In this paper we present optimization algorithms for image restoration based on the total variation (TV) minimization framework of L. Rudin, S. Osher and E. Fatemi (ROF). Our approach formulates TV minimization as a second-order cone program which is then solved by interior-point algorithms that are e#cient both in practice (using nested dissection and domain decomposition) and in theory (i.e., they obtain solutions in polynomial time). In addition to the original ROF minimization model, we show how to apply our approach to other TV models including ones that are not solvable by PDE based methods. Numerical results on a varied set of images are presented to illustrate the e#ectiveness of our approach.

this paper can be downloaded from http://www.compgeom.com/meb/. P. Kumar and J. Mitchell are partially supported by a grant from the National Science Foundation (CCR0098172) . J. Mitchell is also partially supported by grants from the Honda Fundamental Research Labs, Metron Aviation, NASAAmes Research (NAG2-1325), and the US-Israel Binational Science Foundation. E. A. Yldrm is partially supported by an NSF CAREER award (DMI-0237415)

In this paper, we present the logarithmic total variation (LTV) model for face recognition under varying illumination, including natural lighting condition, where we can hardly know the strength, the directions, and the number of light sources. The proposed LTV model has the capability to factorize a single face image and obtain the illumination invariant facial structure, which is then used for face recognition. The merit of this model is that neither does it require any lighting assumption nor does it need any training process. Besides, there is only one parameter which could be easily set. The LTV model is able to reach very high recognition rates on both Yale and CMU PIE face databases as well as on a face database containing 765 subjects under outdoor lighting conditions. Keywords: I.5.4.d Face and gesture recognition; I.5.4.m Signal processing; I.4 Image Processing and Computer Vision; I.5.2.c Pattern analysis;

Abstract—In this paper,we present a methodology for generating guaranteed passive time-domain models of subsystems described by tabulated frequency-domain data obtained through measurement or through physical simulation. Such descriptions are commonly used to represent on- and off-chip interconnect effects,package parasitics,and passive devices common in high-frequency integrated circuit applications. The approach,which incorporates passivity constraints via convex optimization algorithms,is guaranteed to produce a passive-system model that is optimal in the sense of having minimum error in the frequency band of interest over all models with a prescribed set of system poles. We demonstrate that this algorithm is computationally practical for generating accurate high-order models of data sets representing realistic, complicated multiinput,multioutput systems. Index Terms—Behavior modeling,convex optimization,convex programming,interconnect modeling,rational fitting,system identification. I.

Abstract. This paper studies the model of minimizing total variation with an L 1-norm fidelity term for decomposing a real image into the sum of cartoon and texture. This model is also analyzed and shown to be able to select features of an image according to their scales. 1

In this paper we study robust convex quadratically constrained programs, a subset of the class of robust convex programs introduced by Ben-Tal and Nemirovski [4]. Unlike [4], our focus in this paper is to identify uncertainty structures that allow the corresponding robust quadratically constrained programs to be reformulated as second-order cone programs. We propose three classes of uncertainty sets that satisfy this criterion and present examples where these classes of uncertainty sets are natural. 1 Problem formulation A generic quadratically constrained program (QCP) is defined as follows.

In this we paper we study techniques for generating valid convex constraints for mixed 0-1 conic programs. We show that many of the techniques developed for generating linear cuts for mixed 0-1 linear programs, such as the Gomory cuts, the lift-and-project cuts, and cuts from other hierarchies of tighter relaxations, extend in a straightforward manner to mixed 0-1 conic programs. We also show that simple extensions of these techniques lead to methods for generating convex quadratic cuts. Gomory cuts for mixed 0-1 conic programs have interesting implications for comparing the semidefinite programming and the linear programming relaxations of combinatorial optimization problems, e.g. we show that all the subtour elimination inequalities for the traveling salesman problem are rank-1 Gomory cuts with respect to a single semidefinite constraint. We also include results from our preliminary computational experiments with these cuts.

Regularized kernel discriminant analysis (RKDA) performs linear discriminant analysis in the feature space via the kernel trick. Its performance depends on the selection of kernels. In this paper, we consider the problem of multiple kernel learning (MKL) for RKDA, in which the optimal kernel matrix is obtained as a linear combination of pre-specified kernel matrices. We show that the kernel learning problem in RKDA can be formulated as convex programs. First, we show that this problem can be formulated as a semidefinite program (SDP). Based on the equivalence relationship between RKDA and least square problems in the binary-class case, we propose a convex quadratically constrained quadratic programming (QCQP) formulation for kernel learning in RKDA. A semi-infinite linear programming (SILP) formulation is derived to further improve the efficiency. We extend these formulations to the multi-class case based on a key result established in this paper. That is, the multi-class RKDA kernel learning problem can be decomposed into a set of binary-class kernel learning problems which are constrained to share a common kernel. Based on this decomposition property, SDP formulations are proposed for the multi-class case. Furthermore, it leads naturally to QCQP and SILP formulations. As the performance of RKDA depends on the regularization parameter, we show that this parameter can also be optimized in a joint framework with the kernel. Extensive experiments have been conducted and analyzed, and connections to other algorithms are discussed.

We study the minimum enclosing ball (MEB) problem for sets of points or balls in high dimensions. Using techniques of second-order cone programming and "coresets ", we have developed (1 + #)-approximation algorithms that perform well in practice, especially for very high dimensions, in addition to having provable guarantees. We prove the existence of core-sets of size O(1/#), improving the previous bound of O(1/# ), and we study empirically how the core-set size grows with dimension. We show that our algorithm, which is simple to implement, results in fast computation of nearly optimal solutions for point sets in much higher dimension than previously computable using exact techniques.

The active contour/snake model [9, 2, 10] is one of the most wellknown segmentation variational models in image processing. However this model suffers from the existence of local minima which makes the initial guess critical for getting satisfactory results. In this paper, we propose to solve this problem by finding global minimizers of the active contour model following the original work of Chan, Esedo¯glu and Nikolova [4]. Our approach uses the weighted total variation norm to link the standard active contour segmentation model with the denoising model of Rudin-Osher-Fatemi [15] and the Chan-Vese active contour segmentation models [5, 18] based on the Mumford-Shah functional [12]. 1