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Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve…
Overfitting is one of the most critical challenges in deep neural networks, and there are various types of regularization methods to improve generalization performance. Injecting noises to hidden units during training, e.g., dropout, is…
In this paper, we consider deep neural networks for solving inverse problems that are robust to forward model mis-specifications. Specifically, we treat sensing problems with model mismatch where one wishes to recover a sparse…
Recurrent convolution (RC) shares the same convolutional kernels and unrolls them multiple steps, which is originally proposed to model time-space signals. We argue that RC can be viewed as a model compression strategy for deep…
The normalizing layer has become one of the basic configurations of deep learning models, but it still suffers from computational inefficiency, interpretability difficulties, and low generality. After gaining a deeper understanding of the…
The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to…
The recovery of magnetic resonance (MR) images from undersampled measurements is a key problem that has seen extensive research in recent years. Unrolled approaches, which rely on end-to-end training of convolutional neural network (CNN)…
Learning meaningful representations using deep neural networks involves designing efficient training schemes and well-structured networks. Currently, the method of stochastic gradient descent that has a momentum with dropout is one of the…
Regularization plays a pivotal role in integrating prior information into inverse problems. While many deep learning methods have been proposed to solve inverse problems, determining where to apply regularization remains a crucial…
Fast data acquisition in Magnetic Resonance Imaging (MRI) is vastly in demand and scan time directly depends on the number of acquired k-space samples. The data-driven methods based on deep neural networks have resulted in promising…
Regularization by denoising (RED) is a widely-used framework for solving inverse problems by leveraging image denoisers as image priors. Recent work has reported the state-of-the-art performance of RED in a number of imaging applications…
We propose a novel data-dependent structured gradient regularizer to increase the robustness of neural networks vis-a-vis adversarial perturbations. Our regularizer can be derived as a controlled approximation from first principles,…
This paper revisits two prominent adaptive filtering algorithms, namely recursive least squares (RLS) and equivariant adaptive source separation (EASI), through the lens of algorithm unrolling. Building upon the unrolling methodology, we…
Clinical MRI encompasses diverse imaging protocols--spanning anatomical targets (cardiac, brain, knee), contrasts (T1, T2, mapping), sampling patterns (Cartesian, radial, spiral, kt-space), and acceleration factors--yet current deep…
Deep learning using multi-layer neural networks (NNs) architecture manifests superb power in modern machine learning systems. The trained Deep Neural Networks (DNNs) are typically large. The question we would like to address is whether it…
In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…
While much work has been devoted to understanding the implicit (and explicit) regularization of deep nonlinear networks in the supervised setting, this paper focuses on unsupervised learning, i.e., autoencoders are trained with the…
Deep neural networks are capable of learning powerful representations to tackle complex vision tasks but expose undesirable properties like the over-fitting issue. To this end, regularization techniques like image augmentation are necessary…
In this study, the problem of computing a sparse representation of multi-dimensional visual data is considered. In general, such data e.g., hyperspectral images, color images or video data consists of signals that exhibit strong local…
We propose a novel regularization algorithm to train deep neural networks, in which data at training time is severely biased. Since a neural network efficiently learns data distribution, a network is likely to learn the bias information to…