Information entropy measure for evaluation of image quality. The defining expression for entropy in the theory of statistical mechanics established by ludwig boltzmann and j. From a physical point of view, information theory has nothing to do with physics. Information theory a tutorial introduction o information.
It was founded by claude shannon toward the middle of the twentieth century and has since then evolved into a vigorous branch of mathematics fostering. Shannon information theory an overview sciencedirect topics. However, classics on information theory such as cover and thomas 2006 and mackay 2003 could be helpful as a reference. Information and entropy electrical engineering and. Entropy a guide for the perplexed roman frigg and charlotte werndl. The possibility that the carnot function could be the temperature as measured from a zero. We shall see that entropy and related information measures provide useful descriptions of the long term behavior of random processes and that this behavior is a key. Entropy and information theory is highly recommended as essential reading to academics and researchers in the field, especially to engineers interested in the mathematical aspects and mathematicians interested in the engineering applications.
The concept of information entropy was introduced by claude shannon in his 1948 paper a mathematical theory of communication. New edge detection technique based on the shannon entropy in gray level images. It was previously mentioned that the information theory aimed to investigate the quantitative laws. Gray 1990, hardcover at the best online prices at ebay. In entropy and information theory robert gray offers an excellent text to stimulate research in this field.
The eventual goal is a general development of shannons mathematical theory of communication, but much of the space is devoted to the tools and methods required to prove the shannon. Information theory is a subfield of mathematics concerned with transmitting data across a noisy channel. If you are new to information theory, then there should be enough background in this book to get you up to speed chapters 2, 10, and 14. S is the reduction in entropy, measured in bits,2 and prxx is simply the probability that the fact would be true of a random person. This format can be read from a web browser by using the acrobat reader helper application, which is available for free downloading from adobe the current version is a corrected and slightly. A mathematical theory of communication harvard mathematics.
Entropy and information theory 3 march 20 this site provides the current version of the first edition of the book entropy and information theory by r. Pdf applications of information theory in chemical graph theory. The publication of shannons 1948 paper, a mathematical theory of communication, in the bell system technical journal was the founding of information theory as we know it today. Entropy and information theory first edition, corrected robert m. Bayesian entropy estimation for countable discrete distributions. Coding and information theory immediately available upon purchase as print book shipments may be delayed due to the covid19 crisis. Examples are entropy, mutual information, conditional entropy, conditional information, and discrimination or relative entropy, along. The information entropy, often just entropy, is a basic quantity in information theory associated. Entropy and related information measures will be shown to provide useful descriptions of the long term behavior of random processes and this behavior is a key factor in. Many developments and applications of the theory have taken place since then, which have made many modern devices for data communication and storage such as cdroms. Entropy information theory provides a theoretical foundation to quantify the information content, or the uncertainty, of a random variable represented as a distribution. Information theory, the mathematical theory of communication, has two primary goals.
Its impact has been crucial to the success of the voyager missions to deep space. The information entropy, often just entropy, is a basic quantity in information theory associated to any random variable, which can be interpreted as the average level of information, surprise, or uncertainty inherent in the variables possible outcomes. Useinconnection withanyformofinformationstorageandretrieval,electronicadaptation. A cornerstone of information theory is the idea of quantifying how much information there is in a message. T c t h a number less than one, kelvin had to evaluate the ratio of the work output to the heat absorbed during the isothermal expansion with the help of the carnotclapeyron equation, which contained an unknown function called the carnot function. Jan 18, 2011 the development of the idea of entropy of random variables and processes by claude shannon provided the beginnings of information theory and of the modern age of ergodic theory. Multitude and diversity of information indicate that the entropy of the data will be low klir and yuan, 2000. New edge detection technique based on the shannon entropy. Marinescu, in classical and quantum information, 2012. Informationentropyisthelogbase2of thenumberofpossibleoutcomes.
Gray information systems laboratory electrical engineering department stanford university springerverlag. Shannon entropy this chapter is a digression in information theory. Yet it is exactly what is needed to simplify the teaching and understanding of fundamental concepts. Entropy as a tool for use in information science and knowledge generation originated with claude shannon and his groundbreaking work on information theory in communications shan48. Along the way, well give some intuitive reasoning behind these values in addition to the formulas.
Shannon, who formulated many of the key ideas of information theory. No, information is conserved, and so does not increase. A primer on information theory and privacy electronic. Entropy and information theory kindle edition by gray, robert m download it once and read it on your kindle device, pc, phones or tablets. Before we can define the difference between entropy and information, we need to understand what information is.
Entropy is a measurement that we have spent some time discussing above, particularly as a means of measuring the goodness of fit of a model. Sustainable urban development system measurement based. This book is an updated version of the information theory classic, first published in 1990. This course explores the ultimate limits to communication and computation, with an emphasis on the physical nature of information and information processing. Entropy and information gain the entropy very common in information theory characterizes the impurityof an arbitrary collection of examples information gain is the expected reduction in entropy caused by partitioning the examples according to a given attribute dip.
Entropy and information theory is highly recommended as essential reading to academics and researchers in the field, especially to engineers interested in the mathematical aspects and mathematicians interested in the engineering. About onethird of the book is devoted to shannon source and channel. We introduce two important concepts from shannons information theory. Entropy information theory entropy and information theory electronic edition, 2000, by robert m. Gray this book is an updated version of the information theory classic, first published in 1990. An introduction to information theory and applications. The quantity dhh 0 in equation 11 is the relative entropy kullbackleibler divergence of distribution h with respect to h 0, and plays an important role in information theory 14. About onethird of the book is devoted to shannon source and channel coding theorems. The information content of one of these partial messages is a measure of how much uncertainty this resolves for the receiver. Information theory an overview sciencedirect topics. The result is originally due to gray and kieffer 54, but the proof here is somewhat.
Information theory studies the quantification, storage, and communication of information. Information entropy is the logbase2 of the number of. Such a theory is not yet well developed, for several historical reasons. However, the concept of shanon entropy shares some intuition with boltzmanns. What is the joint entropy hx, y, and what would it be if the random variables x and. In information theory, the major goal is for one person a transmitter to convey some message over a channel to another person the receiver. In particular, if xk has probability density function pdf p, then hxk elog 1. This is a fascinating subject, which arose once the notion of information got precise and quantifyable. Information, entropy, and coding 6 characters per word, this means such an image is worth more 100,000 words, rather than 1,000 words. Gray information systems laboratory electrical engineering department stanford university springerverlag new york c 1990 by springer verlag. Lets apply the formula to a few facts, just for fun. Entropy is incrasing and this means that the evolution goes from ordered universe towards disordered universe, so exacly the contrary of what you are saying. Entropy and information theory stanford ee stanford university. Information entropy is occasionally called shannons entropy in honor of claude e.
More generally, this can be used to quantify the information in an event and a random variable, called entropy, and is calculated using probability. Video a standard frame rate for video is about 30 framessec. What is the relationship between entropy and information. This book is devoted to the theory of probabilistic information measures and their application to coding theorems for information sources and noisy channels. In order to 2 mathematically quantify the statistical nature of information loss 21, shannon developed a general concept of information theory. Information theory has been used in various branches of science. Use features like bookmarks, note taking and highlighting while reading entropy and information theory. Elements of information theory fundamentals of computational. Thermodynamic entropy is equivalent to information, and that information theory is essential to exorcising maxwells demon.
If the gray level of all pixels under the window homogeneous, p1and h0. The proof follows from the nonnegativity of mutual information later. It was originally proposed by claude shannon in 1948 to find fundamental limits on signal processing and communication operations such as data compression, in a landmark paper titled a mathematical theory of communication. Examples are entropy, mutual information, conditional entropy, conditional information, and relative entropy discrimination, kullbackleibler information, along with the limiting normalized versions of these quantities such as entropy rate and information rate. Recall that the table comparison of two encodings from m to s showed that the second encoding scheme would transmit an average of 5. In this case, the central pixel is not an edge pixel.
Peterson university of toronto entropy, a concept derived from thermodynamics and information theory, describes the amount of. Introduction the concept of entropy in information theory describes how much information there is in a signal or event. The short answer is that they are proportional to each other. For example, entropy provides an important tool for quantifying the information carried by neural signals, and there is an extensive literature in neuroscience devoted to estimating the entropy of.
To do so, the transmitter sends a series possibly just one partial messages that give clues towards the original message. If the uncertainty is measured before and after imaging, the reduction in the uncertainty, i. In information theory, systems are modeled by a trans mitter, channel. Information theory provides a resolution to the measurement problem in quantum mechanics. Information, entropy, and coding princeton university. About onethird of the book is devoted to shannon source and channel coding theorems the remainder addresses sources, channels, and codes and on. Information theory is the mathematical treatment of the concepts, parameters and rules governing the transmission of messages through communication systems. The entropy in the case of two possibilities with probabilities p and q 1p, namely. June 2010 contents 1 introduction 1 2 entropy in thermodynamics 2 3 information theory 4 4 statistical mechanics 9 5 dynamical systems theory 18 6 fractal geometry 26 7 conclusion 30 1 introduction entropy is ubiquitous in physics, and it plays important roles in numerous. Entropy in thermodynamics and information theory wikipedia. Entropy a guide for the perplexed charlotte werndl. Jun 19, 2007 the concept of information entropy describes how much randomness or uncertainty there is in a signal or an image. Entropy january 26, 2011 contents 1 reaching equilibrium after removal of constraint 2 2 entropy and irreversibility 3 3 boltzmanns entropy expression 6 4 shannons entropy and information theory 6 5 entropy of ideal gas 10 in this lecture, we will rst discuss the relation between entropy and irreversibility.
Entropy and information theory electronic edition, 2000, by robert m. Information theory must be introduced into physical theories at the same fundamental level as concepts such as energy. A framework for understanding uncertaintyrelated anxiety jacob b. Thermodynamicsbased evaluation of various improved shannon entropies for configurational information of gray level images peichao gao, zhilin li, hong zhang mathematics, computer science.
Entropy will be used together with the concept of information. But suppose that, instead of the distribution of characters shown in the table, a long series of as were transmitted. The development of the idea of entropy of random variables and processes by claude shannon provided the beginnings of information theory and of the modern age of ergodic theory. During recent years it is applied extensively in chemical graph theory for describing chemical structures and for providing good.
1137 480 408 1252 821 1011 292 1303 1040 1438 118 1148 485 1316 972 902 1237 635 803 135 421 106 331 1333 847 889 290 1493 444 1411 849 478 751 1206