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In this research paper, the authors propose a new approach to digital image compression using crack coding This method starts with the original image and develop crack codes in a recursive manner, marking the pixels visited earlier and…
Statistical processing of speckle data enables observation of speed of processes. In intensity-based pointwise dynamic speckle analysis, a map related to speed's spatial distribution is extracted from a sequence of speckle patterns formed…
The enclosure method was originally introduced for inverse problems of concerning non-destructive evaluation governed by elliptic equations. It was developed as one of useful approaches in inverse problems and applied for various equations.…
Storage systems often rely on multiple copies of the same compressed data, enabling recovery in case of binary data errors, of course, at the expense of a higher storage cost. In this paper we show that a wiser method of duplication entails…
We present a Deep Image Compression neural network that relies on side information, which is only available to the decoder. We base our algorithm on the assumption that the image available to the encoder and the image available to the…
The search for image compression optimization techniques is a topic of constant interest both in and out of academic circles. One method that shows promise toward future improvements in this field is image colorization since image…
The problem of inpainting involves reconstructing the missing areas of an image. Inpainting has many applications, such as reconstructing old damaged photographs or removing obfuscations from images. In this paper we present the directional…
Lossless image compression is an important technique for image storage and transmission when information loss is not allowed. With the fast development of deep learning techniques, deep neural networks have been used in this field to…
We consider efficient methods for computing solutions to dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change at different time instances but we want to solve for all the…
The Rytov approximation has been commonly used to obtain reconstructed images for optical tomography. However, the method requires linearization of the nonlinear inverse problem. Here, we demonstrate nonlinear Rytov approximations by…
A blind compressive sensing algorithm is proposed to reconstruct hyperspectral images from spectrally-compressed measurements.The wavelength-dependent data are coded and then superposed, mapping the three-dimensional hyperspectral datacube…
Image retrieval based on deep convolutional features has demonstrated state-of-the-art performance in popular benchmarks. In this paper, we present a unified solution to address deep convolutional feature aggregation and image re-ranking by…
Detecting electronic hot spots is important for understanding the heat dissipation and thermal management of electronic and semiconductor devices. Optical thermoreflective imaging is being used to perform precise temporal and spatial…
Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the spatial dimensions of the PDEs are high, due to large number of spatial grid points. For multidimensional…
Edge-enhancing diffusion (EED) can reconstruct a close approximation of an original image from a small subset of its pixels. This makes it an attractive foundation for PDE based image compression. In this work, we generalize second-order…
We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank-Nicolson method with predictor-corrector algorithm…
Analytic solutions to the nonlinear radiation diffusion equation with an instantaneous point source for a non-homogeneous medium with a power law spatial density profile, are presented. The solutions are a generalization of the well known…
Many phenomena in collisionless plasma physics require a kinetic description. The evolution of the phase space density can be modeled by means of the Vlasov equation, which has to be solved numerically in most of the relevant cases. One of…
We present a preconditioner based on spectral projection that is combined with a deflated Krylov subspace method for solving ill conditioned linear systems of equations. Our results show that the proposed algorithm requires many fewer…
Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the…