C-HiLasso: A Collaborative Hierarchical Sparse Modeling Framework

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this work we combine the sparsity-inducing property of the Lasso model at the individual feature level, with the block-sparsity property of the Group Lasso model, where sparse groups of features are jointly encoded, obtaining a sparsity pattern hierarchically structured. This results in the Hierarchical Lasso (HiLasso), which shows important practical modeling advantages. We then extend this approach to the collaborative case, where a set of simultaneously coded signals share the same sparsity pattern at the higher (group) level, but not necessarily at the lower (inside the group) level, obtaining the collaborative HiLasso model (C-HiLasso). Such signals then share the same active groups, or classes, but not necessarily the same active set. This model is very well suited for applications such as source identification and separation. An efficient optimization procedure, which guarantees convergence to the global optimum, is developed for these new models. The underlying presentation of the new framework and optimization approach is complemented with experimental examples and theoretical results regarding recovery guarantees for the proposed models

C-blox: A Scalable and Consistent TSDF-based Dense Mapping Approach

In many applications, maintaining a consistent dense map of the environment is key to enabling robotic platforms to perform higher level decision making. Several works have addressed the challenge of creating precise dense 3D maps from visual sensors providing depth information. However, during operation over longer missions, reconstructions can easily become inconsistent due to accumulated camera tracking error and delayed loop closure. Without explicitly addressing the problem of map consistency, recovery from such distortions tends to be difficult. We present a novel system for dense 3D mapping which addresses the challenge of building consistent maps while dealing with scalability. Central to our approach is the representation of the environment as a collection of overlapping TSDF subvolumes. These subvolumes are localized through feature-based camera tracking and bundle adjustment. Our main contribution is a pipeline for identifying stable regions in the map, and to fuse the contributing subvolumes. This approach allows us to reduce map growth while still maintaining consistency. We demonstrate the proposed system on a publicly available dataset and simulation engine, and demonstrate the efficacy of the proposed approach for building consistent and scalable maps. Finally we demonstrate our approach running in real-time on-board a lightweight MAV.Comment: 8 pages, 5 figures, conferenc