We consider the problem of regularized Poisson Non-negative Matrix
Factorization (NMF) problem, encompassing various regularization terms such as
Lipschitz and relatively smooth functions, alongside linear constraints. This
problem holds significant relevance in numerous Machine Learning applications,
particularly within the domain of physical linear unmixing problems. A notable
challenge arises from the main loss term in the Poisson NMF problem being a KL
divergence, which is non-Lipschitz, rendering traditional gradient
descent-based approaches inefficient. In this contribution, we explore the
utilization of Block Successive Upper Minimization (BSUM) to overcome this
challenge. We build approriate majorizing function for Lipschitz and relatively
smooth functions, and show how to introduce linear constraints into the
problem. This results in the development of two novel algorithms for
regularized Poisson NMF. We conduct numerical simulations to showcase the
effectiveness of our approach.

我们研究了正则化泊松非负矩阵分解（NMF）问题，包括利普希茨和相对平滑函数以及线性约束的各种正则化项。我们利用块递进上界最小化（BSUM）来克服主要损失项为 KL 散度的挑战，构建适当的上界函数，并展示如何引入线性约束进入该问题中。这导致了两种新的正则化泊松 NMF 算法的发展。我们进行了数值模拟展示我们方法的有效性。

正则化泊松非负矩阵分解的高效算法

Efficient algorithms for regularized Poisson Non-negative Matrix  Factorization

Developing and integrating advanced image sensors with novel algorithms in
camera systems is prevalent with the increasing demand for computational
photography and imaging on mobile platforms. However, the lack of high-quality
data for research and the rare opportunity for in-depth exchange of views from
industry and academia constrain the development of mobile intelligent
photography and imaging (MIPI). To bridge the gap, we introduce the first MIPI
challenge including five tracks focusing on novel image sensors and imaging
algorithms. In this paper, RGB+ToF Depth Completion, one of the five tracks,
working on the fusion of RGB sensor and ToF sensor (with spot illumination) is
introduced. The participants were provided with a new dataset called
TetrasRGBD, which contains 18k pairs of high-quality synthetic RGB+Depth
training data and 2.3k pairs of testing data from mixed sources. All the data
are collected in an indoor scenario. We require that the running time of all
methods should be real-time on desktop GPUs. The final results are evaluated
using objective metrics and Mean Opinion Score (MOS) subjectively. A detailed
description of all models developed in this challenge is provided in this
paper. More details of this challenge and the link to the dataset can be found
at this https URL

本文介绍了包含五个跟新型图像处理和图像传感器算法相关的主题的 MIPI 挑战，着重介绍了 RGB+ToF 深度完成，在这个主题中，RGB 传感器和 ToF 传感器的数据融合被探究，为此我们提供了一个新数据集 TetrasRGBD。

MIPI 2022 RGB+ToF 深度补全竞赛：数据集与报告

MIPI 2022 Challenge on RGB+ToF Depth Completion: Dataset and Report

This paper addresses the problem of synchronizing orthogonal matrices over
directed graphs. For synchronized transformations (or matrices), composite
transformations over loops equal the identity. We formulate the synchronization
problem as a least-squares optimization problem with nonlinear constraints. The
synchronization problem appears as one of the key components in applications
ranging from 3D-localization to image registration. The main contributions of
this work can be summarized as the introduction of two novel algorithms; one
for symmetric graphs and one for graphs that are possibly asymmetric. Under
general conditions, the former has guaranteed convergence to the solution of a
spectral relaxation to the synchronization problem. The latter is stable for
small step sizes when the graph is quasi-strongly connected. The proposed
methods are verified in numerical simulations.

本文讨论如何在有向图上实现正交矩阵的同步化问题，提出了两种新算法，分别适用于对称图和非对称图，并经过数值模拟验证了其效果。