Related papers: Recovering Missing Slices of the Discrete Fourier …
Fractional Fourier transform and chaos functions play a key role in many of encryption-decryption algorithms. In this work performance of image encryption-decryption algorithms is quantified and compared using the computation time i.e. the…
We provide a rigorous convergence proof demonstrating that the well-known semi-analytical Fourier cosine (COS) formula for the inverse Fourier transform of continuous probability distributions can be extended to discrete probability…
Sampling strategies are important for sparse imaging methodologies, especially those employing the discrete Fourier transform (DFT). Chaotic sensing is one such methodology that employs deterministic, fractal sampling in conjunction with…
The one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…
Ghost imaging (GI) is an unconventional imaging method that retrieves the image of an object by correlating a series of known illumination patterns with the total reflected (or transmitted) intensity. We here demonstrate a scheme which can…
Knowledge gained through X-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. Atomic details of sample structures is achievable by…
Despite that convolutional neural networks (CNN) have recently demonstrated high-quality reconstruction for single-image super-resolution (SR), recovering natural and realistic texture remains a challenging problem. In this paper, we show…
In this paper, we focus on Fourier analysis and holographic transforms for signal representation. For instance, in the case of image processing, the holographic representation has the property that an arbitrary portion of the transformed…
This paper investigates the Schur product of constacyclic codes via the constacyclic discrete Fourier transform (DFT). We first characterize key properties of the constacyclic DFT, highlighting its differences from the ordinary DFT. We then…
The graph Fourier transform (GFT) is an important tool for graph signal processing, with applications ranging from graph-based image processing to spectral clustering. However, unlike the discrete Fourier transform, the GFT typically does…
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…
In this paper, we propose a new convolutional layer called Depthwise-STFT Separable layer that can serve as an alternative to the standard depthwise separable convolutional layer. The construction of the proposed layer is inspired by the…
This paper extends the Radon transform, a classical image processing tool for fast tomography and denoising, to the quantum computing platform. A new kind of periodic discrete Radon transform (PDRT), called quantum Radon transform (QRT), is…
The Discrete Fourier Transform (DFT) is a fundamental computational primitive, and the fastest known algorithm for computing the DFT is the FFT (Fast Fourier Transform) algorithm. One remarkable feature of FFT is the fact that its runtime…
Multi-frame high dynamic range (HDR) imaging aims to reconstruct ghost-free images with photo-realistic details from content-complementary but spatially misaligned low dynamic range (LDR) images. Existing HDR algorithms are prone to…
One of the most prominent challenges in the field of diffractive imaging is the phase retrieval (PR) problem: In order to reconstruct an object from its diffraction pattern, the inverse Fourier transform must be computed. This is only…
Given an $n$-length input signal $\mbf{x}$, it is well known that its Discrete Fourier Transform (DFT), $\mbf{X}$, can be computed in $O(n \log n)$ complexity using a Fast Fourier Transform (FFT). If the spectrum $\mbf{X}$ is exactly…
Inspired by the multiple-exposure fusion approach in computational photography, recently, several practitioners have explored the idea of high dynamic range (HDR) X-ray imaging and tomography. While establishing promising results, these…
One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the…
Ghost imaging leverages a single-pixel detector with no spatial resolution to acquire object echo intensity signals, which are correlated with illumination patterns to reconstruct an image. This architecture inherently mitigates scattering…