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Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
Event cameras are novel bio-inspired sensors that measure per-pixel brightness differences asynchronously. Recovering brightness from events is appealing since the reconstructed images inherit the high dynamic range (HDR) and high-speed…
We describe and examine an algorithm for tomographic image reconstruction where prior knowledge about the solution is available in the form of training images. We first construct a nonnegative dictionary based on prototype elements from the…
We present a method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; however, the operators…
This article adapts the framework of metamorphosis to solve inverse problems in imaging that includes joint reconstruction and image registration. The deformations in question have two components, one that is a geometric deformation moving…
Image denoising can be described as the problem of mapping from a noisy image to a noise-free image. The best currently available denoising methods approximate this mapping with cleverly engineered algorithms. In this work we attempt to…
In nanoscale imaging technique and ultrafast laser, the reconstruction procedure is normally formulated as a blind phase retrieval (BPR) problem, where one has to recover both the sample and the probe (pupil) jointly from phaseless data.…
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for…
One of the advantages of spectral computed tomography (CT) is it can achieve accurate material components using the material decomposition methods. The image-based material decomposition is a common method to obtain specific material…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
We propose a new image restoration model based on the minimized surface regularization. The proposed model closely relates to the classical smoothing ROF model \cite{4}. We can reformulate the proposed model as a min-max problem and solve…
In this paper, we suggest a general model for the fixed-valued impulse noise and propose a two-stage method for high density noise suppression while preserving the image details. In the first stage, we apply an iterative impulse detector,…
When images are statistically described by a generative model we can use this information to develop optimum techniques for various image restoration problems as inpainting, super-resolution, image coloring, generative model inversion, etc.…
When capturing and storing images, devices inevitably introduce noise. Reducing this noise is a critical task called image denoising. Deep learning has become the de facto method for image denoising, especially with the emergence of…
This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show…
The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…
The non-uniform photoelectric response of infrared imaging systems results in fixed-pattern stripe noise being superimposed on infrared images, which severely reduces image quality. As the applications of degraded infrared images are…
Unsupervised image segmentation and denoising are two fundamental tasks in image processing. Usually, graph based models such as multicut are used for segmentation and variational models are employed for denoising. Our approach addresses…
Iterative projection algorithms are successfully being used as a substitute of lenses to recombine, numerically rather than optically, light scattered by illuminated objects. Images obtained computationally allow aberration-free…
Several important classes of images such as text, barcode and pattern images have the property that pixels can only take a distinct subset of values. This knowledge can benefit the restoration of such images, but it has not been widely…