PAR-constrained sequences are widely used in communication systems and radars due to various practical needs; specifically, sequences are required to be unimodular or of low peak-to-average power ratio (PAR). For unimodular sequence design, plenty of efforts have been devoted to obtaining good correlation properties. Regarding channel estimation, however, sequences of such properties do not necessarily help produce optimal estimates. Tailored unimodular sequences for the specific criterion concerned are desirable especially when the prior knowledge of the channel is taken into account as well. In this paper, we formulate the problem of optimal unimodular sequence design for minimum mean square error estimation of the channel impulse response and conditional mutual information maximization, respectively. Efficient algorithms based on the majorization-minimization framework are proposed for both problems with guaranteed convergence. As the unimodular constraint is a special case of the low PAR constraint, optimal sequences of low PAR are also considered. Numerical examples are provided to show the performance of the proposed training sequences, with the efficiency of the derived algorithms demonstrated.
Motivated by reachability questions in coherently controlled open quantum systems coupled to a thermal bath, as well as recent progress in the field of thermo-/vector-majorization we generalize classical majorization from unital quantum channels to channels with an arbitrary fixed point $D$ of full rank. Such channels preserve some Gibbs-state and thus play an important role in the resource theory of quantum thermodynamics, in particular in thermo-majorization. Based on this we investigate $D$-majorization on matrices in terms of its topological and order properties, such as existence of uniqu…
We present a primal-dual majorization-minimization method for solving large-scale linear programs. A smooth barrier augmented Lagrangian (SBAL) function with strict convexity for the dual linear program is derived. The majorization-minimization approach is naturally introduced to develop the smoothness and convexity of the SBAL function. Our method only depends on a factorization of the constant matrix independent of iterations and does not need any computation on step sizes, thus can be expected to be particularly appropriate for large-scale linear programs. The method shares some similar pro…
Variable Bregman Majorization-Minimization algorithms for nonconvex nonsmooth optimization, with application to Poisson imaging
Université Paris-Saclay, CentraleSupélec, Inria, Centre pour la Vision Numérique（巴黎萨克雷大学、中央苏佩莱克学院、法国国家信息与自动化研究所、数字视觉中心）；Université Paris-Saclay, Laboratoire BioMaps, CEA（巴黎萨克雷大学、BioMaps实验室、法国原子能和替代能源委员会）
We propose and examine two optimal $(0,1)$-matrix completion problems with majorization ordered objectives. They elevate the seminal study by Gale and Ryser from feasibility to optimality in partial order programming (POP), referring to optimization with partially ordered objectives. We showcase their applications in electric vehicle charging, portfolio optimization, and secure data storage. Solving such integer POP (iPOP) problems is challenging because of the possible non-comparability among objective values and the integer requirements. Nevertheless, we prove the essential uniqueness of all…
Automated methods for facial animation are a necessary tool in the modern industry since the standard blendshape head models consist of hundreds of controllers and a manual approach is painfully slow. Different solutions have been proposed that produce output in real-time or generalize well for different face topologies. However, all these prior works consider a linear approximation of the blendshape function and hence do not provide a high-enough level of details for modern realistic human face reconstruction. We build a method for solving the inverse rig in blendshape animation using quadrat…
In this paper, we introduce a novel iterative algorithm for the problem of phase-retrieval where the measurements consist of only the magnitude of linear function of the unknown signal, and the noise in the measurements follow Poisson distribution. The proposed algorithm is based on the principle of majorization-minimization (MM); however, the application of MM here is very novel and distinct from the way MM has been usually used to solve optimization problems in the literature. More precisely, we reformulate the original minimization problem into a saddle point problem by invoking Fenchel dua…
Block Majorization Minimization with Extrapolation and Application to $β$-NMF
Acapela Group（Acapela集团）；Institute of data sciences（数据科学研究所）；Faculty of Engineering（工程学院）；University of Mons（蒙斯大学）；Department of Mathematics and Operational Research（数学与运筹学系）
We consider the problem of distributed pose graph optimization (PGO) that has important applications in multi-robot simultaneous localization and mapping (SLAM). We propose the majorization minimization (MM) method for distributed PGO ($\mathsf{MM-PGO}$) that applies to a broad class of robust loss kernels. The $\mathsf{MM-PGO}$ method is guaranteed to converge to first-order critical points under mild conditions. Furthermore, noting that the $\mathsf{MM-PGO}$ method is reminiscent of proximal methods, we leverage Nesterov's method and adopt adaptive restarts to accelerate convergence. The res…
