Research On Total Variation Denoising And Compressed Sensing Based On Multiscale Analysis

Image denoising and representation are two basic tasks in image processing.How to efficiently denoise contaminated image and represent image with less data are issues discussed widely in recent research.Multiscale analysis can represent the image via scaling and shifting operation under multiple scales both in spatial domain and frequency domain,and extract structural features of signals under multiscale and multidirection.Therefore,multiscale analysis is an effective analysis tool in many fields including image denoising and compressed sensing.This thesis concentrates on studying the total variation denoising model based on multiscale analysis,and on the image reconstruction technique via compressed sensing with multiscale geometric analysis.The methods proposed in this thesis are also applied to the reconstruction of cross section images of photonic crystal fibers(PCFs)to evaluate optical properties.The work includes following contents:Firstly,a denoising algorithm based on the total variation model with wavelet is raised.It takes use of the gradient information of data in both low-frequency sub-band and horizontal,vertical and diagonal directions in high-frequency sub-bands in wavelet domain.This gradient information is set as the regularization term to remove the noise and preserve the image details in various scales and directions due to multiscale analysis.It can simultaneously suppress the staircase brought by total variation and the Gibbs phenomenon brought by wavelet.Secondly,a new compressed sensing based on the non-sampled Contourlet transform(NSCT)with optimal-dual-based l1 analysis is proposed.NSCT has excellent localization properties and outstanding directional selectivity within the space domain.NSCT has property of shift-invariant which enable it effectively extracts image features and provides sparser representation than Contourlet.Split Bregman algorithm is introduced here to minimize l1 optimal problem accurately with a fast convergence rate.The proposed method can reconstruct the images with detail structural information.Finally,these two proposed algorithms are applied to reconstruct the cross section images of PCFs.The compressed sensing based on optimal-dual NSCT can recover cross section images of PCFs with a small amount of data.The total variation denoising model can effectively remove the noise and the artifact brought during the compressed sensing reconstruction.The experimental results validate that these two models can work efficiently to obtain distinct boundary of air holes so that the evaluated accuracy of optical properties of PCFs can be improved.The proposed method has the distinct advantages of low cost,widely applicability and capability for evaluating properties of PCFs without the requirement of expensive apparatus.