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.
Astronomical images suffer a constant presence of multiple defects that are consequences of the intrinsic properties of the acquisition equipments, and atmospheric conditions. One of the most frequent defects in astronomical imaging is the presence of additive noise which makes a denoising step mandatory before processing data. During the last decade, a particular modeling scheme, based on sparse representations, has drawn the attention of an ever growing community of researchers. Sparse representations offer a promising framework to many image and signal processing tasks, especially denoising…
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…
Universidad Técnica Federico Santa María（费德里科·圣玛丽亚技术大学）
The intrinsically hierarchical and blended structure of interstellar molecular clouds, plus the always increasing resolution of astronomical instruments, demand advanced and automated pattern recognition techniques for identifying and connecting source components in spectroscopic cubes. We extend the work done in multiresolution analysis using Wavelets for astronomical 2D images to 3D spectroscopic cubes, combining the results with the Dendrograms approach to offer a hierarchical representation of connections between sources at different scale levels. We test our approach in real data from the…
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…
Hangzhou Innovation Institute, Beihang University（北京航空航天大学杭州创新研究院）；Department of Computer Science, University of Oxford（牛津大学计算机科学系）
The past few years have witnessed fast development in video quality enhancement via deep learning. Existing methods mainly focus on enhancing the objective quality of compressed video while ignoring its perceptual quality. In this paper, we focus on enhancing the perceptual quality of compressed video. Our main observation is that enhancing the perceptual quality mostly relies on recovering high-frequency sub-bands in wavelet domain. Accordingly, we propose a novel generative adversarial network (GAN) based on multi-level wavelet packet transform (WPT) to enhance the perceptual quality of comp…
Compressive sensing promises to enable bandwidth-efficient on-board compression of astronomical data by lifting the encoding complexity from the source to the receiver. The signal is recovered off-line, exploiting GPUs parallel computation capabilities to speedup the reconstruction process. However, inherent GPU hardware constraints limit the size of the recoverable signal and the speedup practically achievable. In this work, we design parallel algorithms that exploit the properties of circulant matrices for efficient GPU-accelerated sparse signals recovery. Our approach reduces the memory req…
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）
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 algori…
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…
Higher Institute of Technology Diego-Suarez（迭戈-苏亚雷斯高等技术学院）；Higher Polytechnic School of Antananarivo（塔那那利佛高等理工学院）
Digital image compression is a technique that allows to reduce the size of an image in order to increase the capacity storage devices and to optimize the use of network bandwidth. The quality of compressed images with the techniques based on the discrete cosine transform or the wavelet transform is generally measured with PSNR or SSIM. Theses metrics are not suitable to images compressed with the singular values decomposition. This paper presents a new metric based on the energy ratio to measure the quality of the images coded with the SVD. A series of tests on 512 * 512 pixels images show tha…
Jiangsu Key Lab of Spectral Imaging & Intelligence Sense, Nanjing University of Science and Technology（南京理工大学江苏省光谱成像与智能感知重点实验室）；Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology（南京理工大学高维信息智能感知与系统教育部重点实验室）
Photon counting 3D imaging allows to obtain 3D images with single-photon sensitivity and sub-ns temporal resolution. However, it is challenging to scale to high spatial resolution. In this work, we demonstrate a photon counting 3D imaging technique with short-pulsed structured illumination and a single-pixel photon counting detector. The proposed multi-resolution photon counting 3D imaging technique acquires a high-resolution 3D image from a coarse image and edges at successfully finer resolution sampled by Hadamard multiplexing along the wavelet trees. The detected power is significantly incr…
University of Trento（特伦托大学）；Technische Universität Berlin（柏林工业大学）
To reduce the storage requirements, remote sensing (RS) images are usually stored in compressed format. Existing scene classification approaches using deep neural networks (DNNs) require to fully decompress the images, which is a computationally demanding task in operational applications. To address this issue, in this paper we propose a novel approach to achieve scene classification in JPEG 2000 compressed RS images. The proposed approach consists of two main steps: i) approximation of the finer resolution sub-bands of reversible biorthogonal wavelet filters used in JPEG 2000; and ii) charact…
Motivated with the concept of transform learning and the utility of rational wavelet transform in audio and speech processing, this paper proposes Rational Wavelet Transform Learning in Statistical sense (RWLS) for natural images. The proposed RWLS design is carried out via lifting framework and is shown to have a closed form solution. The efficacy of the learned transform is demonstrated in the application of compressed sensing (CS) based reconstruction. The learned RWLS is observed to perform better than the existing standard dyadic wavelet transforms.
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of Cambridge（剑桥大学）
Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees(HMTs). However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence of a sensing or observation matrix produces a linear mixing of the simple Markovian dependency structure. This leads to reconstruction problems that are non-convex optimizations. Past work has dealt with this issue by resorting to greedy or suboptimal iterative reconstruction methods. In this paper, we propose new modeling approaches based on group-sparsity …
The scattering transform network (STN), which has a similar structure as that of a popular convolutional neural network except its use of predefined convolution filters and a small number of layers, can generates a robust representation of an input signal relative to small deformations. We propose a novel Monogenic Wavelet Scattering Network (MWSN) for 2D texture image classification through a cascade of monogenic wavelet filtering with nonlinear modulus and averaging operators by replacing the 2D Morlet wavelet filtering in the standard STN. Our MWSN can extract useful hierarchical and direct…
The visual analysis of retina and of its vascular characteristics is important in the diagnosis and monitoring of diseases of visual perception. In the related medical diagnoses, the digital processing of the fundus images is used to obtain the segmentation of retinal vessels. However, an image segmentation is often requiring methods based on peculiar or complex algorithms: in this paper we will show some alternative approaches obtained by applying freely available tools to enhance, without a specific segmentation, the images of the fundus of the eye. We will see in particular, that combining …
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…
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 …
Mangalore University（芒格洛尔大学）；KVG College of Engineering（KVG工程学院）
In this paper, we propose a gradient difference based approach to text localization in videos and scene images. The input video frame/ image is first compressed using multilevel 2-D wavelet transform. The edge information of the reconstructed image is found which is further used for finding the maximum gradient difference between the pixels and then the boundaries of the detected text blocks are computed using zero crossing technique. We perform logical AND operation of the text blocks obtained by gradient difference and the zero crossing technique followed by connected component analysis to e…
Minimal mutual coherence of discrete noiselets and Haar wavelets makes this pair of bases an essential choice for the measurement and compression matrices in compressed-sensing-based single-pixel detectors. In this paper we propose an efficient way of using complex-valued and non-binary noiselet functions for object sampling in single-pixel cameras with binary spatial light modulators and incoherent illumination. The proposed method allows to determine m complex noiselet coefficients from m+1 binary sampling measurements. Further, we introduce a modification to the complex fast noiselet transf…
JPEG2000 (j2k) is a highly popular format for image and video compression.With the rapidly growing applications of cloud based image classification, most existing j2k-compatible schemes would stream compressed color images from the source before reconstruction at the processing center as inputs to deep CNNs. We propose to remove the computationally costly reconstruction step by training a deep CNN image classifier using the CDF 9/7 Discrete Wavelet Transformed (DWT) coefficients directly extracted from j2k-compressed images. We demonstrate additional computation savings by utilizing shallower …
Joint Research Institute for Signal and Image Processing, Edinburgh University（爱丁堡大学信号与图像处理联合研究所）；Heriot-Watt University（赫瑞-瓦特大学）
We propose the notion of a sample distortion (SD) function for independent and identically distributed (i.i.d) compressive distributions to fundamentally quantify the achievable reconstruction performance of compressed sensing for certain encoder-decoder pairs at a given sampling ratio. Two lower bounds on the achievable performance and the intrinsic convexity property is derived. A zeroing procedure is then introduced to improve non convex SD functions. The SD framework is then applied to analyse compressed imaging with a multi-resolution statistical image model using both the generalized Gau…
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…
Fraunhofer Institute for Telecommunications–Heinrich Hertz Institute（弗劳恩霍夫电信研究所-海因里希·赫兹研究所）；Technische Universität Berlin（柏林工业大学）；Experimental and Clinical Research Center（实验与临床研究中心）；Charité Medical Faculty（夏里特医学院）；Max-Delbrueck Center for Molecular Medicine（马克斯·德尔布吕克分子医学中心）；HELIOS Klinikum Berlin Buch（柏林布赫赫利俄斯医院）；Physikalisch-Technische Bundesanstalt (PTB)（德国联邦物理技术研究院（PTB））；King’s College London（伦敦国王学院）
High-resolution three-dimensional (3D) cardiovascular magnetic resonance (CMR) is a valuable medical imaging technique, but its widespread application in clinical practice is hampered by long acquisition times. Here we present a novel compressed sensing (CS) reconstruction approach using shearlets as a sparsifying transform allowing for fast 3D CMR (3DShearCS). Shearlets are mathematically optimal for a simplified model of natural images and have been proven to be more efficient than classical systems such as wavelets. Data is acquired with a 3D Radial Phase Encoding (RPE) trajectory and an it…
Leiden University Medical Center（莱顿大学医学中心）；Delft University of Technology（代尔夫特理工大学）；Philips Research Hamburg（飞利浦汉堡研究院）
Purpose: Design of a preconditioner for fast and efficient parallel imaging and compressed sensing reconstructions. Theory: Parallel imaging and compressed sensing reconstructions become time consuming when the problem size or the number of coils is large, due to the large linear system of equations that has to be solved in l_1 and l_2-norm based reconstruction algorithms. Such linear systems can be solved efficiently using effective preconditioning techniques. Methods: In this paper we construct such a preconditioner by approximating the system matrix of the linear system, which comprises the…
