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Super-resolution results are usually measured by full-reference image quality metrics or human rating scores. However, these evaluation methods are general image quality measurement, and do not account for the nature of the super-resolution…
We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…
Phase retrieval, i.e., the problem of recovering a function from the squared magnitude of its Fourier transform, arises in many applications such as X-ray crystallography, diffraction imaging, optics, quantum mechanics, and astronomy. This…
In the practical applications of computed tomography imaging, the projection data may be acquired within a limited-angle range and corrupted by noises due to the limitation of scanning conditions. The noisy incomplete projection data…
Modern technology for producing extremely bright and coherent X-ray laser pulses provides the possibility to acquire a large number of diffraction patterns from individual biological nanoparticles, including proteins, viruses, and DNA.…
We consider several problems that involve lines in three dimensions, and present improved algorithms for solving them. The problems include (i) ray shooting amid triangles in $R^3$, (ii) reporting intersections between query lines…
If the phase retrieval problem can be solved by a method similar to that of solving a system of linear equations under the context of FFT, the time complexity of computer based phase retrieval algorithm would be reduced. Here I present such…
High-precision optical phase stabilization in quantum networks is fundamentally constrained by the strict photon-flux and duty-cycle limits required to avoid disturbing fragile quantum states. This challenge becomes especially critical when…
We introduce a method to recover a continuous domain representation of a piecewise constant two-dimensional image from few low-pass Fourier samples. Assuming the edge set of the image is localized to the zero set of a trigonometric…
Fourier ptychography is a recently developed imaging approach for large field-of-view and high-resolution microscopy. Here we model the Fourier ptychographic forward imaging process using a convolution neural network (CNN) and recover the…
Precision measurement has been an important research area in sensing and metrology. In classical physics, the Fisher information determines the maximum extractable information from statistically unknown signals, based on a joint probability…
Quantum error detection can produce unbiased expectation values that exponentially converge to noiseless results as the code distance is increased. Despite this, its performance as an error mitigation technique is relatively understudied on…
Detecting boundary of an image based on noisy observations is a fundamental problem of image processing and image segmentation. For a $d$-dimensional image ($d = 2, 3, \ldots$), the boundary can often be described by a closed smooth $(d -…
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…
In this paper, we study the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements in a bounded domain. We aim to provide a mathematical foundation for…
In this paper, we tackle the compressive phase retrieval problem in the presence of noise. The noisy compressive phase retrieval problem is to recover a $K$-sparse complex signal $s \in \mathbb{C}^n$, from a set of $m$ noisy quadratic…
We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…
While spike trains are obviously not band-limited, the theory of super-resolution tells us that perfect recovery of unknown spike locations and weights from low-pass Fourier transform measurements is possible provided that the minimum…
The main objective of this paper is to find algorithms accompanied by explicit error bounds for phase retrieval from noisy magnitudes of frame coefficients when the underlying frame has a low redundancy. We achieve these goals with frames…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…