There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

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Table Of Integrals Series And Products

Tables of integrals

Probability and Measure

The goal of this paper is to design a statistical test for the camera model identification problem. The approach is based on the heteroscedastic noise model, which more accurately describes a natural raw image. This model is characterized by only two parameters, which are considered as unique fingerprint to identify camera models. The camera model identification problem is cast in the framework of hypothesis testing theory. In an ideal context where all model parameters are perfectly known, the likelihood ratio test (LRT) is presented and its performances are theoretically established. For a practical use, two generalized LRTs are designed to deal with unknown model parameters so that they can meet a prescribed false alarm probability while ensuring a high detection performance. Numerical results on simulated images and real natural raw images highlight the relevance of the proposed approach.

Camera Model Identification Based on the Heteroscedastic Noise Model

The goal of this paper is to propose an accurate method for estimating quantization steps from an image that has been previously JPEG-compressed and stored in lossless format. The method is based on the combination of the quantization effect and the statistics of discrete cosine transform (DCT) coefficient characterized by the statistical model that has been proposed in our previous works. The analysis of quantization effect is performed within a mathematical framework, which justifies the relation of local maxima of the number of integer quantized forward coefficients with the true quantization step. From the candidate set of the true quantization step given by the previous analysis, the statistical model of DCT coefficients is used to provide the optimal quantization step candidate. The proposed method can also be exploited to estimate the secondary quantization table in a double-JPEG compressed image stored in lossless format and detect the presence of JPEG compression. Numerical experiments on large image databases with different image sizes and quality factors highlight the high accuracy of the proposed method.

/pdf/jpeg-quantization-step-estimation-and-its-applications-to-3sc5empvib.pdf

JPEG Quantization Step Estimation and Its Applications to Digital Image Forensics

The goal of this paper is to propose a statistical model of quantized discrete cosine transform (DCT) coefficients. It relies on a mathematical framework of studying the image processing pipeline of a typical digital camera instead of fitting empirical data with a variety of popular models proposed in this paper. To highlight the accuracy of the proposed model, this paper exploits it for the detection of hidden information in JPEG images. By formulating the hidden data detection as a hypothesis testing, this paper studies the most powerful likelihood ratio test for the steganalysis of Jsteg algorithm and establishes theoretically its statistical performance. Based on the proposed model of DCT coefficients, a maximum likelihood estimator for embedding rate is also designed. Numerical results on simulated and real images emphasize the accuracy of the proposed model and the performance of the proposed test.

Statistical Model of Quantized DCT Coefficients: Application in the Steganalysis of Jsteg Algorithm

This paper investigates the detection of information hidden in digital media by the least significant bit (LSB) matching scheme. In a theoretical context of known medium parameters, two important results are presented. First, based on the likelihood ratio test, we present a test that asymptotically maximizes the detection power whatever the embedding rate might be. Second, the statistical properties of this test are analytically calculated; it is particularly shown that the decision threshold which warrants a given probability of false-alarm is independent of inspected medium parameters. This provides an asymptotic upper-bound for the detection power of any test that aims at detecting data hidden with the LSB matching method. In practice, when detecting LSB matching, the unknown medium parameters have to be estimated. Based on a local model of digital media, a generalized likelihood ratio test is presented by replacing the unknown parameters by their estimation. Numerical results on large databases highlight the relevance of the proposed methodology and comparison with state-of-the-art detectors shows that the proposed tests perform well.

An Asymptotically Uniformly Most Powerful Test for LSB Matching Detection

https://hal.archives-ouvertes.fr/hal-01915650/document

Florent Retraint

Papers

Camera Model Identification Based on the Heteroscedastic Noise Model

JPEG Quantization Step Estimation and Its Applications to Digital Image Forensics

Statistical Model of Quantized DCT Coefficients: Application in the Steganalysis of Jsteg Algorithm

An Asymptotically Uniformly Most Powerful Test for LSB Matching Detection

Camera model identification based on the generalized noise model in natural images