Reports on Image Processing

Research Expository

• CAM 02-61 (pdf)   Tony F. Chan , Jianhong (Jackie) Shen , and Luminita Vese , Variational PDE Models in Image Processing. ( The preprint version with expanded bibliography. )
  [ Notice of American Mathematical Society . Vol 50, No.1, 14-26, Jan, 2003.]
• CAM 02-63 (pdf)  Tony F. Chan and Jianhong (Jackie) Shen, Variational Image Inpainting, 2002.
  
• CAM 02-43 (ps) ,  Stanley Osher , Level Set Method: Applciations to Imaging Science , July 2002.
• Internal Report (pdf)  Jianhong (Jackie) Shen, Inpainting & the Fundamental Problem of Image Processing, November 2002. SIAM News, 36(5), June, 2003.
  

Reconstruction & Inpainting

• Inpainting and Geometric Image Interpolation

• CAM 02-14 , Tony F. Chan and Jianhong Shen , On the Role of the BV Image Model in Image Restoration, April 2002.
  [ AMS Contemporary Mathematics, accepted (by two referees); Dedicated to Stan Osher on the occasion of his 60th birthday]
• CAM 02-11 , Sung Ha Kang, Tony F. Chan and Stefano Soatto , Landmark Based Inpainting from Multiple Views March 2002.
  


• CAM 02-31 , Sung Ha Kang, Tony F. Chan and Stefano Soatto , Inpainting from Multiple Views March 2002. (4 Page version of CAM 02-11.)
• CAM 01-26 , Selim Esedoglu and Jianhong (Jackie) Shen , Digital Inpainting Based on the Mumford-Shah-Euler Image Model, September 2001.
  [European J. Appl. Math., 13, pp. 353-370, 2002]
• CAM 01-15 , Tony Chan and Jianhong (JACKIE) Shen, Morphologically Invariant PDE Inpainting , May 2001.
  [IEEE, submitted 2001]
• CAM 01-12 , Tony Chan, Sung Ha Kang and Jianhong Shen, Euler's Elastica and Curvature Based Inpainting , April 2001.
  [SIAM J. Appl. Math., 63(2): pp.564-592, 2002]
• CAM 00-35 , Tony Chan and Jianhong Shen, Non-Texture Inpainting by Curvature-Driven Diffusions (CDD), September 2000.
  [J. Visual Comm. Image Rep., 12(4),436-449, 2001]
• CAM 00-11 , Tony Chan and Jianhong Shen , Mathematical Models for Local Non-Texture Inpainting, March 2000.
  [SIAM J. Appl. Math, 62(3), 1019-1043, 2001]

• Non-Flat Image Features: Representation & Restoration

• CAM 00-25 , Tony Chan, Sung Ha Kang and Jianhong Shen , Total Variation Denoising and Enhancement of Color Images Based on the CB and HSV Color Representation , June 2000.
  [J. Visual Comm. Image Rep., 12(4), 422-435, 2001]
• Internal Report , Tony Chan and Jianhong Shen, Rotational Invariance for Prior Models in Image Analysis , 2000.
• CAM 99-20 , Tony Chan and Jianhong Shen, Variational Restoration of Non-Flat Image Features: Models and Algorithms , June 1999.
  [SIAM J. Appl. Math., 61(4):1338-1361, 2000]

• Vector Valued Images ( Color Images )

• CAM 00-25 , Tony Chan, Sung Ha Kang and Jianhong Shen , Total Variation Denoising and Enhancement of Color Images Based on the CB and HSV Color , June 2000
  [J. of Visual Comm. and Image Rep, 12(4), 422-435, 2001]
• CAM 99-35 , Tony Chan, B. Yezrielev Sandberg and Luminita A. Vese , Active Contours without Edges for Vector-Valued Images , October 1999
  [J. of Visual Comm. and Image Rep. June 2000]
• CAM 98-30 , Peter Blomgren, Total Variation Methods for Restoration of Vector Valued Images (Ph.D. thesis), June 1998.
• CAM 96-5 , Peter Blomgren and Tony F. Chan, Color TV: Total Variation Methods for Restoration of Vector Valued Images , February 1996.
  [IEEE Image proc. March 1998]

• (Blind) Deconvolution and Deblurring

• CAM 99-19 , Tony F. Chan and C.K. Wong, Convergence of the Alternating Minimization Algorithm for Blind Deconvolution , June 1999.
• CAM 98-22 , C.R. Vogel, T.F. Chan and R. Plemmons , B Fast Algorithms for Phase-Diversity-Based Blind Deconvolution , April 1998.
• CAM 96-45 , Tony F. Chan and C.K. Wong, Total Variation Blind Deconvolution, November 1996.
  [IEEE Image Proc. March 1998.

• CAM 00-45 Francois Malgouyres , Combining Total Variation and Wavelet Packet Approach for Image Deblurring, December 2000.
• CAM 00-39 Francois Malgouyres , Convolution Approximation by Mean of an Operator Diagonal in a Wavelet Packet Basis and Application to Image Deblurring, November 2000.
• CAM 99-5 , Antonio Marquina and Stanley Osher, Explicit Algorithms for a New Time Dependent Model Based on Level Set Motion for Nonlinear Deblurring and Noise Removal, January 1999.
• CAM 97-44 ,Raymond H. Chan, Tony F. Chan, and Chiu-Kwong Wong Cosine Transform Based Preconditioners of Total Variation Deblurring , September 1999.
  [IEEE Image Proc. Oct 1999]
  
  
• Denoising and Enhancement

• CAM 02-57 , Stanley Osher, Andres Sole, and Luminita Vese, Image decomposition and restoration using total variation minimization and the $H^{-1$ norm} , October 2002.
• CAM 02-56 , Tolga Tasdizen, Ross Whitaker, Paul Burchard and Stanley Osher , Geometric Surface Smoothing via Anisotropic Diffusion of Normals , October 2002.
• CAM 02-55 , Mark L. Green, Statistics of Images, the TV Algorithm of Rudin-Osher-Fatemi for Image Denoising and an Improved Denoising Algorithm , October 2002. 
• CAM 99-34 , Tony F. Chan, Stanley Osher, and Jianhong Shen , The Digital TV Filter and Nonlinear Denoising ,Oct 1999.
  [IEEE Trans. Image Process., 10(2):231-241, 2001]
• CAM 00-25 , Tony F. Chan, Sung Ha Kang, and Jianhong Shen , Total Variation Denoising and Enhancement of Color Images Based on the CB and HSV Color Representation , June 2000.
  [J. Visual Comm. Image Rep., 12(4), 422-435, 2001]

• Video Restoration

• CAM 02-64 ,  Jianhong Shen, Bayesian Video Dejittering by BV Image Model , December 2002.
  
  

Computational Techniques 

• Numerical Methods
• CAM 01-22 , Luminita A. Vese and Stanley Osher , Numerical Methods for $p-harmonic$ Flows and Applications to Image Processing , August 2001
  
• The Digital TV Filter on Graphs and Lattices
• CAM 99-34 , Tony Chan, Stanley Osher and Jianhong Shen , The Digital TV Filter and Nonlinear Denoising ,Oct 1999.
  [IEEE Trans. Image Process., 10(2):231-241, 2001]
• Preconditioners
• CAM 99-17 , Michael K. Ng, Raymond H. Chan, Tony F. Chan and Andy M. Yip, Cosine Transform Preconditioners for High Resolution Image Reconstruction, April 1999.
• CAM 99-6 , Raymond H. Chan, Tony F. Chan, Michael K. Ng, Wun-Cheung Tang and Chiu-Kwong Wong, Preconditioned Iterative Methods for High-resolution Image Reconstruction with Multisensors , February 1999.
• CAM 97-58 , Tony Chan and Victor Eijkhout, Design of a Library of Parallel Preconditioners, December 1997
• CAM 97-44 , Raymond H. Chan, Tony F. Chan, and Chiu-Kwong Wong . Cosine Transform Based Preconditioners of Total Variation Deblurring, September 1997.
• CAM 97-34 , T. F. Chan, W. P. Tang, and W. L. Wan, Wavelet Sparse Approximate Inverse Preconditioners, August 1997
• CAM 97-24 , Victor Eijkhout and Tony Chan, ParPre: A Parallel Preconditioners Package reference manual for version 2.0.17 , June 1997
• CAM 96-33 Tony F. Chan, W. P. Tang, and W. L. Wan, Wavelet Sparse Approximate Inverse Preconditioners, September 1996
• CAM 95-23 , Raymond H. Chan, Tony F. Chan and Chiu-Kwong Wong , Cosine Transform Based Preconditioners for Total Variation Minimization Problems in Image Processing , April 1995.
• Functional Approximations
• CAM 98-35 , Tony Chan, Antonio Marquina and Pep Mulet , Second Order Differential Functionals in Total Variation-Based Image Restoration, August 1998.
• CAM 97-56 , Luminita Vese and Tony F. Chan, Reduced Non-Convex Functional Approximations for Image Restoration & Segmentation , December 1997.
• Iterative Methods
• CAM 98-29 , Wing Lok Wan, Scalable and Multilevel Iterative Methods, (Ph.D. thesis), June 1998
• CAM 96-38 , Tony F. Chan and Pep Mulet, Iterative Methods for Total Variation Image Restoration, October 1996.
  [SIAM J. Num. Anal, vol. 36 1999]
• Modular Solvers
• CAM 97-52 , Peter Blomgren and Tony F. Chan, Modular Solvers for Constrained Image Restoration , November 1997.
  [Submitted to IEEE Transactions on Image Processing].
• Total Variation
• CAM 02-13 , Jamylle Laurice Carter , Dual Methods for Total Variation-Based Image Restoration (Ph.D. Thesis) , April 2002
• CAM 00-40 , Francois Malgouyres , Total Variation Based Oversampling of Noisy Images, December 2000
• CAM 00-38 , David M. Strong and Tony F. Chan , Edge-Preserving and Scale-Dependent Properties of Total Variation Regularization , October 2000
  [SIAM Journal on Applied Mathematics, submitted 2000]
• CAM 97-50 , Peter Blomgren, Tony F. Chan, Pep Mulet, and C.K. Wong, Total Variation Image Restoration: Numerical Methods and Extensions , October 1997.
  [IEEE image proc. Proceedings of the 1997 IEEE International Conference on Image Processing.]
• CAM 97-42 , Peter Blomgren, Tony F. Chan, and Pep Mulet . Extensions to Total Variation Denoising, September 1997.
  [Proceedings of SPIE. vol 3162]
• CAM 97-38 , David M. Strong, Adaptive Total Variation Minimizing Image Restoration (Ph.D. Thesis), August 1997
• CAM 96-41 , David M. Strong and Tony F. Chan, Exact Solutions to the Total Variation Regularization Problem , October 1996.
• CAM 96-7 , David M. Strong and Tony F. Chan, Relation of Regularization Parameter and Scale in Total Variation Based Image Denoising, February 1996.
• Fixed Point Methods
• CAM 97-46 , Tony F. Chan and Pep Mulet. On the Convergence of the Lagged Diffusivity Fixed Point Method in Total Variation Image Restoration, September 1997.
• Spatially Adaptive TV
• CAM 97-32 , David M. Strong, Peter Blomgren, and Tony F. Chan , Spatially Adaptive Local Feature-Driven Total Variation Minimizing Image Restoration, July 1997.
  [Proceedings of SPIE. vol 3167]
• CAM 96-46 , David M. Strong and Tony F. Chan, Spatially and Scale Adaptive Total Variation Based Regularization and Anisotropic Diffusion in Image Processing , November 1996.
• Multigrid for Differential-Convolution
• CAM 97-20 , Raymond H. Chan, Tony F. Chan and W.L. Wan , Multigrid for Differential-Convolution Problems Arising from Image Processing, May 1997.
• Primal_Dual
• CAM 02-13 , Jamylle Laurice Carter , Dual Methods for Total Variation-Based Image Restoration (Ph.D. Thesis), April 2002
• CAM 95-43 Tony F. Chan, Gene H. Golub, and Pep Mulet, A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration , September 1995
• Continuation Method
• CAM 95-28, Tony F. Chan, H.M. Zhou and Raymond H. Chan , Continuation Method for Total Variation Denoising Problems , June 1995.
• CAM 95-18 , Tony F. Chan, H.M. Zhou, and Raymond H. Chan , Continuation Method for Total Variation Denoising Problems, April 1995.

Segmentations

• CAM 01-25 , Luminita A. Vese and Tony F. Chan , A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model, September 2001
• Level Set Methods
• CAM 00-14 , Tony Chan and Luminita A. Vese , Image Segmentation Using Level Sets and the Mumford-Shah Model , April 2000
• CAM 00-13 , Tony Chan and Luminita A. Vese , A Level Set Algorithm for Minimizing the Mumford-Shah Functional in Image Processing, April 2000
• Active Contours
• CAM 00-41 , Tony Chan and Luminita A. Vese , Active Contour and Segmentation Models Using Geometric PDE's for Medical Imaging, December 2000
• CAM 99-35 , Tony Chan, B. Yezrielev Sandberg and Luminita A. Vese , Active Contours without Edges for Vector-Valued Images , October 1999
• CAM 98-53 , Tony Chan and Luminita A. Vese , Active Contours Without Edges, December 1998
  [IEEE Image Proc. Feb 2001]
• CAM 97-56 , Luminita Vese and Tony F. Chan, Reduced Non-Convex Functional Approximations for Image Restoration & Segmentation , December 1997.
• CAM 97-47 , Tony Chan and Luminita Vese, Variational Image Restoration & Segmentation Models and Approximations , September 1997.

Level Set Methods

• CAM 01-05 , Yen-Hsi Richard Tsai, Yoshikazu Giga and Stanley Osher , A Level Set Approach for Computing Discontinuous Solutions of a Class of Hamilton-Jacobi Equations , February 2001
• CAM 01-01 , Hong-Kai Zhao, Stanley Osher and Ronald Fedkiw , Implicit Surface Reconstruction and Deformation Using the Level Set Method, January 2001
• CAM 00-37 , Li-Tien Cheng, Ronald P. Fedkiw, Frederic Gibou and Myungjoo Kang, A Symmetric Method for Implicit Time Discretization of the Stefan Problem, October 2000
• CAM 00-36 , Yen-Hsi Richard Tsai , Rapid and Accurate Computation of the Distance Function Using Grids. , October 2000
• CAM 00-32 , Li-Tien Cheng, Paul Burchard, Barry Merriman and Stanley Osher , Motion of Curves Constrained on Surfaces Using a Level Set Approach , September 2000
• CAM 00-31 , Stanley J. Osher and Fadil Santosa , Level Set Methods for Optimization Problems Involving Geometry and Constraints I. Frequencies of a Two-Density Inhomogeneous Drum , August 2000
• CAM 00-29 , Paul Burchard, Li-Tien Cheng, Barry Merriman and Stanley Osher , Motion of Curves in Three Spatial Dimensions Using a Level Set Approach , July 2000
• CAM 00-23 , Marcelo Bertalmio, Li-Tien Cheng, Stanley Osher and Guillermo Sapiro , Variational Problems and Partial Differential Equations on Implicit Surface : The Framework and Examples in Image Processing and Pattern Formation , June 2000
• CAM 00-20 , Li-Tien Cheng , The Level Set Method Applied to Geometrically Based Motion, Materials Science, and Image Processing, (Ph.D. Thesis), June 2000
• CAM 00-18 , Hyeseon Shim , Level Set Based Simulations of Two-Phase Oil-Water Flows in Pipes, May 2000
• CAM 00-14 , Tony Chan and Luminita A. Vese , Image Segmentation Using Level Sets and the Mumford-Shah Model , April 2000
• CAM 00-13 , Tony Chan and Luminita A. Vese , A Level Set Algorithm for Minimizing the Mumford-Shah Functional in Image Processing, April 2000
• CAM 00-08 , Stanley Osher and Ronald P. Fedkiw Level Set Methods , February 2000
• CAM 00-03 , Susan Chen, Barry Merriman, Myungjoo Kang, Russel E. Caflisch, Christian Ratsch, Li-Tien Cheng, Mark Gyure, Ronald P. Fedkiw and Stanley Osher, Level Set Method for Thin Film Epitaxial Growth, January 2000
• CAM 99-22 , Steven J. Ruuth, Barry Merriman and Stanley Osher , A Fixed Grid Method for Capturing the Motion of Self-Intersecting Interfaces and Related PDEs, July 1999
• CAM 99-3 , Barry Merriman, Russel Caflisch, Stanley Osher, Christian Ratsch, Susan Chen and Myungjoo Kang, Island Dynamics and Level Set Methods for Continuum Modeling of Epitaxial Growth , January 1999
• CAM 99-1 , Guojun Liao, Feng Liu, Gary C. de la Pena, Danping Peng, and Stanley Osher, Level Set Based Deformation Methods for Adaptive Grids, January 1999
• CAM 98-25, Danping Peng, Barry Merriman, Stanley Osher, Hongkai Zhao and M. Kang, A PDE Based Fast Local Level Set Method , April 1998
• CAM 98-20 , Russel E. Caflisch, Mark Gyure, Barry Merriman, Stanley Osher, Christian Ratsch, Dimitri Vvedensky and Jenna Zinck , Island Dynamics and the Level Set Method for Epitaxial Growth , April 1998
• CAM 98-10 , Barry Merriman, Russel Caflisch and Stanley Osher , Level Set Methods, with an Application to Modeling the Growth of Thin Films, February 1998
• CAM 98-7 , Hong-Kai Zhao, Stanley Osher, Barry Merriman and Myungjoo Kang, Implicit, Nonparametric Shape Reconstruction from Unorganized Points Using A Variational Level Set Method, February 1998 (revised February 1999)
• CAM 96-39 , Hong-Kai Zhao, Barry Merriman, Stanley Osher, Lihe Wang , Capturing the Behavior of Bubbles and Drops Using the Variational Level Set Approach, October 1996
• CAM 96-21 , S. Chen, B. Merriman, S. Osher and P. Smereka , A Simple Level Set Method for Solving Stefan Problems , July 1996
• CAM 96-19 Myungjoo Kang, A Level Set Approach for the Motion of Soap Bubbles with Curvature Dependent Velocity or Acceleration , (Ph.D. thesis), July 1996
• CAM 95-36 , Hong-Kai Zhao, T. Chan, B. Merriman and S. Osher , A Variational Level set Approach to Multiphase Motion , July 1995

Compressions

• CAM 00-27 , Tony F. Chan and H.M. Zhou , Optimal Construction of Wavelet Coefficients Using Total Variation Regularization in Image Compression, July 2000
• CAM 00-21 , Hao Min Zhou , Wavelet Transforms and PDE Techniques in Image Compression,(Ph.D. Thesis) , June 2000
• CAM 98-12 , Tony Chan and Hao Min Zhou , Feature Preserving Lossy Image Compression Using Nonlinear PDE's March 1998
  [IEEE Proceedings Data Comp. Conf. 1998]

Wavelets

• Internal Report,   Jianhong Shen , A Note on Wavelets and Diffusions, J. Comput. Anal. Appl., vol.5, no. 1, 2003.
• CAM 00-45 , Francois Malgouyres, Combining Total Variation and Wavelet Packet Approach for Image Deblurring , December 2000
• CAM 00-39 , Francois Malgouyres, Convolution Approximation by Mean of an Operator Diagonal in a Wavelet Packet Basis and Application to Image Deblurring, November 2000
• CAM 00-27 , Tony F. Chan and H.M. Zhou , Optimal Construction of Wavelet Coefficients Using Total Variation Regularization in Image Compression, July 2000
• CAM 00-26 , Tony F. Chan and Ke Chen , Two-Stage Preconditioners using Wavelet Band Splitting and Sparse Approximation, July 2000
• CAM 00-21 , Hao Min Zhou , Wavelet Transforms and PDE Techniques in Image Compression,(Ph.D. Thesis) , June 2000
• CAM 99-21 , Tony Chan and Hao Min Zhou , Adaptive ENO-Wavelet Transforms for Discontinuous Functions , June 1999
• CAM 99-18 , Jianhong Shen and Gilbert Strang, On Wavelets Fundamental Solutions to the Heat Equation -- Heatlets , May 1999
• CAM 97-34 , T. F. Chan, W. P. Tang, and W. L. Wan, Wavelet Sparse Approximate Inverse Preconditioners, August 1997
• CAM 96-33 Tony F. Chan, W. P. Tang, and W. L. Wan, Wavelet Sparse Approximate Inverse Preconditioners, September 1996

Tomography

• CAM 98-48 , Elias Jonsson, Sung-Cheng Huang and Tony Chan , Total Variation Regularization in Positron Emission Tomography , November 1998