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In the field of digital image processing, JPEG image compression technique has been widely applied. And numerous image processing software suppose this. It is likely for the images undergoing double JPEG compression to be tampered.…
Joint Photographic Experts Group (JPEG) achieves data compression by quantizing Discrete Cosine Transform (DCT) coefficients, which inevitably introduces compression artifacts. Most existing JPEG quality enhancement methods operate in the…
In the paper, a new method of blind estimation of noise variance in a single highly textured image is proposed. An input image is divided into 8x8 blocks and discrete cosine transform (DCT) is performed for each block. A part of 64 DCT…
This paper examines finite field trigonometry as a tool to construct trigonometric digital transforms. In particular, by using properties of the k-cosine function over GF(p), the Finite Field Discrete Cosine Transform (FFDCT) is introduced.…
The discrete Fourier transform is approximated by summing over part of the terms with corresponding weights. The approximation reduces significantly the requirement for computer memory storage and enhances the numerical computation…
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of…
This report elaborates on approximations for the discrete Fourier transform by means of replacing the exact Cooley-Tukey algorithm twiddle-factors by low-complexity integers, such as $0, \pm \frac{1}{2}, \pm 1$.
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…
This paper presents a general expression for a number-theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform (DHT) matrix together with alternating values in each row being…
Recovering color images and videos from highly undersampled data is a fundamental and challenging task in face recognition and computer vision. By the multi-dimensional nature of color images and videos, in this paper, we propose a novel…
This work presents a method of computing Voigt functions and their derivatives, to high accuracy, on a uniform grid. It is based on an adaptation of Fourier-transform based convolution. The relative error of the result decreases as the…
Image fusion in visual sensor networks (VSNs) aims to combine information from multiple images of the same scene in order to transform a single image with more information. Image fusion methods based on discrete cosine transform (DCT) are…
Density-corrected density functional theory (DC-DFT) is enjoying substantial success in improving semilocal DFT calculations in a wide variety of chemical problems. This paper provides the formal theoretical framework and assumptions for…
Object detection in images has reached unprecedented performances. The state-of-the-art methods rely on deep architectures that extract salient features and predict bounding boxes enclosing the objects of interest. These methods essentially…
A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex…
Convolutional neural networks (CNNs) learn filters in order to capture local correlation patterns in feature space. We propose to learn these filters as combinations of preset spectral filters defined by the Discrete Cosine Transform (DCT).…
In this paper we present a new fast and deterministic algorithm for the inverse discrete cosine transform of type II for reconstructing the input vector $\mathbf x\in\mathbb R^N$, $N=2^J$, with short support of length $m$ from its discrete…
This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…
Due to the factors like processing power limitations and channel capabilities images are often down sampled and transmitted at low bit rates resulting in a low resolution compressed image. High resolution images can be reconstructed from…
Guided depth super-resolution (GDSR) is an essential topic in multi-modal image processing, which reconstructs high-resolution (HR) depth maps from low-resolution ones collected with suboptimal conditions with the help of HR RGB images of…