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The Variational Quantum Eigensolver (VQE) is widely regarded as a promising algorithm for calculating ground states of quantum systems that are intractable for classical computers. This promise is typically motivated by the hope of…
We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…
We propose and study a new quasi-interpolation method on spheres featuring the following two-phase construction and analysis. In Phase I, we analyze and characterize a large family of zonal kernels (e.g., the spherical version of Poisson…
The support vector machine (SVM) is a supervised learning algorithm that finds a maximum-margin linear classifier, often after mapping the data to a high-dimensional feature space via the kernel trick. Recent work has demonstrated that in…
Deep CNNs have achieved significant successes in image processing and its applications, including single image super-resolution (SR). However, conventional methods still resort to some predetermined integer scaling factors, e.g., x2 or x4.…
A kernelization is an efficient algorithm that given an instance of a parameterized problem returns an equivalent instance of size bounded by some function of the input parameter value. It is quite well understood which problems do or…
For the next generation of radio interferometric telescopes it is of paramount importance to incorporate wide field-of-view (WFOV) considerations in interferometric imaging, otherwise the fidelity of reconstructed images will suffer…
Algorithm unrolling methods have proven powerful for solving the regularized least squares problem in computational magnetic resonance imaging (MRI). These approaches unfold an iterative algorithm with a fixed number of iterations,…
Fourier ptychography has attracted a wide range of focus for its ability of large space-bandwidth-produce, and quantative phase measurement. It is a typical computational imaging technique which refers to optimizing both the imaging…
Diffusion MRI (dMRI) is the primary imaging modality used to study brain microstructure in vivo. Reliable and computationally efficient parameter inference for common dMRI biophysical models is a challenging inverse problem, due to factors…
We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…
Kernel interpolation is a versatile tool for the approximation of functions from data, and it can be proven to have some optimality properties when used with kernels related to certain Sobolev spaces. In the context of interpolation, the…
This paper proposes an image interpolation algorithm exploiting sparse representation for natural images. It involves three main steps: (a) obtaining an initial estimate of the high resolution image using linear methods like FIR filtering,…
We propose an unfolded accelerated projected-gradient descent procedure to estimate model and algorithmic parameters for image super-resolution and molecule localization problems in image microscopy. The variational lower-level constraint…
We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…
We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from spectral approximations of the transfer operators mapping initial values for a given time interval to…
We present a new image scaling method both for downscaling and upscaling, running with any scale factor or desired size. The resized image is achieved by sampling a bivariate polynomial which globally interpolates the data at the new scale.…
Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of…
Neural Radiance Fields (NeRFs) have unmatched fidelity on large, real-world scenes. A common approach for scaling NeRFs is to partition the scene into regions, each of which is assigned its own parameters. When implemented naively, such an…