Continuous Generative Neural Networks

In this work, we present and study Continuous Generative Neural Networks (CGNNs), namely, generative models in the continuous setting: the output of a CGNN belongs to an infinite-dimensional function space. The architecture is inspired by DCGAN, with one fully connected layer, several convolutional layers and nonlinear activation functions. In the continuous $L^2$ setting, the dimensions of the spaces of each layer are replaced by the scales of a multiresolution analysis of a compactly supported wavelet. We present conditions on the convolutional filters and on the nonlinearity that guarantee that a CGNN is injective. This theory finds applications to inverse problems, and allows for deriving Lipschitz stability estimates for (possibly nonlinear) infinite-dimensional inverse problems with unknowns belonging to the manifold generated by a CGNN. Several numerical simulations, including signal deblurring, illustrate and validate this approach.Comment: 40 pages, 8 figure

Parametric Scattering Networks

La plupart des percées dans l'apprentissage profond et en particulier dans les réseaux de neurones convolutifs ont impliqué des efforts importants pour collecter et annoter des quantités massives de données. Alors que les mégadonnées deviennent de plus en plus répandues, il existe de nombreuses applications où la tâche d'annoter plus d'un petit nombre d'échantillons est irréalisable, ce qui a suscité un intérêt pour les tâches d'apprentissage sur petits échantillons. Il a été montré que les transformées de diffusion d'ondelettes sont efficaces dans le cadre de données annotées limitées. La transformée de diffusion en ondelettes crée des invariants géométriques et une stabilité de déformation. Les filtres d'ondelettes utilisés dans la transformée de diffusion sont généralement sélectionnés pour créer une trame serrée via une ondelette mère paramétrée. Dans ce travail, nous étudions si cette construction standard est optimale. En nous concentrant sur les ondelettes de Morlet, nous proposons d'apprendre les échelles, les orientations et les rapports d'aspect des filtres. Nous appelons notre approche le Parametric Scattering Network. Nous illustrons que les filtres appris par le réseau de diffusion paramétrique peuvent être interprétés en fonction de la tâche spécifique sur laquelle ils ont été entrainés. Nous démontrons également empiriquement que notre transformée de diffusion paramétrique partage une stabilité aux déformations similaire à la transformée de diffusion traditionnelle. Enfin, nous montrons que notre version apprise de la transformée de diffusion génère des gains de performances significatifs par rapport à la transformée de diffusion standard lorsque le nombre d'échantillions d'entrainement est petit. Nos résultats empiriques suggèrent que les constructions traditionnelles des ondelettes ne sont pas toujours nécessaires.Most breakthroughs in deep learning have required considerable effort to collect massive amounts of well-annotated data. As big data becomes more prevalent, there are many applications where annotating more than a small number of samples is impractical, leading to growing interest in small sample learning tasks and deep learning approaches towards them. Wavelet scattering transforms have been shown to be effective in limited labeled data settings. The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations than other non-learned representations and to outperform learned representations in certain tasks, particularly on limited labeled data and highly structured signals. The wavelet filters used in the scattering transform are typically selected to create a tight frame via a parameterized mother wavelet. In this work, we investigate whether this standard wavelet filterbank construction is optimal. Focusing on Morlet wavelets, we propose to learn the scales, orientations, and aspect ratios of the filters to produce problem-specific parameterizations of the scattering transform. We call our approach the Parametric Scattering Network. We illustrate that filters learned by parametric scattering networks can be interpreted according to the specific task on which they are trained. We also empirically demonstrate that our parametric scattering transforms share similar stability to deformations as the traditional scattering transforms. We also show that our approach yields significant performance gains in small-sample classification settings over the standard scattering transform. Moreover, our empirical results suggest that traditional filterbank constructions may not always be necessary for scattering transforms to extract useful representations

Probabilistic methods for high dimensional signal processing

This thesis investigates the use of probabilistic and Bayesian methods for analysing high dimensional signals. The work proceeds in three main parts sharing similar objectives. Throughout we focus on building data efficient inference mechanisms geared toward high dimensional signal processing. This is achieved by using probabilistic models on top of informative data representation operators. We also improve on the fitting objective to make it better suited to our requirements. Variational Inference We introduce a variational approximation framework using direct optimisation of what is known as the scale invariant Alpha-Beta divergence (sAB-divergence). This new objective encompasses most variational objectives that use the Kullback-Leibler, the Rényi or the gamma divergences. It also gives access to objective functions never exploited before in the context of variational inference. This is achieved via two easy to interpret control parameters, which allow for a smooth interpolation over the divergence space while trading-off properties such as mass-covering of a target distribution and robustness to outliers in the data. Furthermore, the sAB variational objective can be optimised directly by re-purposing existing methods for Monte Carlo computation of complex variational objectives, leading to estimates of the divergence instead of variational lower bounds. We show the advantages of this objective on Bayesian models for regression problems. Roof-Edge hidden Markov Random Field We propose a method for semi-local Hurst estimation by incorporating a Markov random field model to constrain a wavelet-based pointwise Hurst estimator. This results in an estimator which is able to exploit the spatial regularities of a piecewise parametric varying Hurst parameter. The pointwise estimates are jointly inferred along with the parametric form of the underlying Hurst function which characterises how the Hurst parameter varies deterministically over the spatial support of the data. Unlike recent Hurst regularisation methods, the proposed approach is flexible in that arbitrary parametric forms can be considered and is extensible in as much as the associated gradient descent algorithm can accommodate a broad class of distributional assumptions without any significant modifications. The potential benefits of the approach are illustrated with simulations of various first-order polynomial forms. Scattering Hidden Markov Tree We here combine the rich, over-complete signal representation afforded by the scattering transform together with a probabilistic graphical model which captures hierarchical dependencies between coefficients at different layers. The wavelet scattering network result in a high-dimensional representation which is translation invariant and stable to deformations whilst preserving informative content. Such properties are achieved by cascading wavelet transform convolutions with non-linear modulus and averaging operators. The network structure and its distributions are described using a Hidden Markov Tree. This yields a generative model for high dimensional inference and offers a means to perform various inference tasks such as prediction. Our proposed scattering convolutional hidden Markov tree displays promising results on classification tasks of complex images in the challenging case where the number of training examples is extremely small. We also use variational methods on the aforementioned model and leverage the objective sAB variational objective defined earlier to improve the quality of the approximation

Real-time Ultrasound Signals Processing: Denoising and Super-resolution

Ultrasound acquisition is widespread in the biomedical field, due to its properties of low cost, portability, and non-invasiveness for the patient. The processing and analysis of US signals, such as images, 2D videos, and volumetric images, allows the physician to monitor the evolution of the patient's disease, and support diagnosis, and treatments (e.g., surgery). US images are affected by speckle noise, generated by the overlap of US waves. Furthermore, low-resolution images are acquired when a high acquisition frequency is applied to accurately characterise the behaviour of anatomical features that quickly change over time. Denoising and super-resolution of US signals are relevant to improve the visual evaluation of the physician and the performance and accuracy of processing methods, such as segmentation and classification. The main requirements for the processing and analysis of US signals are real-time execution, preservation of anatomical features, and reduction of artefacts. In this context, we present a novel framework for the real-time denoising of US 2D images based on deep learning and high-performance computing, which reduces noise while preserving anatomical features in real-time execution. We extend our framework to the denoise of arbitrary US signals, such as 2D videos and 3D images, and we apply denoising algorithms that account for spatio-temporal signal properties into an image-to-image deep learning model. As a building block of this framework, we propose a novel denoising method belonging to the class of low-rank approximations, which learns and predicts the optimal thresholds of the Singular Value Decomposition. While previous denoise work compromises the computational cost and effectiveness of the method, the proposed framework achieves the results of the best denoising algorithms in terms of noise removal, anatomical feature preservation, and geometric and texture properties conservation, in a real-time execution that respects industrial constraints. The framework reduces the artefacts (e.g., blurring) and preserves the spatio-temporal consistency among frames/slices; also, it is general to the denoising algorithm, anatomical district, and noise intensity. Then, we introduce a novel framework for the real-time reconstruction of the non-acquired scan lines through an interpolating method; a deep learning model improves the results of the interpolation to match the target image (i.e., the high-resolution image). We improve the accuracy of the prediction of the reconstructed lines through the design of the network architecture and the loss function. %The design of the deep learning architecture and the loss function allow the network to improve the accuracy of the prediction of the reconstructed lines. In the context of signal approximation, we introduce our kernel-based sampling method for the reconstruction of 2D and 3D signals defined on regular and irregular grids, with an application to US 2D and 3D images. Our method improves previous work in terms of sampling quality, approximation accuracy, and geometry reconstruction with a slightly higher computational cost. For both denoising and super-resolution, we evaluate the compliance with the real-time requirement of US applications in the medical domain and provide a quantitative evaluation of denoising and super-resolution methods on US and synthetic images. Finally, we discuss the role of denoising and super-resolution as pre-processing steps for segmentation and predictive analysis of breast pathologies

A survey of handwritten character recognition with MNIST and EMNIST

This article belongs to the Special Issue Computer Vision and Pattern Recognition in the Era of Deep Learning.This paper summarizes the top state-of-the-art contributions reported on the MNIST dataset for handwritten digit recognition. This dataset has been extensively used to validate novel techniques in computer vision, and in recent years, many authors have explored the performance of convolutional neural networks (CNNs) and other deep learning techniques over this dataset. To the best of our knowledge, this paper is the first exhaustive and updated review of this dataset; there are some online rankings, but they are outdated, and most published papers survey only closely related works, omitting most of the literature. This paper makes a distinction between those works using some kind of data augmentation and works using the original dataset out-of-the-box. Also, works using CNNs are reported separately; as they are becoming the state-of-the-art approach for solving this problem. Nowadays, a significant amount of works have attained a test error rate smaller than 1% on this dataset; which is becoming non-challenging. By mid-2017, a new dataset was introduced: EMNIST, which involves both digits and letters, with a larger amount of data acquired from a database different than MNIST's. In this paper, EMNIST is explained and some results are surveyed

A Partially Learned Algorithm for Joint Photoacoustic Reconstruction and Segmentation

In an inhomogeneously illuminated photoacoustic image, important information like vascular geometry is not readily available when only the initial pressure is reconstructed. To obtain the desired information, algorithms for image segmentation are often applied as a post-processing step. In this work, we propose to jointly acquire the photoacoustic reconstruction and segmentation, by modifying a recently developed partially learned algorithm based on a convolutional neural network. We investigate the stability of the algorithm against changes in initial pressures and photoacoustic system settings. These insights are used to develop an algorithm that is robust to input and system settings. Our approach can easily be applied to other imaging modalities and can be modified to perform other high-level tasks different from segmentation. The method is validated on challenging synthetic and experimental photoacoustic tomography data in limited angle and limited view scenarios. It is computationally less expensive than classical iterative methods and enables higher quality reconstructions and segmentations than state-of-the-art learned and non-learned methods.Comment: "copyright 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.