Contents

1 Sparse Optimization
 1.1 ₁-Minimization
 1.2 Iterative Support Detection
 1.3 Total Variation Minimization
2 Computational Optimization
 2.1 Optimization on Manifold
3 Image Processing
 3.1 Total Variation Minimization
 3.2 Face Recognition / Processing
 3.3 Flatnorm

1 Sparse Optimization

An Introduction:
* W. Yin and Y. Zhang. Extracting salient features from less data via l1-minimization. SIAG/Optimization Views and News, 19(1), 2008. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR08-A3.PDF.

1.1 ₁-Minimization

• Linearized Bregman:
  * W. Yin. Analysis and generalizations of the linearized Bregman method. Rice University CAAM Technical Report TR09-02, 2009. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR09-02.PDF.
  * S. Osher, Y. Mao, B. Dong, and W. Yin. Fast linearized Bregman iteration for compressive sensing and sparse denoising. To appear in Communications in Mathematical Sciences. Rice University CAAM Technical Report TR08-07., 2008. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR08-07.PDF.
• Bregman:
  * W. Yin, S. Osher, D. Goldfarb, and J. Darbon. Bregman iterative algorithms for l1-minimization with applications to compressed sensing. SIAM Journal on Imaging Sciences, 1(1):143-168, 2008. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR07-13.PDF.
  * S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin. An iterative regularization method for total variation-based image restoration. SIAM Journal on Multiscale Modeling and Simulation, 4(2):460-489, 2005. URL http://www.caam.rice.edu/~wy1/paperfiles/CU˙IEOR˙TR05-A4.PDF.
• FPC-AS (Fixed-Point Continuation and Active Set):
  * Z. Wen, W. Yin, D. Goldfarb, and Y. Zhang. A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization and continuation. Submitted to SIAM Journal on Scientific Computing. Rice University CAAM Technical Report TR09-01, 2009. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR09-01.PDF.
• FPC (Fixed-Point Continuation):
  * E. T. Hale, W. Yin, and Y. Zhang. Fixed-point continuation for l1-minimization: Methodology and convergence. SIAM Journal on Optimization, 19(3):1107-1130, 2008a. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR08-A1.PDF.
  * E. T. Hale, W. Yin, and Y. Zhang. A numerical study of fixed-point continuation applied to compressed sensing. Rice University CAAM Technical Report TR08-24, 2008b. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR08-24.PDF.
• Nonconvex Lp (p¡1) Minimization
  * R. Chartrand and W. Yin. Iteratively reweighted algorithms for compressive sensing. International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pages 3869-2872, 2008. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR08-01.PDF.
• Sparse Logistic Regression:
  * J. Shi, W. Yin, S. Osher, and P. Sajda. A fast algorithm for large scale L1-regularized logistic regression. Rice University CAAM Technical Report TR08-08, 2008. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR08-08.PDF.

1.2 Iterative Support Detection

• Iterative Support Detection:
  * Y. Wang and W. Yin. Compressed sensing via iterative support detection. Rice University CAAM Technical Report TR09-30, 2009. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR09-30.PDF.

1.3 Total Variation Minimization

• TV / Wavelets-L1:
  * J. Yang, Y. Zhang, and W. Yin. A fast TVL1-L2 algorithm for image reconstruction from partial fourier data. Submitted to IEEE Journal of Selected Topics in Signal Processing Special Issue on Compressed Sensing. Rice University CAAM Technical Report TR08-27, 2008b. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR08-27.PDF.
  * S. Ma, W. Yin, Y. Zhang, and A. Chakraborty. An efficient algorithm for compressed MR imaging using total variation and wavelets. IEEE International Conference on Computer Vision and Pattern Recognition (CVPR) 2008, (1-8), 2008. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR08-16.PDF.
• Graph-cut Code
  * D. Goldfarb and W. Yin. Parametric maximum flow algorithms for fast total variation minimization. To appear in SIAM Journal on Scientific Computing. Rice University CAAM Technical Report TR07-09, 2007. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR07-09.PDF.

2 Computational Optimization

2.1 Optimization on Manifold

• Curvilinear Search on Sphere:
  * D. Goldfarb, Z. Wen, and W. Yin. A curvilinear search method for p-harmonic flows on spheres. SIAM Journal on Imaging Sciences, 2(1):84-109, 2008. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR08-02.PDF.

3 Image Processing

3.1 Total Variation Minimization

• TV-L1 Computation:
  * J. Yang, Y. Zhang, and W. Yin. An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise. SIAM Journal on Scientific Computing, 31(4):2842-2865, 2009. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR08-12.PDF.
• TV-L1 Image Decomposition, Theory and Applications:
  * W. Yin, D. Goldfarb, and S. Osher. A comparison of three total variation based texture extraction models. Journal of Visual Communication and Image Representation, 18(3):240-252, 2007. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR07-01.PDF.
  * W. Yin, D. Goldfarb, and S. Osher. The total variation regularized L1 model for multiscale decomposition. SIAM Journal on Multiscale Modeling and Simulation, 6(1):190-211, 2006. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR06-16.PDF.
  * O. Scherzer, W. Yin, and S. Osher. Slope and G-set characterization of set-valued functions and applications to non-differentiable optimization problems. Communications in Mathematical Sciences, 3(4):479-492, 2005. URL http://www.caam.rice.edu/~wy1/paperfiles/CU˙IEOR˙TR05-A2.PDF.
  * W. Yin, D. Goldfarb, and S. Osher. Image cartoon-texture decomposition and feature selection using the total variation regularized L1 functional. Variational, Geometric, and Level Set Methods in Computer Vision, 3752:73-84, 2005b. URL http://www.caam.rice.edu/~wy1/paperfiles/CU˙IEOR˙TR05-A3.PDF.
  * W. Yin, T. Chen, X. S. Zhou, and A. Chakraborty. Background correction for cDNA microarray image using the TV+L1 model. Bioinformatics, 21(10):2410-2416, 2005a. URL http://www.caam.rice.edu/~wy1/paperfiles/CU˙IEOR˙TR05-A5.PDF.
  * T. Chen, T. Huang, W. Yin, and X. S. Zhou. A new coarse-to-fine framework for 3D brain MR image registration. Computer Vision for Biomedical Image, 3765:114-124, 2005a. URL http://www.caam.rice.edu/~wy1/paperfiles/CU˙IEOR˙TR05-A6.PDF.
• Multi-channel Deblurring:
  * J. Yang, W. Yin, Y. Zhang, and Y. Wang. A fast algorithm for edge-preserving variational multichannel image restoration. SIAM Journal on Imaging Sciences, 2 (2):569-592, 2008a. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR08-09.PDF.
• Single-channel Deblurring:
  * Y. Wang, J. Yang, W. Yin, and Y. Zhang. A new alternating minimization algorithm for total variation image reconstruction. SIAM Journal on Imaging Sciences, 1(3): 248-272, 2008. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR07-10.PDF.
• Second-Order Cone Programming (SOCP):
  * D. Goldfarb and W. Yin. Second-order cone programming methods for total variation based image restoration. SIAM Journal on Scientific Computing, 27(2): 622-645, 2005. URL http://www.caam.rice.edu/~wy1/paperfiles/CU˙IEOR˙TR05-A1.PDF.

3.2 Face Recognition / Processing

• Relighting:
  * Q. Li, W. Yin, and Z. Deng. Image-based face illumination transferring using the logarithmic total variation model. Visual Computer, online first. DOI: 10.1007/s00371-009-0375-8, 2009. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR09-34.PDF.
• Recognition:
  * T. Chen, W. Yin, X. S. Zhou, D. Comaniciu, and T. Huang. Total variation models for variable lighting face recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), 28(9):1519-1524, 2006. URL http://www.caam.rice.edu/~wy1/paperfiles/CU˙IEOR˙TR06-A1.PDF.
  * T. Chen, W. Yin, X. S. Zhou, D. Domaniciu, and T. Huang. Illumination normalization for face recognition and uneven background correction using total variation based image models. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), 2:532-539, 2005b. URL http://www.caam.rice.edu/~wy1/paperfiles/CU˙IEOR˙TR05-A7.PDF.

3.3 Flatnorm

• Edge Matching:
  * S. P. Morgan, W. Yin, and K. R. Vixie. A MATLAB implementation of a flat norm motivated polygonal edge matching method using a decomposition of boundary into four 1-dimensional currents. arXiv:0812.0340v1. Rice University CAAM Technical Report TR09-35, 2009. URL http://www.caam.rice.edu/~wy1/paperfiles/Rice˙CAAM˙TR09-35.PDF.