Related papers: Low-complexity Multidimensional DCT Approximations

Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel…

Visual tracking usually requires an object appearance model that is robust to changing illumination, pose and other factors encountered in video. In this paper, we construct an appearance model using the 3D discrete cosine transform…

This paper studies the cosine as basis function for the approximation of univariate and continuous functions without memory. This work studies a supervised learning to obtain the approximation coefficients, instead of using the Discrete…

A fast Discrete Cosine Transform (DCT) algorithm is introduced that can be of particular interest in image processing. The main features of the algorithm are regularity of the graph and very low arithmetic complexity. The 16-point version…

We present algorithms for the discrete cosine transform (DCT) and discrete sine transform (DST), of types II and III, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing…

Due to the confined focal length of optical sensors, focusing all objects in a scene with a single sensor is a difficult task. To handle such a situation, image fusion methods are used in multi-focus environment. Discrete Cosine Transform…

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…

Discrete Cosine Transform (DCT) is very important in image compression. Classical 1-D DCT and 2-D DCT has time complexity O(NlogN) and O(N²logN) respectively. This paper presents a quantum DCT iteration, and constructs a quantum 1-D…

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…

Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on…

We present algorithms for the type-IV discrete cosine transform (DCT-IV) and discrete sine transform (DST-IV), as well as for the modified discrete cosine transform (MDCT) and its inverse, that achieve a lower count of real multiplications…

The discrete cosine transform (DCT) is a widely-used and important signal processing tool employed in a plethora of applications. Typical fast algorithms for nearly-exact computation of DCT require floating point arithmetic, are multiplier…

With the integration of communication and computing, it is expected that part of the computing is transferred to the transmitter side. In this paper we address the general problem of Frequency Modulation (FM) for function approximation…

In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing…

Discrete trigonometric transforms (DTTs), such as the DCT-2 and the DST-7, are widely used in video codecs for their balance between coding performance and computational efficiency. In contrast, data-dependent transforms, such as the…

Typical convolutional networks are trained and conducted on RGB images. However, images are often compressed for memory savings and efficient transmission in real-world applications. In this paper, we explore methods for performing semantic…

Self-attention is central to the success of Transformer architectures; however, learning the query, key, and value projections from random initialization remains challenging and computationally expensive. In this paper, we propose two…

As an extension of the 2D fractional Fourier transform (FRFT) and a special case of the 2D linear canonical transform (LCT), the gyrator transform was introduced to produce rotations in twisted space/spatial-frequency planes. It is a useful…

Two algorithms are introduced for the computation of discrete integral transforms with a multiscale approach operating in discrete three-dimensional (3D) volumes while considering its real-time implementation. The first algorithm, referred…

Binary grid mask representation is broadly used in instance segmentation. A representative instantiation is Mask R-CNN which predicts masks on a $28\times 28$ binary grid. Generally, a low-resolution grid is not sufficient to capture the…