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

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2D image fragments (e.g., blocks) into 3D data arrays which we call "groups." Collaborative Altering is a special procedure developed to deal with these 3D groups. We realize it using the three successive steps: 3D transformation of a group, shrinkage of the transform spectrum, and inverse 3D transformation. The result is a 3D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.

Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering

BIOE 402. Medical Technology Assessment. 2 or 3 hours. Bioentrepreneur course. Assessment of medical technology in the context of commercialization. Objectives, competition, market share, funding, pricing, manufacturing, growth, and intellectual property; many issues unique to biomedical products. Course Information: 2 undergraduate hours. 3 graduate hours. Prerequisite(s): Junior standing or above and consent of the instructor.

“Bioinformatics” 특집을 내면서

Two nonlinear algorithms for processing vector-valued signals are introduced. The algorithms, called vector median operations, are derived from two multidimensional probability density functions using the maximum-likelihood-estimate approach. The underlying probability densities are exponential, and the resulting operations have properties very similar to those of the median filter. In the vector median approach, the samples of the vector-valued input signal are processed as vectors. The operation inherently utilizes the correlation between the signal components, giving the filters some desirable properties. General properties as well as the root signals of the vector median filters are studied. The vector median operation is combined with linear filtering, resulting in filters with improved noise attenuation and filters with very good edge response. An efficient algorithm for implementing long vector median filters is presented. The noise attenuation of the filters is discussed, and an application to velocity filtering is shown. >

Vector median filters

This paper describes a recently created image database, TID2013, intended for evaluation of full-reference visual quality assessment metrics. With respect to TID2008, the new database contains a larger number (3000) of test images obtained from 25 reference images, 24 types of distortions for each reference image, and 5 levels for each type of distortion. Motivations for introducing 7 new types of distortions and one additional level of distortions are given; examples of distorted images are presented. Mean opinion scores (MOS) for the new database have been collected by performing 985 subjective experiments with volunteers (observers) from five countries (Finland, France, Italy, Ukraine, and USA). The availability of MOS allows the use of the designed database as a fundamental tool for assessing the effectiveness of visual quality. Furthermore, existing visual quality metrics have been tested with the proposed database and the collected results have been analyzed using rank order correlation coefficients between MOS and considered metrics. These correlation indices have been obtained both considering the full set of distorted images and specific image subsets, for highlighting advantages and drawbacks of existing, state of the art, quality metrics. Approaches to thorough performance analysis for a given metric are presented to detect practical situations or distortion types for which this metric is not adequate enough to human perception. The created image database and the collected MOS values are freely available for downloading and utilization for scientific purposes. We have created a new large database.This database contains larger number of distorted images and distortion types.MOS values for all images are obtained and provided.Analysis of correlation between MOS and a wide set of existing metrics is carried out.Methodology for determining drawbacks of existing visual quality metrics is described.

https://hal.archives-ouvertes.fr/hal-01109219/document

Image database TID2013

Nonlinear Signal Processing Signal Processing Model Signal and Noise Models Fundamental Problems in Noise Removal Algorithms Statistical Preliminaries Random Variables and Distributions Signal and Noise Models Estimation Some Useful Distributions 1001 Solutions Trimmed Mean Filters Other Trimmed Mean Filters L-Filters C-Filters (Ll-Filters) Weighted Median Filters Ranked-Order and Weighted Order Statistic Filters Multistage Median Filters Median Hybrid Filters Edge-Enhancing Selective Filters Rank Selection Filters M-Filters R-Filters Weighted Majority with Minimum Range Filters Nonlinear Mean Filters Stack Filters Generalizations of Stack Filters Morphological Filters Soft Morphological Filters Polynomial Filters Data-Dependent Filters Decision-Based Filters Iterative, Cascaded, and Recursive Filters Some Numerical Measures of Nonlinear Filters Discussion Statistical Analysis and Optimization of Nonlinear Filters Methods Based on Order Statistics Stack Filters Multistage and Hybrid Filters Discussion Exercises Bibliography Index

Fundamentals of nonlinear digital filtering

Visual quality of color images is an important aspect in various applications of digital image processing and multimedia. A large number of visual quality metrics (indices) has been proposed recently. In order to assess their reliability, several databases of color images with various sets of distortions have been exploited. Here we present a new database called TID2013 that contains a larger number of images. Compared to its predecessor TID2008, seven new types and one more level of distortions are included. The need for considering these new types of distortions is briefly described. Besides, preliminary results of experiments with a large number of volunteers for determining the mean opinion score (MOS) are presented. Spearman and Kendall rank order correlation factors between MOS and a set of popular metrics are calculated and presented. Their analysis shows that adequateness of the existing metrics is worth improving. Special attention is to be paid to accounting for color information and observers focus of attention to locally active areas in images.

http://www.comlab.uniroma3.it/BattistiPapers/EUVIP2013_Battisti.pdf

Color image database TID2013: Peculiarities and preliminary results

We review the evolution of the nonparametric regression modeling in imaging from the local Nadaraya-Watson kernel estimate to the nonlocal means and further to transform-domain filtering based on nonlocal block-matching. The considered methods are classified mainly according to two main features: local/nonlocal and pointwise/multipoint. Here nonlocal is an alternative to local, and multipoint is an alternative to pointwise. These alternatives, though obvious simplifications, allow to impose a fruitful and transparent classification of the basic ideas in the advanced techniques. Within this framework, we introduce a novel single- and multiple-model transform domain nonlocal approach. The Block Matching and 3-D Filtering (BM3D) algorithm, which is currently one of the best performing denoising algorithms, is treated as a special case of the latter approach.

/pdf/from-local-kernel-to-nonlocal-multiple-model-image-denoising-2jmisljpta.pdf

Jaakko Astola

Papers

Vector median filters

Image database TID2013

Fundamentals of nonlinear digital filtering

Color image database TID2013: Peculiarities and preliminary results

From Local Kernel to Nonlocal Multiple-Model Image Denoising