The Internet has turned the entire world into a small village;this is because it has made it possible to share millions of images and videos. However, sending and receiving a huge amount of data is considered to be a main challenge. To address this issue, a new algorithm is required to reduce image bits and represent the data in a compressed form. Nevertheless, image compression is an important application for transferring large files and images. This requires appropriate and efficient transfers in this field to achieve the task and reach the best results. In this work, we propose a new algorithm based on discrete Hermite wavelets transformation (DHWT) that shows the efficiency and quality of the color images. By compressing the color image, this method analyzes it and divides it into approximate coefficients and detail coefficients after adding the wavelets into MATLAB. With Multi-Resolution Analyses (MRA), the appropriate filter is derived, and the mathematical aspects prove to be validated by testing a new filter and performing its operation. After the decomposition of the rows and upon the process of the reconstruction, taking the inverse of the filter and dealing with the columns of the matrix, the original matrix is improved by measuring the parameters of the image to achieve the best quality of the resulting image, such as the peak signal-to-noise ratio (PSNR), compression ratio (CR), bits per pixel (BPP), and mean square error (MSE).
University of Science and Technology of China（中国科学技术大学）；Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥综合性国家科学中心人工智能研究院）
Volumetric image compression has become an urgent task to effectively transmit and store images produced in biological research and clinical practice. At present, the most commonly used volumetric image compression methods are based on wavelet transform, such as JP3D. However, JP3D employs an ideal, separable, global, and fixed wavelet basis to convert input images from pixel domain to frequency domain, which seriously limits its performance. In this paper, we first design a 3-D trained wavelet-like transform to enable signal-dependent and non-separable transform. Then, an affine wavelet basis…
Matoshri College of Engineering and Research Centre（马托什里工程与研究中心学院）；University of Pune（浦那大学）
In Image Compression, the researchers' aim is to reduce the number of bits required to represent an image by removing the spatial and spectral redundancies. Recently discrete wavelet transform and wavelet packet has emerged as popular techniques for image compression. The wavelet transform is one of the major processing components of image compression. The result of the compression changes as per the basis and tap of the wavelet used. It is proposed that proper selection of mother wavelet on the basis of nature of images, improve the quality as well as compression ratio remarkably. We suggest …
University of Science and Technology of China（中国科学技术大学）
With the rapid development of whole brain imaging technology, a large number of brain images have been produced, which puts forward a great demand for efficient brain image compression methods. At present, the most commonly used compression methods are all based on 3-D wavelet transform, such as JP3D. However, traditional 3-D wavelet transforms are designed manually with certain assumptions on the signal, but brain images are not as ideal as assumed. What's more, they are not directly optimized for compression task. In order to solve these problems, we propose a trainable 3-D wavelet transform…
Convolutional Neural Networks (CNNs) are known for requiring extensive computational resources, and quantization is among the best and most common methods for compressing them. While aggressive quantization (i.e., less than 4-bits) performs well for classification, it may cause severe performance degradation in image-to-image tasks such as semantic segmentation and depth estimation. In this paper, we propose Wavelet Compressed Convolution (WCC) -- a novel approach for high-resolution activation maps compression integrated with point-wise convolutions, which are the main computational cost of m…
We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the approximation subband coefficients (much less noisy). The new algorithm is called Projection Onto Approximation Coefficients (POAC). As a result of this approach, only the approximation subband coefficients and three scalars are stored and/or transmitted to the channel. Besides, with the elimination of the details subbands coefficients, we obtain a bigger compression …
We study image compression by a separable wavelet basis $\big\{ψ(2^{k_1}x-i)ψ(2^{k_2}y-j),$ $ϕ(x-i)ψ(2^{k_2}y-j),$ $ψ(2^{k_1}(x-i)ϕ(y-j),$ $ϕ(x-i)ϕ(y-i)\big\},$ where $k_1, k_2 \in \mathbb{Z}_+$; $i,j\in\mathbb{Z}$; and $ϕ,ψ$ are elements of a standard biorthogonal wavelet basis in $L_2(\mathbb{R})$. Because $k_1\ne k_2$, the supports of the basis elements are rectangles, and the corresponding transform is known as the {\em rectangular wavelet transform}. We prove that if one-dimensional wavelet basis has $M$ dual vanishing moments then the rate of approximation by $N$ coefficients of rectangu…
With the development of human communications the usage of Visual Communications has also increased. The advancement of image compression methods is one of the main reasons for the enhancement. This paper first presents main modes of image compression methods such as JPEG and JPEG2000 without mathematical details. Also, the paper describes gradient Haar wavelet transforms in order to construct a preliminary image compression algorithm. Then, a new image compression method is proposed based on the preliminary image compression algorithm that can improve standards of image compression. The new me…
A variety of new and powerful algorithms have been developed for image compression over the years. Among them the wavelet-based image compression schemes have gained much popularity due to their overlapping nature which reduces the blocking artifacts that are common phenomena in JPEG compression and multiresolution character which leads to superior energy compaction with high quality reconstructed images. This paper provides a detailed survey on some of the popular wavelet coding techniques such as the Embedded Zerotree Wavelet (EZW) coding, Set Partitioning in Hierarchical Tree (SPIHT) coding…
ChWDTA: Channel-wise Wavelet-Domain Transformer Attention and Entropy Modeling for Learned Image Compression
Electrical and Computer Engineering Department, The University of British Columbia（英属哥伦比亚大学电气与计算机工程系）；School of Engineering Science, Simon Fraser University（西蒙弗雷泽大学工程科学学院）；School of Electronic Science and Technology, Eastern Institute of Technology（电子科学与技术学院，东部技术学院）；Google LLC（谷歌公司）
A simple approach for orthogonal wavelets in compressed sensing (CS) applications is presented. We compare efficient algorithm for different orthogonal wavelet measurement matrices in CS for image processing from scanned photographic plates (SPP). Some important characteristics were obtained for astronomical image processing of SPP. The best orthogonal wavelet choice for measurement matrix construction in CS for image compression of images of SPP is given. The image quality measure for linear and nonlinear image compression method is defined.
WaveLLM: Wavelet-Domain LLM Entropy Modeling for Lossless Image Compression
University of Science and Technology of China（中国科学技术大学）；Nanyang Technological University（南洋理工大学）；Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥综合性国家科学中心人工智能研究院）
Fractal image compression, Culik's image compression and zerotree prediction coding of wavelet image decomposition coefficients succeed only because typical images being compressed possess a significant degree of self-similarity. Besides the common concept, these methods turn out to be even more tightly related, to the point of algorithmical reducibility of one technique to another. The goal of the present paper is to demonstrate these relations. The paper offers a plain-term interpretation of Culik's image compression, in regular image processing terms, without resorting to finite state machi…
Cornell University（康奈尔大学）；Indian Institute of Information Technology, Allahabad（阿拉哈巴德印度信息技术学院）；Indian Institute of Science Education and Research - Kolkata（加尔各答印度科学教育与研究学院）
The paper presents a non-uniform quantization method for the Detail components in the JPEG2000 standard. Incorporating the fact that the coefficients lying towards the ends of the histogram plot of each Detail component represent the structural information of an image, the quantization step sizes become smaller at they approach the ends of the histogram plot. The variable quantization step sizes are determined by the actual statistics of the wavelet coefficients. Mean and standard deviation are the two statistical parameters used iteratively to obtain the variable step sizes. Moreover, the mea…
Universität Bremen（不来梅大学）；Fraunhofer Heinrich Hertz Institute（弗劳恩霍夫海因里希·赫兹研究所）；Technische Universität Berlin（柏林工业大学）；Berlin Institute of Technology（柏林工业大学）
In most practical situations, the compression or transmission of images and videos creates distortions that will eventually be perceived by a human observer. Vice versa, image and video restoration techniques, such as inpainting or denoising, aim to enhance the quality of experience of human viewers. Correctly assessing the similarity between an image and an undistorted reference image as subjectively experienced by a human viewer can thus lead to significant improvements in any transmission, compression, or restoration system. This paper introduces the Haar wavelet-based perceptual similarity…
In this work, we present a comparison between different techniques of image compression. First, the image is divided in blocks which are organized according to a certain scan. Later, several compression techniques are applied, combined or alone. Such techniques are: wavelets (Haar's basis), Karhunen-Loeve Transform, etc. Simulations show that the combined versions are the best, with minor Mean Squared Error (MSE), and higher Peak Signal to Noise Ratio (PSNR) and better image quality, even in the presence of noise.
Wavelet domain inpainting refers to the process of recovering the missing coefficients during the image compression or transmission stage. Recently, an efficient algorithm framework which is called Bregmanized operator splitting (BOS) was proposed for solving the classical variational model of wavelet inpainting. However, it is still time-consuming to some extent due to the inner iteration. In this paper, a novel variational model is established to formulate this reconstruction problem from the view of image decomposition. Then an efficient iterative algorithm based on the split-Bregman method…
Centre of Excellence IT4Innovations（IT4Innovations卓越中心）；Faculty of Information Technology Brno University of Technology（布尔诺理工大学信息技术学院）
In this paper, we introduce several new schemes for calculation of discrete wavelet transforms of images. These schemes reduce the number of steps and, as a consequence, allow to reduce the number of synchronizations on parallel architectures. As an additional useful property, the proposed schemes can reduce also the number of arithmetic operations. The schemes are primarily demonstrated on CDF 5/3 and CDF 9/7 wavelets employed in JPEG 2000 image compression standard. However, the presented method is general, and it can be applied on any wavelet transform. As a result, our scheme requires only…
Transform image processing methods are methods that work in domains of image transforms, such as Discrete Fourier, Discrete Cosine, Wavelet and alike. They are the basic tool in image compression, in image restoration, in image re-sampling and geometrical transformations and can be traced back to early 1970-ths. The paper presents a review of these methods with emphasis on their comparison and relationships, from the very first steps of transform image compression methods to adaptive and local adaptive transform domain filters for image restoration, to methods of precise image re-sampling and …
Qualcomm AI Research, Qualcomm Technologies, Inc.（高通技术公司高通人工智能研究院）；University of California Irvine（加州大学欧文分校）；Qualcomm AI Research, Qualcomm Technologies Netherlands B.V.（高通技术荷兰有限公司高通人工智能研究院）
We present PLONQ, a progressive neural image compression scheme which pushes the boundary of variable bitrate compression by allowing quality scalable coding with a single bitstream. In contrast to existing learned variable bitrate solutions which produce separate bitstreams for each quality, it enables easier rate-control and requires less storage. Leveraging the latent scaling based variable bitrate solution, we introduce nested quantization, a method that defines multiple quantization levels with nested quantization grids, and progressively refines all latents from the coarsest to the fines…
In this paper offers a simple and lossless compression method for compression of medical images. Method is based on wavelet decomposition of the medical images followed by the correlation analysis of coefficients. The correlation analyses are the basis of prediction equation for each sub band. Predictor variable selection is performed through coefficient graphic method to avoid multicollinearity problem and to achieve high prediction accuracy and compression rate. The method is applied on MRI and CT images. Results show that the proposed approach gives a high compression rate for MRI and CT im…
Graph Convolutional Networks (GCNs) are widely used in a variety of applications, and can be seen as an unstructured version of standard Convolutional Neural Networks (CNNs). As in CNNs, the computational cost of GCNs for large input graphs (such as large point clouds or meshes) can be high and inhibit the use of these networks, especially in environments with low computational resources. To ease these costs, quantization can be applied to GCNs. However, aggressive quantization of the feature maps can lead to a significant degradation in performance. On a different note, Haar wavelet transform…
University of California, San Diego（加州大学圣地亚哥分校）；University of Dayton（代顿大学）
We propose a novel lossless and lossy compression scheme for color filter array~(CFA) sampled images based on the wavelet transform of them. Our analysis suggests that the wavelet coefficients of HL and LH subbands are highly correlated. Hence, we decorrelate Mallat wavelet packet decomposition to further sparsify the coefficients. In addition, we develop a camera processing pipeline for compressing CFA sampled images aimed at maximizing the quality of the color images constructed from the compressed CFA sampled images. We validated our theoretical analysis and the performance of the proposed …
Sichuan University（四川大学）；UC San Diego（加利福尼亚大学圣地亚哥分校）
JPEG is one of the widely used lossy compression methods. JPEG-compressed images usually suffer from compression artifacts including blocking and blurring, especially at low bit-rates. Soft decoding is an effective solution to improve the quality of compressed images without changing codec or introducing extra coding bits. Inspired by the excellent performance of the deep convolutional neural networks (CNNs) on both low-level and high-level computer vision problems, we develop a dual pixel-wavelet domain deep CNNs-based soft decoding network for JPEG-compressed images, namely DPW-SDNet. The pi…
Aliraqia University（伊拉克大学）；University of Technology（科技大学）；Kyiv National University of Construction and Architecture（基辅国立建筑与建筑工程大学）；Al-Farahidi University（法拉希迪大学）
This work is unique in the use of discrete wavelets that were built from or derived from Chebyshev polynomials of the second and third kind, filter the Discrete Second Chebyshev Wavelets Transform (DSCWT), and derive two effective filters. The Filter Discrete Third Chebyshev Wavelets Transform (FDTCWT) is used in the process of analyzing color images and removing noise and impurities that accompany the image, as well as because of the large amount of data that makes up the image as it is taken. These data are massive, making it difficult to deal with each other during transmission. However to …
We describe a new method for superresolution of still images (in the wavelet domain) based on the reconstruction of missing details subbands pixels at a given ith level via Rule of Three (Ro3) between pixels of approximation subband of such level, and pixels of approximation and detail subbands of (i+1)th level. The histogramic profiles demonstrate that Ro3 is the appropriate mechanism to recover missing detail subband pixels in these cases. Besides, with the elimination of the details subbands pixels (in an eventual compression scheme), we obtain a bigger compression rate. Experimental result…
Remarkable achievements have been attained with Generative Adversarial Networks (GANs) in image-to-image translation. However, due to a tremendous amount of parameters, state-of-the-art GANs usually suffer from low efficiency and bulky memory usage. To tackle this challenge, firstly, this paper investigates GANs performance from a frequency perspective. The results show that GANs, especially small GANs lack the ability to generate high-quality high frequency information. To address this problem, we propose a novel knowledge distillation method referred to as wavelet knowledge distillation. Ins…
Department of Physics（物理系）；The Hong Kong University of Science and Technology（香港科技大学）
Wavelet transformation stands as a cornerstone in modern data analysis and signal processing. Its mathematical essence is an invertible transformation that discerns slow patterns from fast ones in the frequency domain. Such an invertible transformation can be learned by a designed normalizing flow model. With a generalized lifting scheme as coupling layers, a factor-out layer resembling the downsampling, and parameter sharing at different levels of the model, one can train the normalizing flow to filter high-frequency elements at different levels, thus extending traditional linear wavelet tran…
Telecom Paris, Institut Polytechnique de Paris（巴黎高等电信学院，巴黎理工学院）
This is the report for the PRIM project in Telecom Paris. This report is about applications based on spatial-frequency transform and deep learning techniques. In this report, there are two main works. The first work is about the enhanced JPEG compression method based on deep learning. we propose a novel method to highly enhance the JPEG compression by transmitting fewer image data at the sender's end. At the receiver's end, we propose a DC recovery algorithm together with the deep residual learning framework to recover images with high quality. The second work is about adversarial examples def…
Chittagong University of Engineering and Technology（吉大港工程与技术大学）；University of Malaya（马来亚大学）；American International University-Bangladesh（美国国际大学-孟加拉）
Digital watermarking is the process to hide digital pattern directly into a digital content. Digital watermarking techniques are used to address digital rights management, protect information and conceal secrets. An invisible non-blind watermarking approach for gray scale images is proposed in this paper. The host image is decomposed into 3-levels using Discrete Wavelet Transform. Based on the parent-child relationship between the wavelet coefficients the Set Partitioning in Hierarchical Trees (SPIHT) compression algorithm is performed on the LH3, LH2, HL3 and HL2 subbands to find out the sign…
New Horizon College of Engineering（新视野工程学院）；Government Engineering College（政府工程学院）；University of Mysore（迈索尔大学）
Periodicity of a texture is one of the important visual characteristics and is often used as a measure for textural discrimination at the structural level. Knowledge about periodicity of a texture is very essential in the field of texture synthesis and texture compression and also in the design of frieze and wall papers. In this paper, we propose a method of periodicity extraction from noisy images based on superposition of distance matching function (DMF) and wavelet decomposition without de-noising the test images. Overall DMFs are subjected to single-level Haar wavelet decomposition to obta…
University of Rajshahi（拉杰沙希大学）；International Islamic University Chittagong（吉大港国际伊斯兰大学）
This paper introduces a novel method for human face detection with its orientation by using wavelet, principle component analysis (PCA) and redial basis networks. The input image is analyzed by two-dimensional wavelet and a two-dimensional stationary wavelet. The common goals concern are the image clearance and simplification, which are parts of de-noising or compression. We applied an effective procedure to reduce the dimension of the input vectors using PCA. Radial Basis Function (RBF) neural network is then used as a function approximation network to detect where either the input image is c…
Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education（教育部智能感知与图像理解重点实验室）；School of Artificial Intelligence, Xidian University（西安电子科技大学人工智能学院）
Model quantization can reduce the model size and computational latency, it has become an essential technique for the deployment of deep neural networks on resourceconstrained hardware (e.g., mobile phones and embedded devices). The existing quantization methods mainly consider the numerical elements of the weights and activation values, ignoring the relationship between elements. The decline of representation ability and information loss usually lead to the performance degradation. Inspired by the characteristics of images in the frequency domain, we propose a novel multiscale wavelet quantiza…
Neural radiance fields (NeRF) have demonstrated the potential of coordinate-based neural representation (neural fields or implicit neural representation) in neural rendering. However, using a multi-layer perceptron (MLP) to represent a 3D scene or object requires enormous computational resources and time. There have been recent studies on how to reduce these computational inefficiencies by using additional data structures, such as grids or trees. Despite the promising performance, the explicit data structure necessitates a substantial amount of memory. In this work, we present a method to redu…
The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging the local correlations of the function values. It then applies a one dimensional wavelet transform to the obtained vector, decimates the points and iterates the procedure. The main drawback of such method is the need to store, for each level of the transform, the path which vectorizes the two dimensional data. Here we propose a variation on the method which c…
In this article, we introduce the concept of samplets by transferring the construction of Tausch-White wavelets to the realm of data. This way we obtain a multilevel representation of discrete data which directly enables data compression, detection of singularities and adaptivity. Applying samplets to represent kernel matrices, as they arise in kernel based learning or Gaussian process regression, we end up with quasi-sparse matrices. By thresholding small entries, these matrices are compressible to O(N log N) relevant entries, where N is the number of data points. This feature allows for the …
Light field cameras provide intriguing possibilities, such as post-capture refocus or the ability to synthesize images from novel viewpoints. This comes, however, at the price of significant storage requirements. Compression techniques can be used to reduce these but refocusing and reconstruction require so far again a dense pixel representation. To avoid this, we introduce local Fourier slice photography that allows for refocused image reconstruction directly from a sparse wavelet representation of a light field, either to obtain an image or a compressed representation of it. The result is ma…
