### Citations

2232 | Nonlinear total variation based noise removal algorithms
- Rudin, Osher, et al.
- 1992
(Show Context)
Citation Context ...fits of our fast algorithms by showing their application to image denoising; we also show their use as efficient subroutines in 1Our definitions of TV are different from the original ROF model of TV (=-=Rudin et al., 1992-=-); also see §5.2. Fast Newton-type Methods for Total Variation Regularization larger solvers for image deconvolution and for solving four variants of fused-lasso. Software: To support our numerical re... |

1025 | A fast iterative shrinkage-thresholding algorithm for linear inverse problems - Beck, Teboulle - 2009 |

548 | A limited memory algorithm for bound constrained minimization
- Byrd, Lu, et al.
- 1995
(Show Context)
Citation Context ...pic TV, the dual (6) becomes minu φ(u) := 1 2‖D Tu‖22−u TDy, s.t. ‖u‖∞ ≤ λ. (8) This is a box-constrained quadratic program; so it can be solved by methods such as TRON (Lin & Moré, 1999), L-BFGS-B (=-=Byrd et al., 1994-=-), or projected-Newton (PN) (Bertsekas, 1982). But these methods can be inefficient if invoked out-of-the-box, and carefully exploiting problem structure is a must. PN lends itself well to such struct... |

388 | Gradient methods for minimizing composite objective function
- Nesterov
(Show Context)
Citation Context ...achine Learning, Bellevue, WA, USA, 2011. Copyright 2011 by the author(s)/owner(s). Within machine learning and related fields, the benefits of invoking the proximity operator (2) are wellrecognized (=-=Nesterov, 2007-=-; Combettes & Pesquet, 2009; Duchi & Singer, 2009), and several choices of R have already been considered. We study a special choice for R: one and higher dimensional total-variation (TV)1; for x ∈ Rn... |

332 | Iterative Methods for Total Variation Denoising - Vogel, Oman - 1996 |

318 | Pathwise coordinate optimization - FRIEDMAN, HASTIE, et al. - 2007 |

256 | Proximal splitting methods in signal processing
- Combettes, Pesquet
- 2011
(Show Context)
Citation Context ... Bellevue, WA, USA, 2011. Copyright 2011 by the author(s)/owner(s). Within machine learning and related fields, the benefits of invoking the proximity operator (2) are wellrecognized (Nesterov, 2007; =-=Combettes & Pesquet, 2009-=-; Duchi & Singer, 2009), and several choices of R have already been considered. We study a special choice for R: one and higher dimensional total-variation (TV)1; for x ∈ Rn, this is defined as Tv1Dp ... |

194 | Trust Region Methods
- Conn, Gould, et al.
- 2000
(Show Context)
Citation Context ...y solving RTq = u. Update α using (15) t← t+ 1. end while return ut Problem (10) is an instance of the well-known trust-region subproblem, whereby a variety of numerical methods are available for it (=-=Conn et al., 2000-=-). Below we derive an algorithm based on the Moré-Sorensen Newton (MSN) iteration (Moré & Sorensen, 1983), which in general is expensive, but in our case proves to be efficient thanks to the tridiag... |

179 | A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration
- Bioucas-Dias, Figueiredo
- 2007
(Show Context)
Citation Context ...Dp,q(X) := ∑m i=1 (∑n−1 j=1 |xi,j+1 − xi,j | p )1/p + ∑n j=1 (∑m−1 i=1 |xi+1,j − xi,j | q )1/q , (4) where usually p, q ∈ {1, 2}. We focus on two key variants of (3) and (4): anisotropic-TV (see e.g. =-=Bioucas-Dias & Figueiredo, 2007-=-), with p, q = 1; and TV with both p and q = 2. Extension of (3) to tensor data is relegated to (Barbero & Sra, 2011), for paucity of space. The regularizers Tv1D1 and Tv2D1,1 arise in many applicatio... |

142 | Projected Newton methods for optimization problems with simple constraints
- Bertsekas
- 1982
(Show Context)
Citation Context ...D Tu‖22−u TDy, s.t. ‖u‖∞ ≤ λ. (8) This is a box-constrained quadratic program; so it can be solved by methods such as TRON (Lin & Moré, 1999), L-BFGS-B (Byrd et al., 1994), or projected-Newton (PN) (=-=Bertsekas, 1982-=-). But these methods can be inefficient if invoked out-of-the-box, and carefully exploiting problem structure is a must. PN lends itself well to such structure exploitation, and we adapt it to develop... |

125 | et al. Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays - Alon, Barkai, et al. - 1999 |

123 | Fast image recovery using variable splitting and constrained optimization
- Afonso, Bioucas-Dias, et al.
- 2010
(Show Context)
Citation Context .... In stark contrast, our solvers do not require any parameter tuning, and run rapidly. Our TV methods can be plugged in directly into solvers such as TwIST (Bioucas-Dias & Figueiredo, 2007) or SALSA (=-=Afonso et al., 2010-=-) for image deblurring, and into methods such as FISTA (Beck & Teboulle, 2009) or TRIP (Kim et al., 2010), for TV-regularized optimization. 2See http://arantxa.ii.uam.es/∼gaa/software.html 2. One dime... |

121 | SLEP: Sparse Learning with Efficient Projections
- Liu, Ji, et al.
- 2009
(Show Context)
Citation Context ... TV-term dominates). 4.1. Results for TV-L1 proximity We compare running times of our PN approach (C implementation) against two methods: (i) the FLSA function (C implementation) of the SLEP library (=-=Liu et al., 2009-=-), which seems to be the state-of-the-art method for Tv1D1 - proximity (Liu et al., 2010); and (ii) the Pathwise Coordinate Optimization method (R + FORTRAN implementation) from (Friedman et al., 2007... |

108 | Newton's method for large bound-constrained optimization problems - Lin, More - 1999 |

100 | Spatial smoothing and hotspot detection for CGH data using the fused lasso - TIBSHIRANI, P - 2008 |

55 | Estimating time-varying networks
- Kolar, Song, et al.
- 2010
(Show Context)
Citation Context ...ucity of space. The regularizers Tv1D1 and Tv2D1,1 arise in many applications—e.g., image denoising and deconvolution (Dahl et al., 2010), fused-lasso (Tibshirani et al., 2005), logistic fused-lasso (=-=Kolar et al., 2010-=-), and change-point detection (Harchaoui & Lévy-Leduc, 2010); also see the related work (Vert & Bleakley, 2010). This fairly broad applicability motivates us to develop efficient proximity operators ... |

43 | The latent process decomposition of cDNA microarray data sets
- Rogers
- 2005
(Show Context)
Citation Context ...ch of the four FL models on binary classification tasks for the following microarray datasets: ArrayCGH (Stransky et al., 2006), Leukemias (Golub et al., 1999), Colon (U. Alon et al., 1999), Ovarian (=-=Rogers et al., 2005-=-) and Rat (Hua et al., 2009). Each dataset was split into three equal parts (ensuring both classes are present in every split) for training, validation and test. The penalty parameters where found by ... |

41 |
Acceleration of iterative image restoration algorithms
- Biggs, Andrews
(Show Context)
Citation Context ...code images subjected to motion blurring. Comparing against SALSA’s default isotropic denoising operator, again an anisotropic model produces a better reconstruction. Results for RichardsonLucy (RL) (=-=Biggs & Andrews, 1997-=-) as implemented in Matlab are also presented, showing much faster filtering times but inferior reconstruction quality. Table 5. Deconvolution results for anisotropic and isotropic models using the SA... |

41 | An efficient algorithm for a class of fused lasso problems
- Liu, Yuan, et al.
- 2010
(Show Context)
Citation Context ...D1 -proximity based on a careful “restart” heuristic; their methods show strong empirical performance but do not extend easily to higher-D TV. Our Newton-type methods outperform the tuned methods of (=-=Liu et al., 2010-=-), and fit nicely in a general algorithmic framework that allows tackling the harder two- and higher-D TV problems. TV regularization in itself arises frequently in image denoising, whereby a large nu... |

34 | Performance of feature-selection methods in the classification of high-dimension data - Hua - 2009 |

25 | Multiple change-point estimation with a total variation penalty - Harchaoui, Lévy-Leduc |

20 | Fast detection of multiple change-points shared by many signals using group lars
- Vert, Bleakley
- 2010
(Show Context)
Citation Context ...nvolution (Dahl et al., 2010), fused-lasso (Tibshirani et al., 2005), logistic fused-lasso (Kolar et al., 2010), and change-point detection (Harchaoui & Lévy-Leduc, 2010); also see the related work (=-=Vert & Bleakley, 2010-=-). This fairly broad applicability motivates us to develop efficient proximity operators for TV. Before beginning the technical discussion, let us summarize our key contributions. Algorithms: For Tv1D... |

17 |
Online and Batch Learning using Forward-Backward Splitting
- Duchi, Singer
- 2009
(Show Context)
Citation Context ...opyright 2011 by the author(s)/owner(s). Within machine learning and related fields, the benefits of invoking the proximity operator (2) are wellrecognized (Nesterov, 2007; Combettes & Pesquet, 2009; =-=Duchi & Singer, 2009-=-), and several choices of R have already been considered. We study a special choice for R: one and higher dimensional total-variation (TV)1; for x ∈ Rn, this is defined as Tv1Dp (x) := (∑n−1 i=1 |xi+1... |

16 | A scalable trust-region algorithm with application to mixed-norm regression
- Kim, Sra, et al.
- 2010
(Show Context)
Citation Context ...e plugged in directly into solvers such as TwIST (Bioucas-Dias & Figueiredo, 2007) or SALSA (Afonso et al., 2010) for image deblurring, and into methods such as FISTA (Beck & Teboulle, 2009) or TRIP (=-=Kim et al., 2010-=-), for TV-regularized optimization. 2See http://arantxa.ii.uam.es/∼gaa/software.html 2. One dimensional TV-Proximity We begin with 1D-TV proximity, and devote most attention to it, since it forms a cr... |

15 | Algorithms and software for total variation image reconstruction via first-order methods,” submitted to Numerical Algorithms
- Dahl, Hansen, et al.
- 2008
(Show Context)
Citation Context ... 2. Extension of (3) to tensor data is relegated to (Barbero & Sra, 2011), for paucity of space. The regularizers Tv1D1 and Tv2D1,1 arise in many applications—e.g., image denoising and deconvolution (=-=Dahl et al., 2010-=-), fused-lasso (Tibshirani et al., 2005), logistic fused-lasso (Kolar et al., 2010), and change-point detection (Harchaoui & Lévy-Leduc, 2010); also see the related work (Vert & Bleakley, 2010). This... |

12 | Anisotropic Total Variation Regularized L1-Approximation and Denoising/Deblurring of 2D Bar Codes - Choksi, Gennip, et al. - 2010 |

8 | Reyal et al., “Regional copy numberindependent deregulation of transcription in cancer - Stransky, Vallot, et al. - 2006 |

5 | et al. LAPACK Users’ Guide. Society for Industrial and Applied Mathematics - Anderson - 1999 |

3 | et al. Molecular classification of cancer - Golub - 1999 |

2 |
http://people.kyb.tuebingen.mpg.de /suvrit/work/icml11.pdf
- Barbero, Sra
- 2011
(Show Context)
Citation Context .... We focus on two key variants of (3) and (4): anisotropic-TV (see e.g. Bioucas-Dias & Figueiredo, 2007), with p, q = 1; and TV with both p and q = 2. Extension of (3) to tensor data is relegated to (=-=Barbero & Sra, 2011-=-), for paucity of space. The regularizers Tv1D1 and Tv2D1,1 arise in many applications—e.g., image denoising and deconvolution (Dahl et al., 2010), fused-lasso (Tibshirani et al., 2005), logistic fuse... |

2 |
Barillot J.-P. Classification of arrayCGH data using fused SVM
- Rapaport, Vert
- 2008
(Show Context)
Citation Context ...2, and R(x) = λ1‖x‖1 + λ2‖Dx‖1; this is the original fused-lasso problem introduced in (Tibshirani et al., 2005), and used in several applications, such as in bioinformatics (Tibshirani & Wang, 2008; =-=Rapaport & Vert, 2008-=-; Friedman et al., 2007). 2. `2-variable fusion (VF): Same as FL but with λ2‖Dx‖2 instead. This FL variant seems to be new. 3. Logistic-fused lasso (LFL): A logistic loss L(x, c) =∑ i log ( 1 + e−yi(a... |