Wavelet inverse scale space for image restoration

This paper proposes a model for image restoration by combining the wavelet shrinkage and inverse scale space （ISS） method. The ISS is applied to the wavelet representation to modify the retained wavelet coefficients, and the coefficients smaller than the threshold are set to zero. The curvature term of the ISS can remove the edge artifacts and preserve sharp edges. For the multiscale interpretation of the ISS and the multiscale property of the wavelet representation, small details are preserved. This paper illustrates that the wavelet ISS model can be deduced from the wavelet based on a total variation minimization problem. A stopping criterion is obtained from this minimization in the sense of the Bregman distance in the wavelet domain. Numerical examples show the improvement for the image denoising with the proposed method in the sense of the signal to noise ratio and with fewer details remained in the residue.

Real-Time Automatic Scaling Method of Oblique Ionogram Parameters Based on Morphological Operator and Inversion Technique

Automatic scaling ionogram can get the parameters of ionogram which are vital to ionosphere detecting. In this paper, a new method is proposed to scale F2 layer trace automatically from oblique ionogram based on morphological operator and inversion technique. This method is verified through the comparison of actual detecting data with statistical analysis. The results show that the proposed automatic scaling method has high acceptable rate and is suitable for scaling oblique ionogram with different high angle wave states. It is fast and precise to fit O-mode echoes in F2 layer without the influence from F1 layer. This method could be applied in real-time ionospheric oblique sounding research with high reliability and versatility.

PIECEWISE SPARSE RECOVERY VIA PIECEWISE INVERSE SCALE SPACE ALGORITHM WITH DELETION RULE

In some applications,there are signals with piecewise structure to be recovered.In this paper,we propose a piecewise_ISS(P_ISS)method which aims to preserve the piecewise sparse structure(or the small-scaled entries)of piecewise signals.In order to avoid selecting redundant false small-scaled elements,we also implement the piecewise_ISS algorithm in parallel and distributed manners equipped with a deletion rule.Numerical experiments indicate that compared with alSS,the P_ISS algorithm is more effective and robust for piecewise sparse recovery.

A GREEDY ALGORITHM FOR SPARSE PRECISION MATRIX APPROXIMATION

Precision matrix estimation is an important problem in statistical data analysis.This paper proposes a sparse precision matrix estimation approach,based on CLIME estimator and an efficient algorithm GISSP that was originally proposed for li sparse signal recovery in compressed sensing.The asymptotic convergence rate for sparse precision matrix estimation is analyzed with respect to the new stopping criteria of the proposed GISSP algorithm.Finally,numerical comparison of GISSP with other sparse recovery algorithms,such as ADMM and HTP in three settings of precision matrix estimation is provided and the numerical results show the advantages of the proposed algorithm.