Global Guarantees for Enforcing Deep Generative Priors by Empirical Risk

We examine the theoretical properties of enforcing priors provided by generative deep neural networks via empirical risk minimization. In particular we consider two models, one in which the task is to invert a generative neural network given access to its last layer and another in which the task is to invert a generative neural network given only compressive linear observations of its last layer. We establish that in both cases, in suitable regimes of network layer sizes and a randomness assumption on the network weights, that the non-convex objective function given by empirical risk minimization does not have any spurious stationary points. That is, we establish that with high probability, at any point away from small neighborhoods around two scalar multiples of the desired solution, there is a descent direction. Hence, there are no local minima, saddle points, or other stationary points outside these neighborhoods. These results constitute the first theoretical guarantees which establish the favorable global geometry of these non-convex optimization problems, and they bridge the gap between the empirical success of enforcing deep generative priors and a rigorous understanding of non-linear inverse problems.Comment: Accepted for presentation at Conference on Learning Theory (COLT) 201

Deep Learning Techniques for Inverse Problems in Imaging

Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy that can be used to categorize different problems and reconstruction methods. Our taxonomy is organized along two central axes: (1) whether or not a forward model is known and to what extent it is used in training and testing, and (2) whether or not the learning is supervised or unsupervised, i.e., whether or not the training relies on access to matched ground truth image and measurement pairs. We also discuss the trade-offs associated with these different reconstruction approaches, caveats and common failure modes, plus open problems and avenues for future work

Deep De-Aliasing for Fast Compressive Sensing MRI

Fast Magnetic Resonance Imaging (MRI) is highly in demand for many clinical applications in order to reduce the scanning cost and improve the patient experience. This can also potentially increase the image quality by reducing the motion artefacts and contrast washout. However, once an image field of view and the desired resolution are chosen, the minimum scanning time is normally determined by the requirement of acquiring sufficient raw data to meet the Nyquist-Shannon sampling criteria. Compressive Sensing (CS) theory has been perfectly matched to the MRI scanning sequence design with much less required raw data for the image reconstruction. Inspired by recent advances in deep learning for solving various inverse problems, we propose a conditional Generative Adversarial Networks-based deep learning framework for de-aliasing and reconstructing MRI images from highly undersampled data with great promise to accelerate the data acquisition process. By coupling an innovative content loss with the adversarial loss our de-aliasing results are more realistic. Furthermore, we propose a refinement learning procedure for training the generator network, which can stabilise the training with fast convergence and less parameter tuning. We demonstrate that the proposed framework outperforms state-of-the-art CS-MRI methods, in terms of reconstruction error and perceptual image quality. In addition, our method can reconstruct each image in 0.22ms--0.37ms, which is promising for real-time applications.Comment: 15 pages, 5 figure

Compressed Sensing with Deep Image Prior and Learned Regularization

We propose a novel method for compressed sensing recovery using untrained deep generative models. Our method is based on the recently proposed Deep Image Prior (DIP), wherein the convolutional weights of the network are optimized to match the observed measurements. We show that this approach can be applied to solve any differentiable linear inverse problem, outperforming previous unlearned methods. Unlike various learned approaches based on generative models, our method does not require pre-training over large datasets. We further introduce a novel learned regularization technique, which incorporates prior information on the network weights. This reduces reconstruction error, especially for noisy measurements. Finally, we prove that, using the DIP optimization approach, moderately overparameterized single-layer networks can perfectly fit any signal despite the non-convex nature of the fitting problem. This theoretical result provides justification for early stopping

Deep Compressed Sensing

Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. CS is flexible and data efficient, but its application has been restricted by the strong assumption of sparsity and costly reconstruction process. A recent approach that combines CS with neural network generators has removed the constraint of sparsity, but reconstruction remains slow. Here we propose a novel framework that significantly improves both the performance and speed of signal recovery by jointly training a generator and the optimisation process for reconstruction via meta-learning. We explore training the measurements with different objectives, and derive a family of models based on minimising measurement errors. We show that Generative Adversarial Nets (GANs) can be viewed as a special case in this family of models. Borrowing insights from the CS perspective, we develop a novel way of improving GANs using gradient information from the discriminator.Comment: ICML 201

A Transfer-Learning Approach for Accelerated MRI using Deep Neural Networks

Purpose: Neural networks have received recent interest for reconstruction of undersampled MR acquisitions. Ideally network performance should be optimized by drawing the training and testing data from the same domain. In practice, however, large datasets comprising hundreds of subjects scanned under a common protocol are rare. The goal of this study is to introduce a transfer-learning approach to address the problem of data scarcity in training deep networks for accelerated MRI. Methods: Neural networks were trained on thousands of samples from public datasets of either natural images or brain MR images. The networks were then fine-tuned using only few tens of brain MR images in a distinct testing domain. Domain-transferred networks were compared to networks trained directly in the testing domain. Network performance was evaluated for varying acceleration factors (2-10), number of training samples (0.5-4k) and number of fine-tuning samples (0-100). Results: The proposed approach achieves successful domain transfer between MR images acquired with different contrasts (T1- and T2-weighted images), and between natural and MR images (ImageNet and T1- or T2-weighted images). Networks obtained via transfer-learning using only tens of images in the testing domain achieve nearly identical performance to networks trained directly in the testing domain using thousands of images. Conclusion: The proposed approach might facilitate the use of neural networks for MRI reconstruction without the need for collection of extensive imaging datasets

Recurrent Generative Adversarial Networks for Proximal Learning and Automated Compressive Image Recovery

Recovering images from undersampled linear measurements typically leads to an ill-posed linear inverse problem, that asks for proper statistical priors. Building effective priors is however challenged by the low train and test overhead dictated by real-time tasks; and the need for retrieving visually "plausible" and physically "feasible" images with minimal hallucination. To cope with these challenges, we design a cascaded network architecture that unrolls the proximal gradient iterations by permeating benefits from generative residual networks (ResNet) to modeling the proximal operator. A mixture of pixel-wise and perceptual costs is then deployed to train proximals. The overall architecture resembles back-and-forth projection onto the intersection of feasible and plausible images. Extensive computational experiments are examined for a global task of reconstructing MR images of pediatric patients, and a more local task of superresolving CelebA faces, that are insightful to design efficient architectures. Our observations indicate that for MRI reconstruction, a recurrent ResNet with a single residual block effectively learns the proximal. This simple architecture appears to significantly outperform the alternative deep ResNet architecture by 2dB SNR, and the conventional compressed-sensing MRI by 4dB SNR with 100x faster inference. For image superresolution, our preliminary results indicate that modeling the denoising proximal demands deep ResNets.Comment: 11 pages, 11 figure

Medical Image Generation using Generative Adversarial Networks

Generative adversarial networks (GANs) are unsupervised Deep Learning approach in the computer vision community which has gained significant attention from the last few years in identifying the internal structure of multimodal medical imaging data. The adversarial network simultaneously generates realistic medical images and corresponding annotations, which proven to be useful in many cases such as image augmentation, image registration, medical image generation, image reconstruction, and image-to-image translation. These properties bring the attention of the researcher in the field of medical image analysis and we are witness of rapid adaption in many novel and traditional applications. This chapter provides state-of-the-art progress in GANs-based clinical application in medical image generation, and cross-modality synthesis. The various framework of GANs which gained popularity in the interpretation of medical images, such as Deep Convolutional GAN (DCGAN), Laplacian GAN (LAPGAN), pix2pix, CycleGAN, and unsupervised image-to-image translation model (UNIT), continue to improve their performance by incorporating additional hybrid architecture, has been discussed. Further, some of the recent applications of these frameworks for image reconstruction, and synthesis, and future research directions in the area have been covered.Comment: 19 pages, 3 figures, 5 table

Adversarial and Perceptual Refinement for Compressed Sensing MRI Reconstruction

Deep learning approaches have shown promising performance for compressed sensing-based Magnetic Resonance Imaging. While deep neural networks trained with mean squared error (MSE) loss functions can achieve high peak signal to noise ratio, the reconstructed images are often blurry and lack sharp details, especially for higher undersampling rates. Recently, adversarial and perceptual loss functions have been shown to achieve more visually appealing results. However, it remains an open question how to (1) optimally combine these loss functions with the MSE loss function and (2) evaluate such a perceptual enhancement. In this work, we propose a hybrid method, in which a visual refinement component is learnt on top of an MSE loss-based reconstruction network. In addition, we introduce a semantic interpretability score, measuring the visibility of the region of interest in both ground truth and reconstructed images, which allows us to objectively quantify the usefulness of the image quality for image post-processing and analysis. Applied on a large cardiac MRI dataset simulated with 8-fold undersampling, we demonstrate significant improvements ($p<0.01$) over the state-of-the-art in both a human observer study and the semantic interpretability score.Comment: To be published at MICCAI 201

Analysis of Deep Complex-Valued Convolutional Neural Networks for MRI Reconstruction

Many real-world signal sources are complex-valued, having real and imaginary components. However, the vast majority of existing deep learning platforms and network architectures do not support the use of complex-valued data. MRI data is inherently complex-valued, so existing approaches discard the richer algebraic structure of the complex data. In this work, we investigate end-to-end complex-valued convolutional neural networks - specifically, for image reconstruction in lieu of two-channel real-valued networks. We apply this to magnetic resonance imaging reconstruction for the purpose of accelerating scan times and determine the performance of various promising complex-valued activation functions. We find that complex-valued CNNs with complex-valued convolutions provide superior reconstructions compared to real-valued convolutions with the same number of trainable parameters, over a variety of network architectures and datasets