The traditional Total Variation (TV) minimization algorithm is a classical iterative reconstruction algorithm based on Compressed Sensing (CS), and can accurately reconstruct images from sparse and noisy data. However, the block artifacts may be brought by the algorithm during the reconstruction of image having not obvious piecewise constant feature. Researches show that the use of High Order Total Variation (HOTV) in the image denoising can effectively suppress the block artifacts brought by the TV model. Therefore, a HOTV image reconstruction model and its Chambolle-Pock (CP) solving algorithm were proposed. Specifically, the second order TV norm was constructed by using the second order gradient, then a data fidelity constrained second order TV minimization model was designed, and the corresponding CP algorithm was derived. The Shepp-Logan phantom in wave background, grayscale gradual changing phantom and real CT phantom were used to perform the image reconstruction experiments and qualitative and quantitative analysis under ideal data projection and noisy data projection conditions. The reconstruction results of ideal data projection show that compared to the traditional TV algorithm, the HOTV algorithm can effectively suppress the block artifacts and improve the reconstruction accuracy. The reconstruction results of noisy data projection show that both the traditional TV algorithm and the HOTV algorithm have good denoising effect but the HOTV algorithm is able to protect the image edge information better and has higher anti-noise performance. The HOTV algorithm is a better reconstruction algorithm than the TV algorithm in the reconstruction of image having not obvious piecewise constant feature and obvious grayscale fluctuation feature. The proposed HOTV algorithm can be extended to CT reconstruction under different scanning modes and other imaging modalities.

In classical heuristic attribute reduction algorithm for positive region, the attribute with the maximum dependency degree of the current positive domain should be added into the selected feature attribute subset in each iteration, leading to the large number of iterations and the low efficiency of the algorithm, and making the algorithm hard to be applied in the feature selection of high-dimensional and large-scale datasets. In order to solve the problems, the monotonic relationship between the positive regions in a decision system was studied and the formal description for the Multi-Scale Attribute Granule (MSAG) was given, and a Multi-scale Attribute Granule based Quick Positive Region reduction algorithm (MAG-QPR) was proposed. Each MSAG contains several attributes and can provide a large positive region for the selected feature attribute subset. As a result, adding MSAG in each iteration can reduce the number of the iteration and make the selected feature attribute subset more quickly approach to the positive region resolving ability of the condition attribute universal set. Therefore, the computational efficiency of the heuristic attribute reduction algorithm for positive region is improved. With 8 UCI datasets used for experiments, on the datasets Lung Cancer, Flag and German, the running time acceleration ratios of MAG-QPR to the general improved Feature Selection algorithm based on the Positive Approximation-Positive Region (FSPA-PR), the general improved Feature Selection algorithm based on the Positive Approximation-Shannon's Conditional Entropy (FSPA-SCE), the Backward Greedy Reduction Algorithm for positive region Preservation (BGRAP) and the Backward Greedy Reduction Algorithm for Generalized decision preservation (BGRAG) are 9.64, 15.70, 5.03, 2.50; 3.93, 7.55, 1.69, 4.57; and 3.61, 6.49, 1.30, 9.51 respectively. The experimental results show that, the proposed algorithm MAG-QPR can improve the algorithm efficiency and has better classification accuracy.