TY - GEN
T1 - MRA-based wavelet frames and applications
T2 - Independent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering X
AU - Dong, Bin
AU - Shen, Zuowei
PY - 2012/12/1
Y1 - 2012/12/1
N2 - Theory of wavelet frames and their applications to image restoration problems have been extensively studied for the past two decades. The success of wavelet frames in solving image restoration problems, which includes denoising, deblurring, inpainting, computed tomography, etc., is mainly due to their capability of sparsely approximating piecewise smooth functions such as images. However, in contrast to the wide applications of wavelet frame based approaches to image restoration problems, they are rarely used for some image/data analysis tasks, such as image segmentation, registration and surface reconstruction from unorganized point clouds. The main reason for this is the lack of geometric interpretations of wavelet frames and their associated transforms. Recently, geometric meanings of wavelet frames have been discovered and connections between the wavelet frame based approach and the differential operator based variational model were established.1 Such discovery enabled us to extend the wavelet frame based approach to some image/data analysis tasks that have not yet been studied before. In this paper, we will provide a unified survey of the wavelet frame based models for image segmentation and surface reconstruction from unorganized point clouds. Advantages of the wavelet frame based approach are illustrated by numerical experiments.
AB - Theory of wavelet frames and their applications to image restoration problems have been extensively studied for the past two decades. The success of wavelet frames in solving image restoration problems, which includes denoising, deblurring, inpainting, computed tomography, etc., is mainly due to their capability of sparsely approximating piecewise smooth functions such as images. However, in contrast to the wide applications of wavelet frame based approaches to image restoration problems, they are rarely used for some image/data analysis tasks, such as image segmentation, registration and surface reconstruction from unorganized point clouds. The main reason for this is the lack of geometric interpretations of wavelet frames and their associated transforms. Recently, geometric meanings of wavelet frames have been discovered and connections between the wavelet frame based approach and the differential operator based variational model were established.1 Such discovery enabled us to extend the wavelet frame based approach to some image/data analysis tasks that have not yet been studied before. In this paper, we will provide a unified survey of the wavelet frame based models for image segmentation and surface reconstruction from unorganized point clouds. Advantages of the wavelet frame based approach are illustrated by numerical experiments.
KW - (tight) wavelet frames
KW - Image segmentation
KW - split Bregman algorithm
KW - surface reconstruction
KW - variational method
UR - http://www.scopus.com/inward/record.url?scp=84874851390&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84874851390&partnerID=8YFLogxK
U2 - 10.1117/12.923203
DO - 10.1117/12.923203
M3 - Conference contribution
AN - SCOPUS:84874851390
SN - 9780819490797
T3 - Proceedings of SPIE - The International Society for Optical Engineering
BT - Independent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering X
Y2 - 25 April 2012 through 27 April 2012
ER -