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Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…

Compressive sensing (CS) is an effective approach for fast Magnetic Resonance Imaging (MRI). It aims at reconstructing MR images from a small number of under-sampled data in k-space, and accelerating the data acquisition in MRI. To improve…

Sparse representation models a signal as a linear combination of a small number of dictionary atoms. As a generative model, it requires the dictionary to be highly redundant in order to ensure both a stable high sparsity level and a low…

Recent reference-based face restoration methods have received considerable attention due to their great capability in recovering high-frequency details on real low-quality images. However, most of these methods require a high-quality…

We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and…

Sparse signal recovery algorithms like sparse Bayesian learning work well but the complexity quickly grows when tackling higher dimensional parametric dictionaries. In this work we propose a novel Bayesian strategy to address the two…

Patch-based sparse representation modeling has shown great potential in image compressive sensing (CS) reconstruction. However, this model usually suffers from some limits, such as dictionary learning with great computational complexity,…

This paper addresses the problem of learning dictionaries for multimodal datasets, i.e. datasets collected from multiple data sources. We present an algorithm called multimodal sparse Bayesian dictionary learning (MSBDL). MSBDL leverages…

We present a data-driven learning approach for unknown nonautonomous dynamical systems with time-dependent inputs based on dynamic mode decomposition (DMD). To circumvent the difficulty of approximating the time-dependent Koopman operators…

Dictionary learning is a popular approach for inferring a hidden basis or dictionary in which data has a sparse representation. Data generated from the dictionary A (an n by m matrix, with m > n in the over-complete setting) is given by Y =…

Magnetic resonance imaging (MRI) is a vital diagnostic tool, but its inherently long acquisition times reduce clinical efficiency and patient comfort. Recent advancements in deep learning, particularly diffusion models, have improved…

There remains an important need for the development of image reconstruction methods that can produce diagnostically useful images from undersampled measurements. In magnetic resonance imaging (MRI), for example, such methods can facilitate…

Memory-based meta-learning is a technique for approximating Bayes-optimal predictors. Under fairly general conditions, minimizing sequential prediction error, measured by the log loss, leads to implicit meta-learning. The goal of this work…

Compressive sensing is an impressive approach for fast MRI. It aims at reconstructing MR image using only a few under-sampled data in k-space, enhancing the efficiency of the data acquisition. In this study, we propose to learn priors based…

Since the first success of Dong et al., the deep-learning-based approach has become dominant in the field of single-image super-resolution. This replaces all the handcrafted image processing steps of traditional sparse-coding-based methods…

Magnetic resonance imaging (MRI) is one of the noninvasive imaging modalities that can produce high-quality images. However, the scan procedure is relatively slow, which causes patient discomfort and motion artifacts in images. Accelerating…

In spite of its extensive adaptation in almost every medical diagnostic and examinatorial application, Magnetic Resonance Imaging (MRI) is still a slow imaging modality which limits its use for dynamic imaging. In recent years, Parallel…

Magnetic Resonance Imaging (MRI) is widely used in clinical practice, but suffered from prolonged acquisition time. Although deep learning methods have been proposed to accelerate acquisition and demonstrate promising performance, they rely…

Deep Learning (DL) based methods for magnetic resonance (MR) image reconstruction have been shown to produce superior performance in recent years. However, these methods either only leverage under-sampled data or require a paired…

There is much recent interest in techniques to accelerate the data acquisition process in MRI by acquiring limited measurements. Often sophisticated reconstruction algorithms are deployed to maintain high image quality in such settings. In…