Optimization with Sparsity-Inducing Penalties

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate non-smooth norms. The goal of this paper is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted $\ell_2$-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view

Learning Spectral-Spatial-Temporal Features via a Recurrent Convolutional Neural Network for Change Detection in Multispectral Imagery

Change detection is one of the central problems in earth observation and was extensively investigated over recent decades. In this paper, we propose a novel recurrent convolutional neural network (ReCNN) architecture, which is trained to learn a joint spectral-spatial-temporal feature representation in a unified framework for change detection in multispectral images. To this end, we bring together a convolutional neural network (CNN) and a recurrent neural network (RNN) into one end-to-end network. The former is able to generate rich spectral-spatial feature representations, while the latter effectively analyzes temporal dependency in bi-temporal images. In comparison with previous approaches to change detection, the proposed network architecture possesses three distinctive properties: 1) It is end-to-end trainable, in contrast to most existing methods whose components are separately trained or computed; 2) it naturally harnesses spatial information that has been proven to be beneficial to change detection task; 3) it is capable of adaptively learning the temporal dependency between multitemporal images, unlike most of algorithms that use fairly simple operation like image differencing or stacking. As far as we know, this is the first time that a recurrent convolutional network architecture has been proposed for multitemporal remote sensing image analysis. The proposed network is validated on real multispectral data sets. Both visual and quantitative analysis of experimental results demonstrates competitive performance in the proposed mode

Ego-motion and Surrounding Vehicle State Estimation Using a Monocular Camera

Understanding ego-motion and surrounding vehicle state is essential to enable automated driving and advanced driving assistance technologies. Typical approaches to solve this problem use fusion of multiple sensors such as LiDAR, camera, and radar to recognize surrounding vehicle state, including position, velocity, and orientation. Such sensing modalities are overly complex and costly for production of personal use vehicles. In this paper, we propose a novel machine learning method to estimate ego-motion and surrounding vehicle state using a single monocular camera. Our approach is based on a combination of three deep neural networks to estimate the 3D vehicle bounding box, depth, and optical flow from a sequence of images. The main contribution of this paper is a new framework and algorithm that integrates these three networks in order to estimate the ego-motion and surrounding vehicle state. To realize more accurate 3D position estimation, we address ground plane correction in real-time. The efficacy of the proposed method is demonstrated through experimental evaluations that compare our results to ground truth data available from other sensors including Can-Bus and LiDAR

Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In this context, the fresh look advocated here permeates benefits from variable selection and compressive sampling, to robustify PCA against outliers. A least-trimmed squares estimator of a low-rank bilinear factor analysis model is shown closely related to that obtained from an $\ell_0$-(pseudo)norm-regularized criterion encouraging sparsity in a matrix explicitly modeling the outliers. This connection suggests robust PCA schemes based on convex relaxation, which lead naturally to a family of robust estimators encompassing Huber's optimal M-class as a special case. Outliers are identified by tuning a regularization parameter, which amounts to controlling sparsity of the outlier matrix along the whole robustification path of (group) least-absolute shrinkage and selection operator (Lasso) solutions. Beyond its neat ties to robust statistics, the developed outlier-aware PCA framework is versatile to accommodate novel and scalable algorithms to: i) track the low-rank signal subspace robustly, as new data are acquired in real time; and ii) determine principal components robustly in (possibly) infinite-dimensional feature spaces. Synthetic and real data tests corroborate the effectiveness of the proposed robust PCA schemes, when used to identify aberrant responses in personality assessment surveys, as well as unveil communities in social networks, and intruders from video surveillance data.Comment: 30 pages, submitted to IEEE Transactions on Signal Processin

Online and Batch Supervised Background Estimation via L1 Regression

We propose a surprisingly simple model for supervised video background estimation. Our model is based on $\ell_1$ regression. As existing methods for $\ell_1$ regression do not scale to high-resolution videos, we propose several simple and scalable methods for solving the problem, including iteratively reweighted least squares, a homotopy method, and stochastic gradient descent. We show through extensive experiments that our model and methods match or outperform the state-of-the-art online and batch methods in virtually all quantitative and qualitative measures