Objective methods for assessing perceptual image quality traditionally attempted to quantify the visibility of errors (differences) between a distorted image and a reference image using a variety of known properties of the human visual system. Under the assumption that human visual perception is highly adapted for extracting structural information from a scene, we introduce an alternative complementary framework for quality assessment based on the degradation of structural information. As a specific example of this concept, we develop a structural similarity index and demonstrate its promise through a set of intuitive examples, as well as comparison to both subjective ratings and state-of-the-art objective methods on a database of images compressed with JPEG and JPEG2000. A MATLAB implementation of the proposed algorithm is available online at http://www.cns.nyu.edu//spl sim/lcv/ssim/.

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Image quality assessment: from error visibility to structural similarity

Digital watermarking is a key ingredient to copyright protection. It provides a solution to illegal copying of digital material and has many other useful applications such as broadcast monitoring and the recording of electronic transactions. Now, for the first time, there is a book that focuses exclusively on this exciting technology. Digital Watermarking covers the crucial research findings in the field: it explains the principles underlying digital watermarking technologies, describes the requirements that have given rise to them, and discusses the diverse ends to which these technologies are being applied. As a result, additional groundwork is laid for future developments in this field, helping the reader understand and anticipate new approaches and applications.

Digital Watermarking

In this article, we have reviewed the reasons why we (collectively) want to love or leave the venerable (but perhaps hoary) MSE. We have also reviewed emerging alternative signal fidelity measures and discussed their potential application to a wide variety of problems. The message we are trying to send here is not that one should abandon use of the MSE nor to blindly switch to any other particular signal fidelity measure. Rather, we hope to make the point that there are powerful, easy-to-use, and easy-to-understand alternatives that might be deployed depending on the application environment and needs. While we expect (and indeed, hope) that the MSE will continue to be widely used as a signal fidelity measure, it is our greater desire to see more advanced signal fidelity measures being used, especially in applications where perceptual criteria might be relevant. Ideally, the performance of a new signal processing algorithm might be compared to other algorithms using several fidelity criteria. Lastly, we hope that we have given further motivation to the community to consider recent advanced signal fidelity measures as design criteria for optimizing signal processing algorithms and systems. It is in this direction that we believe that the greatest benefit eventually lies.

Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures

Preface 1 Introduction 1.1 Compression Techniques 1.1.1 Lossless Compression 1.1.2 Lossy Compression 1.1.3 Measures of Performance 1.2 Modeling and Coding 1.3 Organization of This Book 1.4 Summary 1.5 Projects and Problems 2 Mathematical Preliminaries 2.1 Overview 2.2 A Brief Introduction to Information Theory 2.3 Models 2.3.1 Physical Models 2.3.2 Probability Models 2.3.3. Markov Models 2.3.4 Summary 2.5 Projects and Problems 3 Huffman Coding 3.1 Overview 3.2 "Good" Codes 3.3. The Huffman Coding Algorithm 3.3.1 Minimum Variance Huffman Codes 3.3.2 Length of Huffman Codes 3.3.3 Extended Huffman Codes 3.4 Nonbinary Huffman Codes 3.5 Adaptive Huffman Coding 3.5.1 Update Procedure 3.5.2 Encoding Procedure 3.5.3 Decoding Procedure 3.6 Applications of Huffman Coding 3.6.1 Lossless Image Compression 3.6.2 Text Compression 3.6.3 Audio Compression 3.7 Summary 3.8 Projects and Problems 4 Arithmetic Coding 4.1 Overview 4.2 Introduction 4.3 Coding a Sequence 4.3.1 Generating a Tag 4.3.2 Deciphering the Tag 4.4 Generating a Binary Code 4.4.1 Uniqueness and Efficiency of the Arithmetic Code 4.4.2 Algorithm Implementation 4.4.3 Integer Implementation 4.5 Comparison of Huffman and Arithmetic Coding 4.6 Applications 4.6.1 Bi-Level Image Compression-The JBIG Standard 4.6.2 Image Compression 4.7 Summary 4.8 Projects and Problems 5 Dictionary Techniques 5.1 Overview 5.2 Introduction 5.3 Static Dictionary 5.3.1 Diagram Coding 5.4 Adaptive Dictionary 5.4.1 The LZ77 Approach 5.4.2 The LZ78 Approach 5.5 Applications 5.5.1 File Compression-UNIX COMPRESS 5.5.2 Image Compression-the Graphics Interchange Format (GIF) 5.5.3 Compression over Modems-V.42 bis 5.6 Summary 5.7 Projects and Problems 6 Lossless Image Compression 6.1 Overview 6.2 Introduction 6.3 Facsimile Encoding 6.3.1 Run-Length Coding 6.3.2 CCITT Group 3 and 4-Recommendations T.4 and T.6 6.3.3 Comparison of MH, MR, MMR, and JBIG 6.4 Progressive Image Transmission 6.5 Other Image Compression Approaches 6.5.1 Linear Prediction Models 6.5.2 Context Models 6.5.3 Multiresolution Models 6.5.4 Modeling Prediction Errors 6.6 Summary 6.7 Projects and Problems 7 Mathematical Preliminaries 7.1 Overview 7.2 Introduction 7.3 Distortion Criteria 7.3.1 The Human Visual System 7.3.2 Auditory Perception 7.4 Information Theory Revisted 7.4.1 Conditional Entropy 7.4.2 Average Mutual Information 7.4.3 Differential Entropy 7.5 Rate Distortion Theory 7.6 Models 7.6.1 Probability Models 7.6.2 Linear System Models 7.6.3 Physical Models 7.7 Summary 7.8 Projects and Problems 8 Scalar Quantization 8.1 Overview 8.2 Introduction 8.3 The Quantization Problem 8.4 Uniform Quantizer 8.5 Adaptive Quantization 8.5.1 Forward Adaptive Quantization 8.5.2 Backward Adaptive Quantization 8.6 Nonuniform Quantization 8.6.1 pdf-Optimized Quantization 8.6.2 Companded Quantization 8.7 Entropy-Coded Quantization 8.7.1 Entropy Coding of Lloyd-Max Quantizer Outputs 8.7.2 Entropy-Constrained Quantization 8.7.3 High-Rate Optimum Quantization 8.8 Summary 8.9 Projects and Problems 9 Vector Quantization 9.1 Overview 9.2 Introduction 9.3 Advantages of Vector Quantization over Scalar Quantization 9.4 The Linde-Buzo-Gray Algorithm 9.4.1 Initializing the LBG Algorithm 9.4.2 The Empty Cell Problem 9.4.3 Use of LBG for Image Compression 9.5 Tree-Structured Vector Quantizers 9.5.1 Design of Tree-Structured Vector Quantizers 9.6 Structured Vector Quantizers 9.6.1 Pyramid Vector Quantization 9.6.2 Polar and Spherical Vector Quantizers 9.6.3 Lattice Vector Quantizers 9.7 Variations on the Theme 9.7.1 Gain-Shape Vector Quantization 9.7.2 Mean-Removed Vector Quantization 9.7.3 Classified Vector Quantization 9.7.4 Multistage Vector Quantization 9.7.5 Adaptive Vector Quantization 9.8 Summary 9.9 Projects and Problems 10 Differential Encoding 10.1 Overview 10.2 Introduction 10.3 The Basic Algorithm 10.4 Prediction in DPCM 10.5 Adaptive DPCM (ADPCM) 10.5.1 Adaptive Quantization in DPCM 10.5.2 Adaptive Prediction in DPCM 10.6 Delta Modulation 10.6.1 Constant Factor Adaptive Delta Modulation (CFDM) 10.6.2 Continuously Variable Slope Delta Modulation 10.7 Speech Coding 10.7.1 G.726 10.8 Summary 10.9 Projects and Problems 11 Subband Coding 11.1 Overview 11.2 Introduction 11.3 The Frequency Domain and Filtering 11.3.1 Filters 11.4 The Basic Subband Coding Algorithm 11.4.1 Bit Allocation 11.5 Application to Speech Coding-G.722 11.6 Application to Audio Coding-MPEG Audio 11.7 Application to Image Compression 11.7.1 Decomposing an Image 11.7.2 Coding the Subbands 11.8 Wavelets 11.8.1 Families of Wavelets 11.8.2 Wavelets and Image Compression 11.9 Summary 11.10 Projects and Problems 12 Transform Coding 12.1 Overview 12.2 Introduction 12.3 The Transform 12.4 Transforms of Interest 12.4.1 Karhunen-Loeve Transform 12.4.2 Discrete Cosine Transform 12.4.3 Discrete Sine Transform 12.4.4 Discrete Walsh-Hadamard Transform 12.5 Quantization and Coding of Transform Coefficients 12.6 Application to Image Compression-JPEG 12.6.1 The Transform 12.6.2 Quantization 12.6.3 Coding 12.7 Application to Audio Compression 12.8 Summary 12.9 Projects and Problems 13 Analysis/Synthesis Schemes 13.1 Overview 13.2 Introduction 13.3 Speech Compression 13.3.1 The Channel Vocoder 13.3.2 The Linear Predictive Coder (Gov.Std.LPC-10) 13.3.3 Code Excited Linear Prediction (CELP) 13.3.4 Sinusoidal Coders 13.4 Image Compression 13.4.1 Fractal Compression 13.5 Summary 13.6 Projects and Problems 14 Video Compression 14.1 Overview 14.2 Introduction 14.3 Motion Compensation 14.4 Video Signal Representation 14.5 Algorithms for Videoconferencing and Videophones 14.5.1 ITU_T Recommendation H.261 14.5.2 Model-Based Coding 14.6 Asymmetric Applications 14.6.1 The MPEG Video Standard 14.7 Packet Video 14.7.1 ATM Networks 14.7.2 Compression Issues in ATM Networks 14.7.3 Compression Algorithms for Packet Video 14.8 Summary 14.9 Projects and Problems A Probability and Random Processes A.1 Probability A.2 Random Variables A.3 Distribution Functions A.4 Expectation A.5 Types of Distribution A.6 Stochastic Process A.7 Projects and Problems B A Brief Review of Matrix Concepts B.1 A Matrix B.2 Matrix Operations C Codes for Facsimile Encoding D The Root Lattices Bibliography Index

Introduction to data compression

Single image haze removal is a challenging ill-posed problem. Existing methods use various constraints/priors to get plausible dehazing solutions. The key to achieve haze removal is to estimate a medium transmission map for an input hazy image. In this paper, we propose a trainable end-to-end system called DehazeNet, for medium transmission estimation. DehazeNet takes a hazy image as input, and outputs its medium transmission map that is subsequently used to recover a haze-free image via atmospheric scattering model. DehazeNet adopts convolutional neural network-based deep architecture, whose layers are specially designed to embody the established assumptions/priors in image dehazing. Specifically, the layers of Maxout units are used for feature extraction, which can generate almost all haze-relevant features. We also propose a novel nonlinear activation function in DehazeNet, called bilateral rectified linear unit, which is able to improve the quality of recovered haze-free image. We establish connections between the components of the proposed DehazeNet and those used in existing methods. Experiments on benchmark images show that DehazeNet achieves superior performance over existing methods, yet keeps efficient and easy to use.

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DehazeNet: An End-to-End System for Single Image Haze Removal

Shannon's rate-distortion function provides a potentially useful lower bound against which to compare the rate-versus-distortion performance of practical encoding-transmission systems. However, this bound is not applicable unless one can arrive at a numerically-valued measure of distortion which is in reasonable correspondence with the subjective evaluation of the observer or interpreter. We have attempted to investigate this choice of distortion measure for monochrome still images. This investigation has considered a class of distortion measures for which it is possible to simulate the optimum (in a rate-distortion sense) encoding. Such simulation was performed at a fixed rate for various measures in the class and the results compared subjectively by observers. For several choices of transmission rate and original images, one distortion measure was fairly consistently rated as yielding the most satisfactory appearing encoded images.

The effects of a visual fidelity criterion of the encoding of images

Most methods of encoding images require complicated implementation. Thus it is of interest to compare the transmission rates that can be achieved by classes of encoding methods of different complexity. We consider two classes of encoding operations. The first class allows any possible operation on the two-dimensional image source output. The second class allows only certain restricted operations on the image. In acquisition of images by electronic means, the image intensity is in general scanned line by line, resulting in data that appear as a sequence of ordinary time series. In encoding, a simpler implementation results if one accepts the time series from a single scan line and encodes it independently of adjacent scan lines. This limits storage requirements to a single scan line and limits processing to operations on a one-parameter time series instead of operations on a two-dimensional field. This is the second class of encoding operations that we consider. We choose a distortion measure and discuss the rate-distortion function, which represents the minimum rate required by any encoding method in the first (arbitrary complex encoding). We then derive the minimum rate that can be achieved by any encoder from the second class. These rates are compared for a specific example.

Comparison of line-by-line and two-dimensional encoding of random images

It has long been known that for a mean-square error distortion measure the Gaussian distribution requires the largest rate of all sources of a given variance. It has also been stated that a code designed for the Gaussian source and yielding distortion d when used with a Gaussian source will yield distortion \leq d when used with any independent-letter source of the same variance. In this paper, we extend these results in two directions: a) instead of assuming that the source has a fixed variance, we fix an arbitrary moment; b) instead of mean-square error distortion measures, we consider nearly arbitrary continuous difference distortion measures. For each moment constraint, we show that there is a given distribution that has the largest rate for (nearly) any difference distortion measure and that a code designed for this source yielding distortion d yields distortion \leq d for any ergodic source satisfying the same moment constraint. Furthermore, digital encoding of the output of this encoder may yield a lower rate when this encoder is used with a source for which it was not designed. We also extend these results to the case of a random process or random field of known correlation function under a difference distortion measure.

D. Sakrison

Papers

The effects of a visual fidelity criterion of the encoding of images

Comparison of line-by-line and two-dimensional encoding of random images

Worst sources and robust codes for difference distortion measures