A wide range of systems exhibit high dimensional incomplete data. Accurate estimation of the missing data is often desired, and is crucial for many downstream analyses. Many state-of-the-art recovery methods involve supervised learning using datasets containing full observations. In contrast, we focus on unsupervised estimation of missing image data, where no full observations are available - a common situation in practice. Unsupervised imputation methods for images often employ a simple linear subspace to capture correlations between data dimensions, omitting more complex relationships. In this work, we introduce a general probabilistic model that describes sparse high dimensional imaging data as being generated by a deep non-linear embedding. We derive a learning algorithm using a variational approximation based on convolutional neural networks and discuss its relationship to linear imputation models, the variational auto encoder, and deep image priors. We introduce sparsity-aware network building blocks that explicitly model observed and missing data. We analyze proposed sparsity-aware network building blocks, evaluate our method on public domain imaging datasets, and conclude by showing that our method enables imputation in an important real-world problem involving medical images. The code is freely available as part of the |neuron| library at this http URL.
Several methods define neural networks in other contexts that are not directly related to our task, but still share nomenclature. For example, spatially-sparse CNNs assume a fully observed input, but the content itself is sparse, such as thin writing on a black background @cite_45 @cite_31 . Faster sparse convolutions are proposed by explicitly operating on the pixels that represent content, with the focus of efficient computation. Other methods propose sparsity of the parameter space in neural networks to improve various metrics of network efficiency @cite_7 @cite_32 @cite_10 .
@cite_7 @cite_32 @cite_45 @cite_31 @cite_10
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Conventional deep convolutional neural networks (CNNs) apply convolution operators uniformly in space across all feature maps for hundreds of layers - this incurs a high computational cost for real-time applications. For many problems such as object detection and semantic segmentation, we are able to obtain a low-cost computation mask, either from a priori problem knowledge, or from a low-resolution segmentation network. We show that such computation masks can be used to reduce computation in the high-resolution main network. Variants of sparse activation CNNs have previously been explored on small-scale tasks and showed no degradation in terms of object classification accuracy, but often measured gains in terms of theoretical FLOPs without realizing a practical speedup when compared to highly optimized dense convolution implementations. In this work, we leverage the sparsity structure of computation masks and propose a novel tiling-based sparse convolution algorithm. We verified the effectiveness of our sparse CNN on LiDAR-based 3D object detection, and we report significant wall-clock speed-ups compared to dense convolution without noticeable loss of accuracy. In most computer vision applications, convolutional neural networks (CNNs) operate on dense image data generated by ordinary cameras. Designing CNNs for sparse and irregularly spaced input data is still an open problem with numerous applications in autonomous driving, robotics, and surveillance. To tackle this challenging problem, we introduce an algebraically-constrained convolution layer for CNNs with sparse input and demonstrate its capabilities for the scene depth completion task. We propose novel strategies for determining the confidence from the convolution operation and propagating it to consecutive layers. Furthermore, we propose an objective function that simultaneously minimizes the data error while maximizing the output confidence. Comprehensive experiments are performed on the KITTI depth benchmark and the results clearly demonstrate that the proposed approach achieves superior performance while requiring three times fewer parameters than the state-of-the-art methods. Moreover, our approach produces a continuous pixel-wise confidence map enabling information fusion, state inference, and decision support. To attain a favorable performance on large-scale datasets, convolutional neural networks (CNNs) are usually designed to have very high capacity involving millions of parameters. In this work, we aim at optimizing the number of neurons in a network, thus the number of parameters. We show that, by incorporating sparse constraints into the objective function, it is possible to decimate the number of neurons during the training stage. As a result, the number of parameters and the memory footprint of the neural network are also reduced, which is also desirable at the test time. We evaluated our method on several well-known CNN structures including AlexNet, and VGG over different datasets including ImageNet. Extensive experimental results demonstrate that our method leads to compact networks. Taking first fully connected layer as an example, our compact CNN contains only (30 , ) of the original neurons without any degradation of the top-1 classification accuracy. Conventional deep convolutional neural networks (CNNs) apply convolution operators uniformly in space across all feature maps for hundreds of layers - this incurs a high computational cost for real time applications. For many problems such as object detection and semantic segmentation, we are able to obtain a low-cost computation mask, either from a priori problem knowledge, or from a low resolution segmentation network. We show that such computation masks can be used to reduce computation in the high resolution main network. Variants of sparse activation CNNs have previously been explored on small scale tasks, and showed no degradation in terms of object classification accuracy, but often measured gains in terms of theoretical FLOPs without realizing a practical speed-up when compared to highly optimized dense convolution implementations. In this work, we leverage the sparsity structure of computation masks and propose a novel tiling-based sparse convolution algorithm. We verified the effectiveness of our sparse CNN on LiDAR based 3D object detection, and we report significant wall-clock speed-ups compared to dense convolution, as well as improved detection accuracy.