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Cascaded computation, whereby predictions are recurrently refined over several stages, has been a persistent theme throughout the development of landmark detection models. In this work, we show that the recently proposed Deep Equilibrium…
There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…
Deformable medical image registration is traditionally formulated as an optimization problem. While classical methods solve this problem iteratively, recent learning-based approaches use recurrent neural networks (RNNs) to mimic this…
Plug-and-play (PnP) methods with deep denoisers have shown impressive results in imaging problems. They typically require strong convexity or smoothness of the fidelity term and a (residual) non-expansive denoiser for convergence. These…
Deep equilibrium models (DEQs), as a typical implicit neural network, have demonstrated remarkable success on various tasks. There is, however, a lack of theoretical understanding of the connections and differences between implicit DEQs and…
In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems. However, in their traditional form, such models can require a large amount of…
Inspired by the remarkable success of large neural networks, there has been significant interest in understanding the generalization performance of over-parameterized models. Substantial efforts have been invested in characterizing how…
Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…
Image Quality Assessment (IQA) with references plays an important role in optimizing and evaluating computer vision tasks. Traditional methods assume that all pixels of the reference and test images are fully aligned. Such Aligned-Reference…
Hyperspectral images (HSIs) play a crucial role in remote sensing but are often degraded by complex noise patterns. Ensuring the physical property of the denoised HSIs is vital for robust HSI denoising, giving the rise of deep…
Inverse problems are important mathematical problems that seek to recover model parameters from noisy data. Since inverse problems are often ill-posed, they require regularization or incorporation of prior information about the underlying…
Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…
This paper studies the convergence of the mirror descent algorithm for finite horizon stochastic control problems with measure-valued control processes. The control objective involves a convex regularisation function, denoted as $h$, with…
Uncertainty quantification in inverse medical imaging tasks with deep learning has received little attention. However, deep models trained on large data sets tend to hallucinate and create artifacts in the reconstructed output that are not…
Model-based deep learning methods such as loop unrolling (LU) and deep equilibrium model}(DEQ) extensions offer outstanding performance in solving inverse problems (IP). These methods unroll the optimization iterations into a sequence of…
This paper introduces Physics-Informed Deep Equilibrium Models (PIDEQs) for solving initial value problems (IVPs) of ordinary differential equations (ODEs). Leveraging recent advancements in deep equilibrium models (DEQs) and…
Weight-tied models have attracted attention in the modern development of neural networks. The deep equilibrium model (DEQ) represents infinitely deep neural networks with weight-tying, and recent studies have shown the potential of this…
Deep neural networks have been applied successfully to a wide variety of inverse problems arising in computational imaging. These networks are typically trained using a forward model that describes the measurement process to be inverted,…
We propose a new class of implicit networks, the multiscale deep equilibrium model (MDEQ), suited to large-scale and highly hierarchical pattern recognition domains. An MDEQ directly solves for and backpropagates through the equilibrium…
Deep Equilibrium Models (DEQs) replace a stack of explicit layers with a single operator whose fixed point defines the output, giving the expressive power of an arbitrarily deep network at the memory cost of a single layer. Quantum Deep…