A NONLOCAL KRONECKER-BASIS-REPRESENTATION METHOD FOR LOW-DOSE CT SINOGRAM RECOVERY

Low-dose computed tomography(LDCT)contains the mixed noise of Poisson and Gaus-sian,which makes the image reconstruction a challenging task.In order to describe the statistical characteristics of the mixed noise,we adopt the sinogram preprocessing as a stan-dard maximum a posteriori(MAP).Based on the fact that the sinogram of LDCT has non-local self-similarity property,it exhibits low-rank characteristics.The conventional way of solving the low-rank problem is implemented in matrix forms,and ignores the correlations among similar patch groups.To avoid this issue,we make use of a nonlocal Kronecker-Basis-Representation(KBR)method to depict the low-rank problem.A new denoising model,which consists of the sinogram preprocessing for data fidelity and the nonlocal KBR term,is developed in this work.The proposed denoising model can better illustrate the generative mechanism of the mixed noise and the prior knowledge of the LDCT.Nu-merical results show that the proposed denoising model outperforms the state-of-the-art algorithms in terms of peak-signal-to-noise ratio(PSNR),feature similarity(FSIM),and normalized mean square error(NMSE).

IMPULSE NOISE REMOVAL BY L1 WEIGHTED NUCLEAR NORM MINIMIZATION

In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research interest.By assigning different weights to singular values,the weighted nuclear norm minimization(WNNM)has been utilized in many applications.However,most of the work on WNNM is combined with the l 2-data-fidelity term,which is under additive Gaussian noise assumption.In this paper,we introduce the L1-WNNM model,which incorporates the l 1-data-fidelity term and the regularization from WNNM.We apply the alternating direction method of multipliers(ADMM)to solve the non-convex minimization problem in this model.We exploit the low rank prior on the patch matrices extracted based on the image non-local self-similarity and apply the L1-WNNM model on patch matrices to restore the image corrupted by impulse noise.Numerical results show that our method can effectively remove impulse noise.

Univoque graphs for non-integer base expansions

Unique expansions in non-integer bases have been investigated in many papers during the last thirty years.They are often conveniently generated by labeled directed graphs.We give a precise description of the set of sequences generated by these graphs.This provides a geometric explanation of many former abstract results in this domain.Our results are illustrated by many examples.