Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure

A crucial aspect of mass-mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present results from a new method that reconstructs maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type $\ell_1$-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass-mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artifacts of the reconstruction. Here we present this new formalism, demonstrate the method on illustrative examples, before applying the developed formalism to two observational datasets of the Abel-520 cluster. In our Bayesian framework it is found that neither Abel-520 dataset can conclusively determine the physicality of individual local massive substructure at significant confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data

Confidence Propagation through CNNs for Guided Sparse Depth Regression

Generally, convolutional neural networks (CNNs) process data on a regular grid, e.g. data generated by ordinary cameras. Designing CNNs for sparse and irregularly spaced input data is still an open research problem with numerous applications in autonomous driving, robotics, and surveillance. In this paper, we propose an algebraically-constrained normalized convolution layer for CNNs with highly sparse input that has a smaller number of network parameters compared to related work. We propose novel strategies for determining the confidence from the convolution operation and propagating it to consecutive layers. We also propose an objective function that simultaneously minimizes the data error while maximizing the output confidence. To integrate structural information, we also investigate fusion strategies to combine depth and RGB information in our normalized convolution network framework. In addition, we introduce the use of output confidence as an auxiliary information to improve the results. The capabilities of our normalized convolution network framework are demonstrated for the problem of scene depth completion. Comprehensive experiments are performed on the KITTI-Depth and the NYU-Depth-v2 datasets. The results clearly demonstrate that the proposed approach achieves superior performance while requiring only about 1-5% of the number of parameters compared to the state-of-the-art methods.Comment: 14 pages, 14 Figure

Dense Motion Estimation for Smoke

Motion estimation for highly dynamic phenomena such as smoke is an open challenge for Computer Vision. Traditional dense motion estimation algorithms have difficulties with non-rigid and large motions, both of which are frequently observed in smoke motion. We propose an algorithm for dense motion estimation of smoke. Our algorithm is robust, fast, and has better performance over different types of smoke compared to other dense motion estimation algorithms, including state of the art and neural network approaches. The key to our contribution is to use skeletal flow, without explicit point matching, to provide a sparse flow. This sparse flow is upgraded to a dense flow. In this paper we describe our algorithm in greater detail, and provide experimental evidence to support our claims.Comment: ACCV201

FASTLens (FAst STatistics for weak Lensing) : Fast method for Weak Lensing Statistics and map making

With increasingly large data sets, weak lensing measurements are able to measure cosmological parameters with ever greater precision. However this increased accuracy also places greater demands on the statistical tools used to extract the available information. To date, the majority of lensing analyses use the two point-statistics of the cosmic shear field. These can either be studied directly using the two-point correlation function, or in Fourier space, using the power spectrum. But analyzing weak lensing data inevitably involves the masking out of regions or example to remove bright stars from the field. Masking out the stars is common practice but the gaps in the data need proper handling. In this paper, we show how an inpainting technique allows us to properly fill in these gaps with only $N \log N$ operations, leading to a new image from which we can compute straight forwardly and with a very good accuracy both the pow er spectrum and the bispectrum. We propose then a new method to compute the bispectrum with a polar FFT algorithm, which has the main advantage of avoiding any interpolation in the Fourier domain. Finally we propose a new method for dark matter mass map reconstruction from shear observations which integrates this new inpainting concept. A range of examples based on 3D N-body simulations illustrates the results.Comment: Final version accepted by MNRAS. The FASTLens software is available from the following link : http://irfu.cea.fr/Ast/fastlens.software.ph

Magnitude Attention-based Dynamic Pruning

Existing pruning methods utilize the importance of each weight based on specified criteria only when searching for a sparse structure but do not utilize it during training. In this work, we propose a novel approach - \textbf{M}agnitude \textbf{A}ttention-based Dynamic \textbf{P}runing (MAP) method, which applies the importance of weights throughout both the forward and backward paths to explore sparse model structures dynamically. Magnitude attention is defined based on the magnitude of weights as continuous real-valued numbers enabling a seamless transition from a redundant to an effective sparse network by promoting efficient exploration. Additionally, the attention mechanism ensures more effective updates for important layers within the sparse network. In later stages of training, our approach shifts from exploration to exploitation, exclusively updating the sparse model composed of crucial weights based on the explored structure, resulting in pruned models that not only achieve performance comparable to dense models but also outperform previous pruning methods on CIFAR-10/100 and ImageNet