Related papers: Signal Processing based on Stable radix-2 DCT Algo…

This paper introduced a matrix parametrization method based on the Loeffler discrete cosine transform (DCT) algorithm. As a result, a new class of eight-point DCT approximations was proposed, capable of unifying the mathematical formalism…

Video processing systems such as HEVC requiring low energy consumption needed for the multimedia market has lead to extensive development in fast algorithms for the efficient approximation of 2-D DCT transforms. The DCT is employed in a…

Compressing the sign information of discrete cosine transform (DCT) coefficients is an intractable problem in image coding schemes due to the equiprobable characteristics of the signs. To overcome this difficulty, we propose an efficient…

The ability to resolve detail in the object that is being imaged, named by resolution, is the core parameter of an imaging system. Super-resolution is a class of techniques that can enhance the resolution of an imaging system and even…

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…

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 paper investigates the possibility of reconstruction of images considering that they are sparse in the DCT transformation domain. Two approaches are considered. One when the image is pre-processed in the DCT domain, using 8x8 blocks.…

Recent advances in computing such as the massively parallel GPUs (Graphical Processing Units),coupled with the need to store and deliver large quantities of digital data especially images, has brought a number of challenges for Computer…

In~\cite{sic-magazine-2025}, the authors show that the square index coefficients (SICs) of the $N$-point discrete Fourier transform (DFT) -- that is, the coefficients $X_{k\sqrt{N}}$ for $k = 0, 1, \ldots, \sqrt{N} - 1$ -- can be losslessly…

In this paper, we present two variations of an algorithm for signal reconstruction from one-bit or two-bit noisy observations of the discrete Fourier transform (DFT). The one-bit observations of the DFT correspond to the sign of its real…

In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. Three dimensional DCT (3D DCT) approximations are formalized in terms of high-order tensor theory. The formulation is extended to…

Block frames called directional analytic discrete cosine frames (DADCFs) are proposed for sparse image representation. In contrast to conventional overlapped frames, the proposed DADCFs require a reduced amount of 1) computational…

Ultra sparse-view computed tomography (CT) algorithms can reduce radiation exposure of patients, but those algorithms lack an explicit cycle consistency loss minimization and an explicit log-likelihood maximization in testing. Here, we…

Deep learning methods, in particular, trained Convolutional Neural Networks (CNN) have recently been shown to produce compelling results for single image Super-Resolution (SR). Invariably, a CNN is learned to map the Low Resolution (LR)…

The usage of linear transformations has great relevance for data decorrelation applications, like image and video compression. In that sense, the discrete Tchebichef transform (DTT) possesses useful coding and decorrelation properties. The…

A Fast algorithm for the Discrete Hartley Transform (DHT) is presented, which resembles radix-2 fast Fourier Transform (FFT). Although fast DHTs are already known, this new approach bring some light about the deep relationship between fast…

This letter proposes a fast implementation of the regularity-constrained discrete sine transform (R-DST). The original DST \textit{leaks} the lowest frequency (DC: direct current) components of signals into high frequency (AC: alternating…

Two multiplierless pruned 8-point discrete cosine transform (DCT) approximation are presented. Both transforms present lower arithmetic complexity than state-of-the-art methods. The performance of such new methods was assessed in the image…

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…

This paper introduces a collection of scaling methods for generating $2N$-point DCT-II approximations based on $N$-point low-complexity transformations. Such scaling is based on the Hou recursive matrix factorization of the exact $2N$-point…