Related papers: Sampling High-Dimensional Bandlimited Fields on Lo…
Sparse sampling schemes have the potential to dramatically reduce image acquisition time while simultaneously reducing radiation damage to samples. However, for a sparse sampling scheme to be useful it is important that we are able to…
Heat diffusion processes have found wide applications in modelling dynamical systems over graphs. In this paper, we consider the recovery of a $k$-bandlimited graph signal that is an initial signal of a heat diffusion process from its…
We introduce a new method for the reconstruction of a function from linear measurements by means of oblique projections. The space spanned by the measurement vectors may be different from the subspace in which the function is reconstructed.…
Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…
Ray tracing has become a standard for accurate radio propagation modeling, but suffers from exponential computational complexity, as the number of candidate paths scales with the number of objects raised to the interaction order. This…
We introduce a novel bandlimited manifold framework and an algorithm to recover freebreathing and ungated cardiac MR images from highly undersampled measurements. The image frames in the free breathing and ungated dataset are assumed to be…
Sampling-based motion planners rely on incremental densification to discover progressively shorter paths. After computing feasible path $\xi$ between start $x_s$ and goal $x_t$, the Informed Set (IS) prunes the configuration space…
Graph-based methods play an important role in unsupervised and semi-supervised learning tasks by taking into account the underlying geometry of the data set. In this paper, we consider a statistical setting for semi-supervised learning and…
Single-pixel imaging (SPI) is significant for applications constrained by transmission bandwidth or lighting band, where 3D SPI can be further realized through capturing signals carrying depth. Sampling strategy and reconstruction algorithm…
Accurate estimation of wildlife density is vital for effective ecological monitoring, conservation, and management. Line transect sampling, a central technique in distance sampling, relies on selecting an appropriate detection function to…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of $\mathds{1}_{\{p\leq0\}}$ to the image plane, where $\mathds{1}$ denotes the indicator function…
This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in…
Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…
Binary deterministic sensing matrices are highly desirable for sampling sparse signals, as they require only a small number of sum-operations to generate the measurement vector. Furthermore, sparse sensing matrices enable the use of…
Density-based distances (DBDs) provide a principled approach to metric learning by defining distances in terms of the underlying data distribution. By employing a Riemannian metric that increases in regions of low probability density,…
Four-dimensional Scanning Transmission Electron Microscopy (4D-STEM) is a powerful technique for high-resolution and high-precision materials characterization at multiple length scales, including the characterization of beam-sensitive…
The SPARKLING algorithm was originally developed for accelerated 2D magnetic resonance imaging (MRI) in the compressed sensing (CS) context. It yields non-Cartesian sampling trajectories that jointly fulfill a target sampling density while…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of…