising model incorporating a flower pollination particle swarm optimization (PSO) algorithm is proposed in this paper. The model combines the search advantages of the flower pollination optimization algorithm and the PSO algorithm. The maximization multiobjective equation is designed as the fitness function of the optimization algorithm. The optimal order of the fractional order total variational model is found adaptively according to different features in different regions of the infrared image. The experimental results show that the improved model not only achieves the adaptivity of the adaption of the fractional order of total variational model order but also effectively removes the noise and retains the texture structure of infrared images to the maximum extent.