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As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…
Shack Hartmann Sensor (SHS) is inflicted with significant background noise that deteriorates the wave-front reconstruction accuracy. In this paper, a simple method to remove the back ground noise with the use of Zernike polynomials is…
In this paper, we focus on learning optimal parameters for PDE-based image regularization and decomposition. First we learn the regularization parameter and the differential operator for gray-scale image denoising using the fractional…
We consider Schr\"odinger operators on sparse graphs. The geometric definition of sparseness turn out to be equivalent to a functional inequality for the Laplacian. In consequence, sparseness has in turn strong spectral and functional…
We discuss Schr\"odinger operators on a half-line with decaying oscillatory potentials, such as products of an almost periodic function and a decaying function. We provide sufficient conditions for preservation of absolutely continuous…
There is extensive mathematical literature on the inverse problem of deautoconvolution for a function with support in the unit interval $[0,1] \subset \mathbb R$, but little is known about the multidimensional situation. This article tries…
Traditional image resizing methods usually work in pixel space and use various saliency measures. The challenge is to adjust the image shape while trying to preserve important content. In this paper we perform image resizing in feature…
With the recent advancements in the field of information industry, critical data in the form of digital images is best understood by the human brain. Therefore, digital images play a significant part and backbone role in many areas such as…
Medical image denoising is essential for improving the reliability of clinical diagnosis and guiding subsequent image-based tasks. In this paper, we propose a multi-scale approach that integrates anisotropic Gaussian filtering with…
Nonlocal patch-based methods, in particular the Bayes' approach of Lebrun, Buades and Morel (2013), are considered as state-of-the-art methods for denoising (color) images corrupted by white Gaussian noise of moderate variance. This paper…
Image decomposition is a crucial subject in the field of image processing. It can extract salient features from the source image. We propose a new image decomposition method based on convolutional neural network. This method can be applied…
The eigenvalue problem for one-dimensional Schr\"{o}dinger equation with the rational potential is numerically solved by the operator method. We show that the operator method, applied for solving the Schr\"{o}dinger equation with the…
Many imaging inverse problems$\unicode{x2014}$such as image-dependent in-painting and dehazing$\unicode{x2014}$are challenging because their forward models are unknown or depend on unknown latent parameters. While one can solve such…
This work introduces a Transformer-based image compression system. It has the flexibility to switch between the standard image reconstruction and the denoising reconstruction from a single compressed bitstream. Instead of training separate…
Signal models based on sparsity, low-rank and other properties have been exploited for image reconstruction from limited and corrupted data in medical imaging and other computational imaging applications. In particular, sparsifying…
We establish dispersive estimates and local decay estimates for the time evolution of non-self-adjoint matrix Schr\"odinger operators with threshold resonances in one space dimension. In particular, we show that the decay rates in the…
Shannon in his 1949 paper suggested the use of derivatives to increase the W*T product of the sampled signal. Use of derivatives enables improved reconstruction particularly in the case of non-uniformly sampled signals. An FM-AM…
Image quantization is used in several applications aiming in reducing the number of available colors in an image and therefore its size. De-quantization is the task of reversing the quantization effect and recovering the original…
We devise a new regularization, called self-verification, for image denoising. This regularization is formulated using a deep image prior learned by the network, rather than a traditional predefined prior. Specifically, we treat the output…
Noise is ubiquitous during image acquisition. Sufficient denoising is often an important first step for image processing. In recent decades, deep neural networks (DNNs) have been widely used for image denoising. Most DNN-based image…