Prior Information Guided Image Processing and Compressive Sensing

Signal/image processing and reconstruction based on mathematical modeling and computational techniques have been well developed and still attract much attention due to their broad applications. It becomes challenging to build mathematical models if the given data lacks some certainties. Prior information, including geometric priors, high frequency priors, spatially variant intensity variations and image regularities, assists to establish mathematical models by providing a more accurate description of the underlying signal/image. We have been exploring applications of the extracted prior information in two directions: integrating prior information into the image denoising explained in nonlocal means (NL-means) denoising framework; enhancing the compressive sensing signal/image reconstruction with the guidance of prior information.The first topic is geometric information based image denoising, where we develop a segmentation boosted image denoising scheme, balancing the removal of excessive noise and preservation of fine features. By virtue of segmentation algorithms and more general geometry extraction schemes, we are able to obtain the phase or geometric prior information. Based on the NL-means method, we introduce a mutual position function to ensure that averaging is only taken over pixels in the same image phase. To further improve the performance, we provide the respective selection scheme for the convolution kernel and the weight function. To address the unreliable segmentation due to the presence of excessive noise, the phase prior is relaxed to a more general geometric prior.The second topic is prior information guided compressive sensing signal/image reconstruction. Concerning the 1D signal reconstruction, we extract high frequency subbands as prior to boost the subsequent reconstruction. In 2D image reconstruction realm, we propose a novel two-stage intensity variation prior guided image reconstruction method using pixel-to-pixel varying weights associated to the total variation. By incorporating high order image regularity prior, we develop one total generalized variation (TGV) based image reconstruction model. Unlike the traditional wavelet which is only able to detect locations of singularities, shearlet transform can efficiently provide more geometric information of singularities in images, e.g. direction. Therefore we adopt the shearlet transform to boost the sparsity in image reconstruction algorithms. In addition, our work in signal/image denoising and reconstruction can be easily generalized to deal with other kinds of noise or measurements.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Applied Mathematics

Grantor dc:publisher

Case Western Reserve University School of Graduate Studies

Year dc:date

2013

Author dc:creator

• Qin, Jing

Contributors dc:contributor

• Guo, Weihong

• Applied Mathematics
• image denoising
• compressive sensing
• prior information

Statement dc:rights

• unrestricted
• This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.

Language dc:language

English

Repository record dc:identifier

http://rave.ohiolink.edu/etdc/view?acc_num=case1365020074

OAI identifier oai:identifier

oai:etd.ohiolink.edu:case1365020074