Tomographic inversion using ℓ1\ell_1-norm regularization of wavelet coefficients

We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution $m$ that contains no more fine-scale structure than is necessary to fit the data $d$ to within its assigned errors.Comment: 19 pages, 14 figures. Submitted to GJI July 2006. This preprint does not use GJI style files (which gives wrong received/accepted dates). Corrected typ

Integration of Absolute Orientation Measurements in the KinectFusion Reconstruction pipeline

In this paper, we show how absolute orientation measurements provided by low-cost but high-fidelity IMU sensors can be integrated into the KinectFusion pipeline. We show that integration improves both runtime, robustness and quality of the 3D reconstruction. In particular, we use this orientation data to seed and regularize the ICP registration technique. We also present a technique to filter the pairs of 3D matched points based on the distribution of their distances. This filter is implemented efficiently on the GPU. Estimating the distribution of the distances helps control the number of iterations necessary for the convergence of the ICP algorithm. Finally, we show experimental results that highlight improvements in robustness, a speed-up of almost 12%, and a gain in tracking quality of 53% for the ATE metric on the Freiburg benchmark.Comment: CVPR Workshop on Visual Odometry and Computer Vision Applications Based on Location Clues 201

Deep Generative Modeling of LiDAR Data

Building models capable of generating structured output is a key challenge for AI and robotics. While generative models have been explored on many types of data, little work has been done on synthesizing lidar scans, which play a key role in robot mapping and localization. In this work, we show that one can adapt deep generative models for this task by unravelling lidar scans into a 2D point map. Our approach can generate high quality samples, while simultaneously learning a meaningful latent representation of the data. We demonstrate significant improvements against state-of-the-art point cloud generation methods. Furthermore, we propose a novel data representation that augments the 2D signal with absolute positional information. We show that this helps robustness to noisy and imputed input; the learned model can recover the underlying lidar scan from seemingly uninformative dataComment: Presented at IROS 201

An Improved Observation Model for Super-Resolution under Affine Motion

Super-resolution (SR) techniques make use of subpixel shifts between frames in an image sequence to yield higher-resolution images. We propose an original observation model devoted to the case of non isometric inter-frame motion as required, for instance, in the context of airborne imaging sensors. First, we describe how the main observation models used in the SR literature deal with motion, and we explain why they are not suited for non isometric motion. Then, we propose an extension of the observation model by Elad and Feuer adapted to affine motion. This model is based on a decomposition of affine transforms into successive shear transforms, each one efficiently implemented by row-by-row or column-by-column 1-D affine transforms. We demonstrate on synthetic and real sequences that our observation model incorporated in a SR reconstruction technique leads to better results in the case of variable scale motions and it provides equivalent results in the case of isometric motions

CHARA/MIRC observations of two M supergiants in Perseus OB1: temperature, Bayesian modeling, and compressed sensing imaging

Two red supergiants of the Per OB1 association, RS Per and T Per, have been observed in H band using the MIRC instrument at the CHARA array. The data show clear evidence of departure from circular symmetry. We present here new techniques specially developed to analyze such cases, based on state-of-the-art statistical frameworks. The stellar surfaces are first modeled as limb-darkened discs based on SATLAS models that fit both MIRC interferometric data and publicly available spectrophotometric data. Bayesian model selection is then used to determine the most probable number of spots. The effective surface temperatures are also determined and give further support to the recently derived hotter temperature scales of red su- pergiants. The stellar surfaces are reconstructed by our model-independent imaging code SQUEEZE, making use of its novel regularizer based on Compressed Sensing theory. We find excellent agreement between the model-selection results and the reconstructions. Our results provide evidence for the presence of near-infrared spots representing about 3-5% of the stellar flux

TomograPy: A Fast, Instrument-Independent, Solar Tomography Software

Solar tomography has progressed rapidly in recent years thanks to the development of robust algorithms and the availability of more powerful computers. It can today provide crucial insights in solving issues related to the line-of-sight integration present in the data of solar imagers and coronagraphs. However, there remain challenges such as the increase of the available volume of data, the handling of the temporal evolution of the observed structures, and the heterogeneity of the data in multi-spacecraft studies. We present a generic software package that can perform fast tomographic inversions that scales linearly with the number of measurements, linearly with the length of the reconstruction cube (and not the number of voxels) and linearly with the number of cores and can use data from different sources and with a variety of physical models: TomograPy (http://nbarbey.github.com/TomograPy/), an open-source software freely available on the Python Package Index. For performance, TomograPy uses a parallelized-projection algorithm. It relies on the World Coordinate System standard to manage various data sources. A variety of inversion algorithms are provided to perform the tomographic-map estimation. A test suite is provided along with the code to ensure software quality. Since it makes use of the Siddon algorithm it is restricted to rectangular parallelepiped voxels but the spherical geometry of the corona can be handled through proper use of priors. We describe the main features of the code and show three practical examples of multi-spacecraft tomographic inversions using STEREO/EUVI and STEREO/COR1 data. Static and smoothly varying temporal evolution models are presented.Comment: 21 pages, 6 figures, 5 table

Optimization Methods for Inverse Problems

Optimization plays an important role in solving many inverse problems. Indeed, the task of inversion often either involves or is fully cast as a solution of an optimization problem. In this light, the mere non-linear, non-convex, and large-scale nature of many of these inversions gives rise to some very challenging optimization problems. The inverse problem community has long been developing various techniques for solving such optimization tasks. However, other, seemingly disjoint communities, such as that of machine learning, have developed, almost in parallel, interesting alternative methods which might have stayed under the radar of the inverse problem community. In this survey, we aim to change that. In doing so, we first discuss current state-of-the-art optimization methods widely used in inverse problems. We then survey recent related advances in addressing similar challenges in problems faced by the machine learning community, and discuss their potential advantages for solving inverse problems. By highlighting the similarities among the optimization challenges faced by the inverse problem and the machine learning communities, we hope that this survey can serve as a bridge in bringing together these two communities and encourage cross fertilization of ideas.Comment: 13 page

Linear Global Translation Estimation with Feature Tracks

This paper derives a novel linear position constraint for cameras seeing a common scene point, which leads to a direct linear method for global camera translation estimation. Unlike previous solutions, this method deals with collinear camera motion and weak image association at the same time. The final linear formulation does not involve the coordinates of scene points, which makes it efficient even for large scale data. We solve the linear equation based on $L_1$ norm, which makes our system more robust to outliers in essential matrices and feature correspondences. We experiment this method on both sequentially captured images and unordered Internet images. The experiments demonstrate its strength in robustness, accuracy, and efficiency.Comment: Changes: 1. Adopt BMVC2015 style; 2. Combine sections 3 and 5; 3. Move "Evaluation on synthetic data" out to supplementary file; 4. Divide subsection "Evaluation on general data" to subsections "Experiment on sequential data" and "Experiment on unordered Internet data"; 5. Change Fig. 1 and Fig.8; 6. Move Fig. 6 and Fig. 7 to supplementary file; 7 Change some symbols; 8. Correct some typo