arXiv subjects

Alex M. Bronstein

Publications and source records attributed to Alex M. Bronstein.

67 records · Page 4Linked to original sources

arXiv2018

Class-Aware Fully-Convolutional Gaussian and Poisson Denoising

We propose a fully-convolutional neural-network architecture for image denoising which is simple yet powerful. Its structure allows to exploit the gradual nature of the denoising process, in which shallow layers handle local noise statistics, while deeper layers recover edges and enhance textures. Our method advances the state-of-the-art when trained for different noise levels and distributions (both Gaussian and Poisson). In addition, we show that making the denoiser class-aware by exploiting semantic class information boosts performance, enhances textures and reduces artifacts.

cs.CV↗

arXiv2018

Tradeoffs between Convergence Speed and Reconstruction Accuracy in Inverse Problems

Solving inverse problems with iterative algorithms is popular, especially for large data. Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy. Given an error one is willing to tolerate, an important question is whether it is possible to modify the original iterations to obtain faster convergence to a minimizer achieving the allowed error without increasing the computational cost of each iteration considerably. Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set may lead to faster convergence at the cost of an additional reconstruction error related to the accuracy of the set approximation. Our theory ties to recent advances in sparse recovery, compressed sensing, and deep learning. Particularly, it may provide a possible explanation to the successful approximation of the l1-minimization solution by neural networks with layers representing iterations, as practiced in the learned iterative shrinkage-thresholding algorithm (LISTA).

math.NA↗

arXiv2017

Towards CT-quality Ultrasound Imaging using Deep Learning

The cost-effectiveness and practical harmlessness of ultrasound imaging have made it one of the most widespread tools for medical diagnosis. Unfortunately, the beam-forming based image formation produces granular speckle noise, blurring, shading and other artifacts. To overcome these effects, the ultimate goal would be to reconstruct the tissue acoustic properties by solving a full wave propagation inverse problem. In this work, we make a step towards this goal, using Multi-Resolution Convolutional Neural Networks (CNN). As a result, we are able to reconstruct CT-quality images from the reflected ultrasound radio-frequency(RF) data obtained by simulation from real CT scans of a human body. We also show that CNN is able to imitate existing computationally heavy despeckling methods, thereby saving orders of magnitude in computations and making them amenable to real-time applications.

cs.CV↗

arXiv2017

Subspace Least Squares Multidimensional Scaling

Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the analysis and reconstruction of non-rigid shapes. In this regard, MDS can be thought of as a \textit{shape from metric} algorithm, consisting of finding a configuration of points in the Euclidean space that realize, as isometrically as possible, some given distance structure. In the present work we cast the least squares variant of MDS (LS-MDS) in the spectral domain. This uncovers a multiresolution property of distance scaling which speeds up the optimization by a significant amount, while producing comparable, and sometimes even better, embeddings.

cs.CG↗

arXiv2017

Deep Functional Maps: Structured Prediction for Dense Shape Correspondence

We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label identifying a point on some reference domain; the correspondence is then constructed a posteriori by composing the label predictions of two input shapes. We propose a paradigm shift and design a structured prediction model in the space of functional maps, linear operators that provide a compact representation of the correspondence. We model the learning process via a deep residual network which takes dense descriptor fields defined on two shapes as input, and outputs a soft map between the two given objects. The resulting correspondence is shown to be accurate on several challenging benchmarks comprising multiple categories, synthetic models, real scans with acquisition artifacts, topological noise, and partiality.

cs.CV↗

arXiv2017

Deep Class Aware Denoising

The increasing demand for high image quality in mobile devices brings forth the need for better computational enhancement techniques, and image denoising in particular. At the same time, the images captured by these devices can be categorized into a small set of semantic classes. However simple, this observation has not been exploited in image denoising until now. In this paper, we demonstrate how the reconstruction quality improves when a denoiser is aware of the type of content in the image. To this end, we first propose a new fully convolutional deep neural network architecture which is simple yet powerful as it achieves state-of-the-art performance even without being class-aware. We further show that a significant boost in performance of up to $0.4$ dB PSNR can be achieved by making our network class-aware, namely, by fine-tuning it for images belonging to a specific semantic class. Relying on the hugely successful existing image classifiers, this research advocates for using a class-aware approach in all image enhancement tasks.

cs.CV↗

arXiv2017

Deep Convolutional Denoising of Low-Light Images

Poisson distribution is used for modeling noise in photon-limited imaging. While canonical examples include relatively exotic types of sensing like spectral imaging or astronomy, the problem is relevant to regular photography now more than ever due to the booming market for mobile cameras. Restricted form factor limits the amount of absorbed light, thus computational post-processing is called for. In this paper, we make use of the powerful framework of deep convolutional neural networks for Poisson denoising. We demonstrate how by training the same network with images having a specific peak value, our denoiser outperforms previous state-of-the-art by a large margin both visually and quantitatively. Being flexible and data-driven, our solution resolves the heavy ad hoc engineering used in previous methods and is an order of magnitude faster. We further show that by adding a reasonable prior on the class of the image being processed, another significant boost in performance is achieved.

cs.CV↗

arXiv2016

Deep Neural Networks with Random Gaussian Weights: A Universal Classification Strategy?

Three important properties of a classification machinery are: (i) the system preserves the core information of the input data; (ii) the training examples convey information about unseen data; and (iii) the system is able to treat differently points from different classes. In this work we show that these fundamental properties are satisfied by the architecture of deep neural networks. We formally prove that these networks with random Gaussian weights perform a distance-preserving embedding of the data, with a special treatment for in-class and out-of-class data. Similar points at the input of the network are likely to have a similar output. The theoretical analysis of deep networks here presented exploits tools used in the compressed sensing and dictionary learning literature, thereby making a formal connection between these important topics. The derived results allow drawing conclusions on the metric learning properties of the network and their relation to its structure, as well as providing bounds on the required size of the training set such that the training examples would represent faithfully the unseen data. The results are validated with state-of-the-art trained networks.

cs.NE↗

arXiv2015

On the Stability of Deep Networks

In this work we study the properties of deep neural networks (DNN) with random weights. We formally prove that these networks perform a distance-preserving embedding of the data. Based on this we then draw conclusions on the size of the training data and the networks' structure. A longer version of this paper with more results and details can be found in (Giryes et al., 2015). In particular, we formally prove in the longer version that DNN with random Gaussian weights perform a distance-preserving embedding of the data, with a special treatment for in-class and out-of-class data.

stat.ML↗

arXiv2014

Sparse similarity-preserving hashing

In recent years, a lot of attention has been devoted to efficient nearest neighbor search by means of similarity-preserving hashing. One of the plights of existing hashing techniques is the intrinsic trade-off between performance and computational complexity: while longer hash codes allow for lower false positive rates, it is very difficult to increase the embedding dimensionality without incurring in very high false negatives rates or prohibiting computational costs. In this paper, we propose a way to overcome this limitation by enforcing the hash codes to be sparse. Sparse high-dimensional codes enjoy from the low false positive rates typical of long hashes, while keeping the false negative rates similar to those of a shorter dense hashing scheme with equal number of degrees of freedom. We use a tailored feed-forward neural network for the hashing function. Extensive experimental evaluation involving visual and multi-modal data shows the benefits of the proposed method.

cs.CV↗

arXiv2012

Learning efficient sparse and low rank models

Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with parsimony-promoting terms. The inherently sequential structure and data-dependent complexity and latency of iterative optimization constitute a major limitation in many applications requiring real-time performance or involving large-scale data. Another limitation encountered by these modeling techniques is the difficulty of their inclusion in discriminative learning scenarios. In this work, we propose to move the emphasis from the model to the pursuit algorithm, and develop a process-centric view of parsimonious modeling, in which a learned deterministic fixed-complexity pursuit process is used in lieu of iterative optimization. We show a principled way to construct learnable pursuit process architectures for structured sparse and robust low rank models, derived from the iteration of proximal descent algorithms. These architectures learn to approximate the exact parsimonious representation at a fraction of the complexity of the standard optimization methods. We also show that appropriate training regimes allow to naturally extend parsimonious models to discriminative settings. State-of-the-art results are demonstrated on several challenging problems in image and audio processing with several orders of magnitude speedup compared to the exact optimization algorithms.

cs.LG↗

arXiv2012

Learning Robust Low-Rank Representations

In this paper we present a comprehensive framework for learning robust low-rank representations by combining and extending recent ideas for learning fast sparse coding regressors with structured non-convex optimization techniques. This approach connects robust principal component analysis (RPCA) with dictionary learning techniques and allows its approximation via trainable encoders. We propose an efficient feed-forward architecture derived from an optimization algorithm designed to exactly solve robust low dimensional projections. This architecture, in combination with different training objective functions, allows the regressors to be used as online approximants of the exact offline RPCA problem or as RPCA-based neural networks. Simple modifications of these encoders can handle challenging extensions, such as the inclusion of geometric data transformations. We present several examples with real data from image, audio, and video processing. When used to approximate RPCA, our basic implementation shows several orders of magnitude speedup compared to the exact solvers with almost no performance degradation. We show the strength of the inclusion of learning to the RPCA approach on a music source separation application, where the encoders outperform the exact RPCA algorithms, which are already reported to produce state-of-the-art results on a benchmark database. Our preliminary implementation on an iPad shows faster-than-real-time performance with minimal latency.

cs.LG↗

arXiv2010

Diffusion-geometric maximally stable component detection in deformable shapes

Maximally stable component detection is a very popular method for feature analysis in images, mainly due to its low computation cost and high repeatability. With the recent advance of feature-based methods in geometric shape analysis, there is significant interest in finding analogous approaches in the 3D world. In this paper, we formulate a diffusion-geometric framework for stable component detection in non-rigid 3D shapes, which can be used for geometric feature detection and description. A quantitative evaluation of our method on the SHREC'10 feature detection benchmark shows its potential as a source of high-quality features.

cs.CV↗