We propose a new measure, the method noise, to evaluate and compare the performance of digital image denoising methods. We first compute and analyze this method noise for a wide class of denoising algorithms, namely the local smoothing filters. Second, we propose a new algorithm, the nonlocal means (NL-means), based on a nonlocal averaging of all pixels in the image. Finally, we present some experiments comparing the NL-means algorithm and the local smoothing filters.

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A non-local algorithm for image denoising

We propose a fully functional identity-based encryption (IBE) scheme. The scheme has chosen ciphertext security in the random oracle model assuming a variant of the computational Diffie--Hellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic curves is an example of such a map. We give precise definitions for secure IBE schemes and give several applications for such systems.

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Identity-Based Encryption from the Weil Pairing

The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics In spite of the sophistication of the recently proposed methods, m

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A Review of Image Denoising Algorithms, with a New One

We introduce a short signature scheme based on the Computational Diffie-Hellman assumption on certain elliptic and hyperelliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signatures are typed in by a human or signatures are sent over a low-bandwidth channel.

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Short Signatures from the Weil Pairing

This important text and reference for researchers and students in machine learning, game theory, statistics and information theory offers a comprehensive treatment of the problem of predicting individual sequences. Unlike standard statistical approaches to forecasting, prediction of individual sequences does not impose any probabilistic assumption on the data-generating mechanism. Yet, prediction algorithms can be constructed that work well for all possible sequences, in the sense that their performance is always nearly as good as the best forecasting strategy in a given reference class. The central theme is the model of prediction using expert advice, a general framework within which many related problems can be cast and discussed. Repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and several other problems are viewed as instances of the experts' framework and analyzed from a common nonstochastic standpoint that often reveals new and intriguing connections.

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Prediction, learning, and games

In the past few years elliptic curve cryptography has moved from a fringe activity to a major challenger to the dominant RSA/DSA systems. Elliptic curves offer major advances on older systems such as increased speed, less memory and smaller key sizes. As digital signatures become more and more important in the commercial world the use of elliptic curve-based signatures will become all pervasive. This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. Due to the advanced nature of the mathematics there is a high barrier to entry for individuals and companies to this technology. Hence this book will be invaluable not only to mathematicians wanting to see how pure mathematics can be applied but also to engineers and computer scientists wishing (or needing) to actually implement such systems.

http://www.hpl.hp.com/research/info_theory/errata082900.pdf

Elliptic Curves in Cryptography

LOCO-I (LOw COmplexity LOssless COmpression for Images) is the algorithm at the core of the new ISO/ITU standard for lossless and near-lossless compression of continuous-tone images, JPEG-LS. It is conceived as a "low complexity projection" of the universal context modeling paradigm, matching its modeling unit to a simple coding unit. By combining simplicity with the compression potential of context models, the algorithm "enjoys the best of both worlds." It is based on a simple fixed context model, which approaches the capability of the more complex universal techniques for capturing high-order dependencies. The model is tuned for efficient performance in conjunction with an extended family of Golomb (1966) type codes, which are adaptively chosen, and an embedded alphabet extension for coding of low-entropy image regions. LOCO-I attains compression ratios similar or superior to those obtained with state-of-the-art schemes based on arithmetic coding. Moreover, it is within a few percentage points of the best available compression ratios, at a much lower complexity level. We discuss the principles underlying the design of LOCO-I, and its standardization into JPEC-LS.

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The LOCO-I lossless image compression algorithm: principles and standardization into JPEG-LS

LOCO-I (low complexity lossless compression for images) is a novel lossless compression algorithm for continuous-tone images which combines the simplicity of Huffman coding with the compression potential of context models, thus "enjoying the best of both worlds." The algorithm is based on a simple fixed context model, which approaches the capability of the more complex universal context modeling techniques for capturing high-order dependencies. The model is tuned for efficient performance in conjunction with a collection of (context-conditioned) Huffman codes, which is realized with an adaptive, symbol-wise, Golomb-Rice code. LOCO-I attains, in one pass, and without recourse to the higher complexity arithmetic coders, compression ratios similar or superior to those obtained with state-of-the-art schemes based on arithmetic coding. In fact, LOCO-I is being considered by the ISO committee as a replacement for the current lossless standard in low-complexity applications.

http://www.labs.hp.com/research/info_theory/loco/dcc96copy.pdf

LOCO-I: a low complexity, context-based, lossless image compression algorithm

Part I. Protocols: 1. Elliptic curve base protocols N. P. Smart 2. On the provable security of ECDSA D. Brown 3. Proofs of security for ECIES A. W. Dent Part II. Implementation Techniques: 4. Side channel analysis E. Oswald 5. Defenses against side-channel analysis M. Joye Part III. Mathematical Foundations: 6. Advances in point counting F. Vercauteren 7. Hyperelliptic curves and the HCDLP P. Guadry 8. Weil descent attacks F. Hess Part IV. Pairing Based Techniques: 9. Pairings S. Galbraith 10. Cryptography from pairings K. G. Paterson.

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Advances in Elliptic Curve Cryptography

We derive bounds on the probability that the L1 distance between the empirical distribution of a sequence of independent identically distributed random variables and the true distribution is more than a specified value. We also derive a generalization of Pinsker’s inequality relating the L1 distance to the divergence.

https://www.hpl.hp.com/techreports/2003/HPL-2003-97R1.pdf

Gadiel Seroussi

Papers

Elliptic Curves in Cryptography

The LOCO-I lossless image compression algorithm: principles and standardization into JPEG-LS

LOCO-I: a low complexity, context-based, lossless image compression algorithm

Advances in Elliptic Curve Cryptography

Inequalities for the L1 Deviation of the Empirical Distribution