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Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…
Positron emission tomography (PET) reconstruction has become an ill-posed inverse problem due to low-count projection data, and a robust algorithm is urgently required to improve imaging quality. Recently, the deep image prior (DIP) has…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…
Dual-energy computed tomography (DECT) has shown great potential and promising applications in advanced imaging fields for its capabilities of material decomposition. However, image reconstructions and decompositions under sparse views…
Positron emission tomography (PET) suffers from severe resolution limitations which limit its quantitative accuracy. In this paper, we present a super-resolution (SR) imaging technique for PET based on convolutional neural networks (CNNs).…
We present an approach to accelerating a wide variety of image processing operators. Our approach uses a fully-convolutional network that is trained on input-output pairs that demonstrate the operator's action. After training, the original…
Statistical iterative reconstruction is expected to improve the image quality of megavoltage computed tomography (MVCT). However, one of the challenges of iterative reconstruction is its large computational cost. The purpose of this work is…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
Deep image prior (DIP) has been successfully applied to positron emission tomography (PET) image restoration, enabling represent implicit prior using only convolutional neural network architecture without training dataset, whereas the…
Hyperspectral image (HSI) reconstruction aims to recover 3D HSI from its degraded 2D measurements. Recently great progress has been made in deep learning-based methods, however, these methods often struggle to accurately capture…
List-mode positron emission tomography (PET) image reconstruction is an important tool for PET scanners with many lines-of-response and additional information such as time-of-flight and depth-of-interaction. Deep learning is one possible…
To obtain high-quality positron emission tomography (PET) while minimizing radiation exposure, a range of methods have been designed to reconstruct standard-dose PET (SPET) from corresponding low-dose PET (LPET) images. However, most…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Model-based iterative reconstruction plays a key role in solving inverse problems. However, the associated minimization problems are generally large-scale, nonsmooth, and sometimes even nonconvex, which present challenges in designing…
Diffusion models have shown great promise in medical image denoising and reconstruction, but their application to Positron Emission Tomography (PET) imaging remains limited by tracer-specific contrast variability and high computational…
In semidefinite programming (SDP), a number of pre-processing techniques have been developed including chordal-completion procedures, which reduce the dimension of individual constraints by exploiting sparsity therein, and facial reduction,…
In this paper, we study a class of fractional semi-infinite polynomial programming problems involving s.o.s-convex polynomial functions. For such a problem, by a conic reformulation proposed in our previous work and the quadratic modules…
To acquire high-quality positron emission tomography (PET) images while reducing the radiation tracer dose, numerous efforts have been devoted to reconstructing standard-dose PET (SPET) images from low-dose PET (LPET). However, the success…
Positron Emission Tomography (PET) image reconstruction is inherently challenged by Poisson noise and physical degradation factors, which are further exacerbated in limited-angle acquisitions. While deep learning methods demonstrate…