Related papers: Low-complexity 8-point DCT Approximations Based on…

Based on the discrete fractional random transform (DFRNT), we present the discrete fractional random cosine and sine transforms (DFRNCT and DFRNST). We demonstrate that the DFRNCT and DFRNST can be regarded as special kinds of DFRNT and…

Recent expansions in multimedia devices gather enormous amounts of real-time images for processing and inference. The images are first compressed using compression schemes, like JPEG, to reduce storage costs and power for transmitting the…

In recent year, quantum image processing got a lot of attention in the field of image processing due to opportunity to place huge image data in quantum Hilbert space. Hilbert space or Euclidean space has infinite dimension to locate and…

This chapter presents controlled approximations of Kohn-Sham density functional theory (DFT) that enable very large scale simulations. The work is motivated by the study of defects in crystalline solids, though the ideas can be used in…

Some conventional transforms such as Discrete Walsh-Hadamard Transform (DWHT) and Discrete Cosine Transform (DCT) have been widely used as feature extractors in image processing but rarely applied in neural networks. However, we found that…

Recently a novel approach to find approximate exchange-correlation functionals in density-functional theory (DFT) was presented (U. Mordovina et. al., JCTC 15, 5209 (2019)), which relies on approximations to the interacting wave function…

To efficiently compress the sign information of images, we address a sign retrieval problem for the block-wise discrete cosine transformation (DCT): reconstruction of the signs of DCT coefficients from their amplitudes. To this end, we…

Two multiplierless algorithms are proposed for 4x4 approximate-DCT for transform coding in digital video. Computational architectures for 1-D/2-D realisations are implemented using Xilinx FPGA devices. CMOS synthesis at the 45 nm node…

In this paper we present a new fast and deterministic algorithm for the inverse discrete cosine transform of type II that reconstructs the input vector $\mathbf{x}\in\mathbb{R}^{N}$, $N=2^{J-1}$, with short support of length $m$ from its…

Image computation is a fundamental tool for performance assessment of astronomical instrumentation, usually implemented by Fourier transform techniques. We review the numerical implementation, evaluating a direct implementation of the…

This paper proposes a 4X4 Census Transform (4X4CT) to encourage further research in computer vision and visual computing. Unlike the traditional 3X3 CT which uses a nine pixels kernel, the proposed 4X4CT uses a sixteen pixels kernel with…

The $N$-point discrete Fourier transform (DFT) is a cornerstone for several signal processing applications. Many of these applications operate in real-time, making the computational complexity of the DFT a critical performance indicator to…

This paper is devoted to the development and research of a new compression technology based on Weyl-Heisenberg bases (WH-technology) for modifying the JPEG compression standard and improving its characteristics. For this purpose, the paper…

Directional transforms have recently raised a lot of interest thanks to their numerous applications in signal compression and analysis. In this letter, we introduce a generalization of the discrete Fourier transform, called steerable DFT…

In this paper, we propose a novel Discrete Cosine Transform (DCT)-based neural network layer which we call DCT-perceptron to replace the $3\times3$ Conv2D layers in the Residual neural Network (ResNet). Convolutional filtering operations…

We consider a strictly stationary and ergodic sequence of random elements taking values in some Hilbert space. Our target is to study the weak convergence of the discrete Fourier transforms under sharp conditions. As a side-result we obtain…

The inversion of cosh-Hilbert transform (CHT) is one of the most crucial steps for single-photon emission computed tomography with uniform attenuation from truncated projection data. Although the uniqueness of the CHT inversion had been…

Detecting and localizing image manipulation are necessary to counter malicious use of image editing techniques. Accordingly, it is essential to distinguish between authentic and tampered regions by analyzing intrinsic statistics in an…

We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…

The recent surge of interest in Deep Neural Networks (DNNs) has led to increasingly complex networks that tax computational and memory resources. Many DNNs presently use 16-bit or 32-bit floating point operations. Significant performance…