Regression is one of the important problems in statistical learning theory. This paper proves the global convergence of the piecewise regression algorithm based on deterministic annealing and continuity of global mini...Regression is one of the important problems in statistical learning theory. This paper proves the global convergence of the piecewise regression algorithm based on deterministic annealing and continuity of global minimum of free energy w.r.t temperature, and derives a new simplified formula to compute the initial critical temperature. A new enhanced plecewise regression algorithm by using ＂migration of prototypes＂ is proposed to eliminate ＂empty cell＂ in the annealing process. Numerical experiments on several benchmark datasets show that the new algorithm can remove redundancy and improve generalization of the piecewise regression model.展开更多
Recently, exploiting low rank property of the data accomplished by the non-convex optimization has shown great potential to decrease measurements for compressed sensing. In this paper, the low rank regularization is a...Recently, exploiting low rank property of the data accomplished by the non-convex optimization has shown great potential to decrease measurements for compressed sensing. In this paper, the low rank regularization is adopted to gradient similarity minimization, and applied for highly undersampled magnetic resonance imaging(MRI) reconstruction, termed gradient-based low rank MRI reconstruction(GLRMRI). In the proposed method,by incorporating the spatially adaptive iterative singular-value thresholding(SAIST) to optimize our gradient scheme, the deterministic annealing iterates the procedure efficiently and superior reconstruction performance is achieved. Extensive experimental results have consistently demonstrated that GLRMRI recovers both realvalued MR images and complex-valued MR data accurately, especially in the edge preserving perspective, and outperforms the current state-of-the-art approaches in terms of higher peak signal to noise ratio(PSNR) and lower high-frequency error norm(HFEN) values.展开更多
基金the National Natural Science Foundation of China(Grant Nos.60675013 and 4022500)the National Basic Research Program of China(973 Program)(Grant No.2007CB311002)
文摘Regression is one of the important problems in statistical learning theory. This paper proves the global convergence of the piecewise regression algorithm based on deterministic annealing and continuity of global minimum of free energy w.r.t temperature, and derives a new simplified formula to compute the initial critical temperature. A new enhanced plecewise regression algorithm by using ＂migration of prototypes＂ is proposed to eliminate ＂empty cell＂ in the annealing process. Numerical experiments on several benchmark datasets show that the new algorithm can remove redundancy and improve generalization of the piecewise regression model.
基金the National Natural Science Foundation of China(Nos.61362001,61503176,61661031)Jiangxi Advanced Project for Post-Doctoral Research Fund(No.2014KY02)
文摘Recently, exploiting low rank property of the data accomplished by the non-convex optimization has shown great potential to decrease measurements for compressed sensing. In this paper, the low rank regularization is adopted to gradient similarity minimization, and applied for highly undersampled magnetic resonance imaging(MRI) reconstruction, termed gradient-based low rank MRI reconstruction(GLRMRI). In the proposed method,by incorporating the spatially adaptive iterative singular-value thresholding(SAIST) to optimize our gradient scheme, the deterministic annealing iterates the procedure efficiently and superior reconstruction performance is achieved. Extensive experimental results have consistently demonstrated that GLRMRI recovers both realvalued MR images and complex-valued MR data accurately, especially in the edge preserving perspective, and outperforms the current state-of-the-art approaches in terms of higher peak signal to noise ratio(PSNR) and lower high-frequency error norm(HFEN) values.
