To solve the problems of incomplete reconstruction, blurred boundary and residual noise in Magnetic Resonance (MR) image reconstruction, a non-convex total variation regularization reconstruction model based on L ₂ regularization was proposed. First, Moreau envelope and minmax-concave penalty function were used to construct the non-convex regularization of L ₂ norm, then it was applied into the total variation regularization to construct the sparse reconstruction model based on the isotropic non-convex total variation regularization. The proposed non-convex regularization was able to effectively avoid the underestimation of larger non-zero elements in convex regularization, so as to reconstruct the edge contour of the target more effectively. At the same time, it was able to guarantee the global convexity of objective function under certain conditions. Therefore, Alternating Direction Method of Multipliers (ADMM) was able to be used to solve the model. Simulation experiments were carried out to reconstruct several MR images under different sampling templates and sampling rates. Experimental results show that compared with several typical image reconstruction methods, the proposed model has better performance and lower relative error, its Peak Signal-to-Noise Ratio (PSNR) is significantly improved, which is 4 dB higher than that of traditional reconstruction method based on the non-convex regularization of L ₁ norm; in addition, the visual effects of the reconstructed images are promoted significantly, effectively maintaining the edge details of the original images.

DV-Hop localization algorithm uses the hop count multiplied by the average distance per hop to estimate the distance between nodes. Under the condition of not changing the step of the original DV-Hop algorithm and not needing an additional hardware, the traditional DV-Hop algorithm was improved from two aspects to solve the problem of the large error in the localization. On the one hand, the hop count between the nodes based on the communication radius was corrected. On the other hand, with the help of the deviation between the actual distance and the estimated distance of the beacon nodes, the average hop distance per hop was corrected. In the same network environment, the positioning error of the proposed algorithm was effectively reduced by about 15% compared with the original DV-Hop algorithm, as well as reduced by 5%-7% compared with another improved algorithm which also used the ideal estimated hop count value between the beacon nodes to correct the actual value between them.The experimental results show that the proposed algorithm can effectively reduce the distance estimation error between nodes and improve the positioning accuracy.

DV-Hop algorithm uses the hop number multiplied by the average distance per hop to estimate the distance between nodes and the trilateral measurement or the maximum likelihood to estimate the node coordinate information, which has defects and then causing too many positioning errors. This paper presented an improved DV-Hop algorithm based on node density regional division (Density Zoning DV-Hop, DZDV-Hop), which used the connectivity of network and the node density to limit the hop number of the estimated node coordinate information and the weighted centroid method to estimate the positioning coordinates. Compared with the traditional DV-Hop algorithm in the same network hardware and topology environment, the result of Matlab simulation test shows that, the communication amount of nodes can be effectively reduced and the positioning error rate can be reduced by 13.6% by using the improved algorithm, which can improve the positioning accuracy.