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We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…
Undersampling the k-space during MR acquisitions saves time, however results in an ill-posed inversion problem, leading to an infinite set of images as possible solutions. Traditionally, this is tackled as a reconstruction problem by…
Sparse reconstruction is an important aspect of MRI, helping to reduce acquisition time and improve spatial-temporal resolution. Popular methods are based mostly on compressed sensing (CS), which relies on the random sampling of k-space to…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
We compute all third-order local invariants accessible via randomised measurements and employ them to derive separability criteria. The reconstruction of the invariants yields experimentally accessible entanglement criteria for multipartite…
Accelerated MRI shortens acquisition time by subsampling in the measurement $\kappa$-space. Recovering a high-fidelity anatomical image from subsampled measurements requires close cooperation between two components: (1) a sampler that…
Computed tomography has propelled scientific advances in fields from biology to materials science. This technology allows for the elucidation of 3-dimensional internal structure by the attenuation of x-rays through an object at different…
Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random…
Increasing spatial image resolution is an often required, yet challenging task in image acquisition. Recently, it has been shown that it is possible to obtain a high resolution image by covering a low resolution sensor with a non-regular…
The increasing demand for larger and higher fidelity simulations has made Adaptive Mesh Refinement (AMR) and unstructured mesh techniques essential to focus compute effort and memory cost on just the areas of interest in the simulation…
Inspired by recent advances in deep learning, we propose a framework for reconstructing dynamic sequences of 2D cardiac magnetic resonance (MR) images from undersampled data using a deep cascade of convolutional neural networks (CNNs) to…
For an effective application of compressed sensing (CS), which exploits the underlying compressibility of an image, one of the requirements is that the undersampling artifact be incoherent (noise-like) in the sparsifying transform domain.…
Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with high-dimensional random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter,…
Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in…
This paper presents a deep learning method for faster magnetic resonance imaging (MRI) by reducing k-space data with sub-Nyquist sampling strategies and provides a rationale for why the proposed approach works well. Uniform subsampling is…
Interferometry can measure the shape or the material density of a system that could not be measured otherwise by recording the difference between the phase change of a signal and a reference phase. This difference is always between $-\pi$…
We introduce a new algorithm for finding robust circular coordinates on data that is expected to exhibit recurrence, such as that which appears in neuronal recordings of C. elegans. Techniques exist to create circular coordinates on a…
Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
Undersampling the k-space in MRI allows saving precious acquisition time, yet results in an ill-posed inversion problem. Recently, many deep learning techniques have been developed, addressing this issue of recovering the fully sampled MR…