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 the discrete cosine transform (DCT) matrix. The advantages of using DCT are that (i) the complex arithmetic is not involved in the cosine transform based tensor singular value decomposition, so the computational cost required can be saved; (ii) the intrinsic reflexive boundary condition along the tubes in the third dimension of tensors is employed, so its performance would be better than that by using the periodic boundary condition in DFT. We demonstrate that the tensor product between two tensors by using DCT can be equivalent to the multiplication between a block Toeplitz-plus-Hankel matrix and a block vector. Numerical examples of low-rank tensor completion are further given to illustrate that the efficiency by using DCT is two times faster than that by using DFT and also the errors of video and multispectral image completion by using DCT are smaller than those by using DFT.
Image Compression has become an absolute necessity in today's day and age. With the advent of the Internet era, compressing files to share among other users is quintessential. Several efforts have been made to reduce file sizes while still maintain image quality in order to transmit files even on limited bandwidth connections. This paper discusses the need for Discrete Cosine Transform or DCT in the compression of images in Joint Photographic Experts Group or JPEG file format. Via an intensive literature study, this paper first introduces DCT and JPEG Compression. The section preceding it disc…
Universidad Nacional de Tres de Febrero（特雷斯德费布雷罗国立大学）
In this work, we present a comparison between two techniques of image compression. In the first case, the image is divided in blocks which are collected according to zig-zag scan. In the second one, we apply the Fast Cosine Transform to the image, and then the transformed image is divided in blocks which are collected according to zig-zag scan too. Later, in both cases, the Karhunen-Loeve transform is applied to mentioned blocks. On the other hand, we present three new metrics based on eigenvalues for a better comparative evaluation of the techniques. Simulations show that the combined version…
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 the same scene. To solve the challenges in interpreting the working mechanism, extracting cross-modal features and RGB texture over-transferred, we propose a novel Discrete Cosine Transform Network (DCTNet) to alleviate the problems from three aspects. First, the Discrete Cosine Transform (DCT) module reconstructs the multi-channel HR depth features by using …
Broadband hyperspectral digital holography and Fourier transform spectroscopy are important instruments in various science and application fields. In the digital hyperspectral holography and spectroscopy the variable of interest are obtained as inverse discrete cosine transforms of observed diffractive intensity patterns. In these notes, we provide a variety of algorithms for the inverse cosine transform with the proofs of perfect spectrum reconstruction, as well as we discuss and illustrate some nontrivial features of these algorithms.
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 details, while a high-resolution grid dramatically increases the training complexity. In this paper, we propose a new mask representation by applying the discrete cosine transform(DCT) to encode the high-resolution binary grid mask into a compact vector. Our method, termed DCT-Mask, could be easily integrated into most pixel-based instance segmentation methods…
ADAPT Centre（ADAPT中心）；Trinity College Dublin（都柏林圣三一学院）；Dublin City University（都柏林城市大学）；Maynooth University（梅努斯大学）
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). Our proposed DCT-based harmonic blocks replace conventional convolutional layers to produce partially or fully harmonic versions of new or existing CNN architectures. Using DCT energy compaction properties, we demonstrate how the harmonic networks can be efficiently compressed by truncating high-frequency information in harmonic blocks thanks to the redunda…
Convolutional Neural Network is good at image classification. However, it is found to be vulnerable to image quality degradation. Even a small amount of distortion such as noise or blur can severely hamper the performance of these CNN architectures. Most of the work in the literature strives to mitigate this problem simply by fine-tuning a pre-trained CNN on mutually exclusive or a union set of distorted training data. This iterative fine-tuning process with all known types of distortion is exhaustive and the network struggles to handle unseen distortions. In this work, we propose distortion r…
Visual speech recognition aims to identify the sequence of phonemes from continuous speech. Unlike the traditional approach of using 2D image feature extraction methods to derive features of each video frame separately, this paper proposes a new approach using a 3D (spatio-temporal) Discrete Cosine Transform to extract features of each feasible sub-sequence of an input video which are subsequently classified individually using Support Vector Machines and combined to find the most likely phoneme sequence using a tailor-made Hidden Markov Model. The algorithm is trained and tested on the VidTimi…
Convolutional neural networks are based on a huge number of trained weights. Consequently, they are often data-greedy, sensitive to overtraining, and learn slowly. We follow the line of research in which filters of convolutional neural layers are determined on the basis of a smaller number of trained parameters. In this paper, the trained parameters define a frequency spectrum which is transformed into convolutional filters with Inverse Discrete Cosine Transform (IDCT, the same is applied in decompression from JPEG). We analyze how switching off selected components of the spectra, thereby redu…
China University of Mining and Technology（中国矿业大学）；Engineering Research Center of Mine Digitization, Ministry of Education of the People’s Republic of China（中华人民共和国教育部矿山数字化工程研究中心）
Arbitrary-shaped scene text detection is a challenging task due to the variety of text changes in font, size, color, and orientation. Most existing regression based methods resort to regress the masks or contour points of text regions to model the text instances. However, regressing the complete masks requires high training complexity, and contour points are not sufficient to capture the details of highly curved texts. To tackle the above limitations, we propose a novel light-weight anchor-free text detection framework called TextDCT, which adopts the discrete cosine transform (DCT) to encode …
The conventional authentication technologies, like RFID tags and authentication cards/badges, suffer from different weaknesses, therefore a prompt replacement to use biometric method of authentication should be applied instead. Biometrics, such as fingerprints, voices, and ECG signals, are unique human characters that can be used for authentication processing. In this work, we present an IoT real-time authentication system based on using extracted ECG features to identify the unknown persons. The Discrete Cosine Transform (DCT) is used as an ECG feature extraction, where it has better characte…
Discrete Cosine Transform Based Decorrelated Attention for Vision Transformers
Machine and Hybrid Intelligence Lab, Northwestern University（机器与混合智能实验室，西北大学）；Department of Electrical and Computer Engineering, University of Illinois Chicago（电气与计算机工程系，伊利诺伊大学香槟分校）
Face Recognition using Discrete Cosine Transform (DCT) for Local and Global Features involves recognizing the corresponding face image from the database. The face image obtained from the user is cropped such that only the frontal face image is extracted, eliminating the background. The image is restricted to a size of 128 x 128 pixels. All images in the database are gray level images. DCT is applied to the entire image. This gives DCT coefficients, which are global features. Local features such as eyes, nose and mouth are also extracted and DCT is applied to these features. Depending upon the …
Single image super-resolution(SISR) is an ill-posed problem that aims to obtain high-resolution (HR) output from low-resolution (LR) input, during which extra high-frequency information is supposed to be added to improve the perceptual quality. Existing SISR works mainly operate in the spatial domain by minimizing the mean squared reconstruction error. Despite the high peak signal-to-noise ratios(PSNR) results, it is difficult to determine whether the model correctly adds desired high-frequency details. Some residual-based structures are proposed to guide the model to focus on high-frequency f…
Most robot mapping techniques for lidar sensors tessellate the environment into pixels or voxels and assume uniformity of the environment within them. Although intuitive, this representation entails disadvantages: The resulting grid maps exhibit aliasing effects and are not differentiable. In the present paper, we address these drawbacks by introducing a novel mapping technique that does neither rely on tessellation nor on the assumption of piecewise uniformity of the space, without increasing memory requirements. Instead of representing the map in the position domain, we store the map paramet…
Institute of Information Technology（信息技术学院）；University of Dhaka（达卡大学）
Due to the rapid development of World Wide Web (WWW) and imaging technology, more and more images are available in the Internet and stored in databases. Searching the related images by the querying image is becoming tedious and difficult. Most of the images on the web are compressed by methods based on discrete cosine transform (DCT) including Joint Photographic Experts Group(JPEG) and H.261. This paper presents an efficient content-based image indexing technique for searching similar images using discrete cosine transform features. Experimental results demonstrate its superiority with the exi…
Adept: Annotation-Denoising Auxiliary Tasks with Discrete Cosine Transform Map and Keypoint for Human-Centric Pretraining
College of Electrical Engineering, Zhejiang University（浙江大学电气工程学院）；School of Mechanical Engineering, Zhejiang University（浙江大学机械工程学院）；Ocean College, Zhejiang University（浙江大学海洋学院）；Hainan Institute, Zhejiang University（海南研究院）；Shanghai AI Laboratory（上海人工智能实验室）
University of Adelaide（阿德莱德大学）；Xiamen University（厦门大学）
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 (3D-DCT). The 3D-DCT is based on a set of cosine basis functions, which are determined by the dimensions of the 3D signal and thus independent of the input video data. In addition, the 3D-DCT can generate a compact energy spectrum whose high-frequency coefficients are sparse if the appearance samples are similar. By discarding these high-frequency coefficients, we …
This paper proposes the use of a discrete cosine transform (DCT) instead of the eigenfaces method (Karhunen-Loeve Transform) for biometric identification based on frontal face images. Experimental results show better recognition accuracies and reduced computational burden. This paper includes results with different classifiers and a combination of them.
Seeing Delta Parameters as JPEG Images: Data-Free Delta Compression with Discrete Cosine Transform
Fudan University（复旦大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；The Chinese University of Hong Kong（香港中文大学）；Harbin Institute of Technology（哈尔滨工业大学）
Universidade Federal de Pernambuco（伯南布哥联邦大学）；Universidade Federal de Santa Maria（圣玛丽亚联邦大学）
An orthogonal approximation for the 8-point discrete cosine transform (DCT) is introduced. The proposed transformation matrix contains only zeros and ones; multiplications and bit-shift operations are absent. Close spectral behavior relative to the DCT was adopted as design criterion. The proposed algorithm is superior to the signed discrete cosine transform. It could also outperform state-of-the-art algorithms in low and high image compression scenarios, exhibiting at the same time a comparable computational complexity.
Fast Trainable Multilinear Bases for Image Compression
Institute of Science Tokyo（东京科学大学）；Center for Advanced Intelligence Project (AIP), RIKEN（理化学研究所先进智能项目中心）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
