I am ending my term as the Editor-In-Chief (EIC) of the Proceedings of the IEEE in December 2018. My reflections on the past six years are overwhelmingly good. Since I cannot repeat any tenure with the Proceedings due to term limits (probably a good rule for many positions both in professional societies and politics), I am looking for other opportunities to serve my professional society. After some searching and discussions with colleagues, I have come to the conclusion that I have reached the pinnacle of opportunities in the IEEE. Simply put, this is the best job in the IEEE.

Trends, they are not only for the fashion industry after all. Within the engineering and computer science research communities as well, we periodically observe the phenomenon, see how certain methods suddenly start receiving particular attention, and sometimes, even though they emerge as an attractive solution for a given set of problems, they tend to become a hammer looking for new nails. At fi rst, using a new method on old problems is the natural and reasonable way to proceed. There have been remarkable successes achieved through the adoption of a tool from another fi eld or a new way of looking at old problems that brings new insights and solutions. There have been a number of such trends throughout the years in every field. In signal processing, a few notable ones include maximum entropy, wavelets, kernel methods, and the multiple up and down cycles of neural nets. A current tool that is on the rise is sparsity, more specifically solutions that promote sparsity, including coding, compressive sensing, sparse learning/estimation, sparse factorizations, and of course deep nets, which, without careful use of sparsity, would be useless. We will use sparsity as the major example in this Point of View article because it is current and illustrates the points we are making very well. While we agree that sparsity is very useful and has led to some excellent results in the past decade or so, it also allows us to address the dangers and pitfalls of blindly following trends in research. These problems are reflected in our publications and help define the overall research climate. In the following, we provide an overview on use of sparsity and then discuss a couple of specific problems.

In early 2019, the PROCEEDINGS OF THE IEEE will publish a Special Issue on Building Ethical Autonomous Systems. This topic is a departure from the usual reviews and surveys of highly technical and mathematical areas on the cutting edge of electrical and computer engineering research. You may have to search for the equations in this issue, but the logic can be challenging. The ethical questions that are addressed, while framed as dealing with autonomous systems, are important and applicable to dealing with all research areas under the IEEE umbrella. The methods of addressing these questions draw mainly from artificial intelligence and machine learning.

There has been much recent discussion in the popular press about robots and intelligent machines or programs taking jobs and creating unemployment on a massive scale. Looking at history, technological unemployment or workers being replaced by machines has been a problem for a long time. It would seem that because we have survived the invention of many paradigm-changing devices over many centuries, we will survive this latest one, but, maybe this time is different. This time the machines are autonomous. They are not just an extension of a human’s manual movements, like a steam engine, a sewing machine, or a grain reaper. They are an extension of the human’s mind and can make decisions without human guidance.

Reports on upcoming special issues as well as new development for the journal.

Provides an overview of the technical articles and features presented in this issue. Our regular papers this month focus on 5G related topics such as multipleinput– multipleoutput transmission using finite input signals, and achieving ultrareliable and low-latency wireless communication.

In preparation for writing an article for the Proceedings of the IEEE Centennial issue in May 2012, I reviewed the predictive articles from the 50th Anniversary Issue from 1962. Several articles made interesting predictions that give insight into the world of Electrical Engineering and how we think and even fantasize. Many of the predictions were amazingly accurate, while others were well off the mark, often in the same article. There are a couple of “misses” that I will use as a springboard to discuss current issues in this article and one to follow. This first Point of View reflects on the role of scientists and engineers in government and policy making.

Provides a preview of the upcoming special issues and articles that are planned for 2018. A total of ten special issues will be published with a diverse range of topics that cover such areas as: small satellites, safe and secure cyber-physical systems; high-performance computing; trends in localization technologies; machine ethics; design automation for cyber-physical systems; smart cities; applications of graph theory; principle component analysis for modern data sets; and silicon photonics. Also reports on additions and enhancements to the Proceedings of the IEEE in 2017 such as the new website and the webinar series.

It is well known that many more than three or four spectral measurements are required for accurate measurement of color. Previous work has shown seven to ten measurements can yield accurate results on average, but with significant numbers of errors above the threshold of obvious visual detection. Furthermore, the filters used for these measurements are very difficult to fabricate. We show that such filters are not needed and, in fact, have much poorer performance, in perceptual quality measured in ΔEab, than simple narrow-band filters. This is especially true in the presence of Poisson noise at a level common in current digital cameras. In realistic Poisson noise, our filter sets of up to 12 filters allow average ΔEab values around 0.5, with maximum errors below 3.

As noted on our webpage, the Proceedings of the IEEE specializes in surveys, reviews, and tutorials. The distinction between surveys and reviews is not always clear to readers and authors. Our working definition is that surveys discuss the current state of a subject and give an overview and summary of the published and ongoing work by researchers from all geographical regions and from all organizations contributing to the topic. Reviews contain more technical depth of the topics and usually discuss the technical background needed to understand and evaluate the contributions to the topics under investigation. Tutorials are teaching tools that present the background and current theory and methodologies of a topic. A tutorial is not about presenting new theory or methods, but may use current research as examples of applications of the techniques discussed. Currently, we publish many more surveys and reviews than tutorials.

Presents an editorial which outlines upcoming special issues planned for 2017 as well as other major developments planned for the Proceedings of the IEEE. The publication will also be celebrating is 105th Anniversay (1913-2017).

Discusses the distinction between training and education and examines how current technologies and software programs have and will shape engineering education and the development of skills sets in the future.

Presents the introductory editorial for this issue of the publication.

With the globalization of economy and liberalization of trade, the international education trade market is becoming an increasingly important part of international service trade. Education resources are distributed internationally, and exchanges and cooperation of education among different nations are becoming increasingly frequent. As a result, education in various countries interacts and competes with each other, which eventually promotes the globalized education.

he year 2015 is almost here and we are excited to announce our lineup of special issues for the coming year!As always, the Proceedings of the IEEE strives to offer reviews of broad significance and long-range interest in all areas of electrical, electronics, and computer engineering, as well as in computer science, and to continue to be a tutorial and technical information source with an emphasis on applications-driven technologies.We hope that you, our readers, find the content stimulating and applicable to your everyday work and your overall professional success.Just as a reminder, in 2012, we published a special Centennial Issue with 69 additional articles looking at the past, the present, and the future of technology.This free issue remains available on the Proceedings Xplore homepage under ''Past Issues/2012.''Before highlighting our upcoming issues, let us look at the latest electrical engineering journal citation reports.The Proceedings is the sixth most highly cited journal (by impact factor) in its category.More notably, it is the top ranked journal, if we look at the five-year impact factor and is ranked second by Article Influence Score.Looking at the metrics as a whole, we believe that The Proceedings is performing well and providing important information to its reader community.As mentioned in last year's editorial, we ran a Reader Survey in December 2013.Thank you to all those who participated!We received a lot of valuable feedback and will be running a modified version of the survey again this year before introducing some exciting new features for the journal.A few of the interesting ideas received last year were a request for reintroducing reader comments, availability of free online tutorials to complement the special issue content, more predictive papers, and the introduction of more multimedia into the content.

The dominance of Poisson noise over signal independent Gaussian noise and other types has been demonstrated for commercial digital color cameras. We present a new method for estimating CIE colorimeric values in the presence of Poisson noise. The new methods use multidimensional look-up tables (MLUTs) and are easily adapted to the local statistics of the image. The methods are shown to perform better than common methods that are based on signal independent noise models.

Discusses the ethical, legal, economic, and academic implications of plagiarism with a special emplhasis on the ramifications for IEEE Proceedings and other IEEE publications. Reports on rules the IEEE imposes on authors and identifies the steps the IEEE is taking to ensure copyright protection of intellectual property.

Discusses the content, scope and plans for future special issues of the journal.

The various components that contribute to the noise in digital cameras are primarily Poisson noise from the discrete nature of the photons, Gaussian and Poisson noise from various electronic and thermal processes and uniform noise from quantization. Our experiments show that the photon Poisson noise is the dominant contributor to uncertainty in the raw data captured by high-performance sensors using in color digital cameras. This finding is consistent with previous monochrome work and indicates that research on denoising and demosaicking of color digital images should consider Poisson noise models as more important than the usual Gaussian models.

We develop a method of adaptive sampling for use with image output devices, e.g., displays and projectors, that can produce improved results over sampling the input space with a fixed rectangular grid in a multidimensional space. Fixed sampling requires knowledge of the function shape to be effective. Even then the sampling can be grossly inefficient in some regions and grossly undersampled in others. Our method produces a more efficient sampling over the whole gamut of the device output of oddly shaped gamuts, while producing good results for more usual functions. This increased efficiency is important, since measuring samples is the most time-consuming part of the characterization process.

Reducing the dimensionality of a classification problem produces a more computationally-efficient system. Since the dimensionality of a classification problem is equivalent to the number of neurons in the first hidden layer of a network, this work shows how to eliminate neurons on that layer and simplify the problem. In the cases where the dimensionality cannot be reduced without some degradation in classification performance, we formulate and solve a constrained optimization problem that allows a trade-off between dimensionality and performance. We introduce a novel penalty function and combine it with bilevel optimization to solve the constrained problem. The performance of our method on synthetic and applied problems is superior to other known penalty functions such as weight decay, weight elimination, and Hoyer's function. An example of dimensionality reduction for hyperspectral image classification demonstrates the practicality of the new method. Finally, we show how the method can be extended to multilayer and multiclass neural network problems.

In the design of a multiband imaging device, it is useful to model the response and performance of the instrument mathematically. Determining the device performance requires providing typical input to the device. Currently, there exist databases of hyperspectral images and spectral reflectance measurements that can provide limited input. In this document, methods for generating and modeling reflectance spectra are introduced. These artificial spectra can be useful as additional input to assess the performance of hyperspectal image processing algorithms and devices under specified statistical conditions.

With the proliferation of color display and input devices it has become less expensive to demonstrate and teach color image processing techniques. When teaching color image processing, it is important to emphasize that it is not a multichannel extension of monochrome image processing. This paper indicates the elements of color image processing and color image displays that every student and instructor should know. We give examples that can be used to illustrate these concepts.

Often in dealing with images, the training data must be extracted for a limited data set. In particular, the illumination conditions of the sample images is limited and, in many cases, unknown. In this paper, we show that artificial variation of the illuminant of hyperspectral images can be used to overcome the limitations of a small sample set.

Feature selection is the process of selecting effective subsets of features that are effective in performing a given task. We propose an approach using a penalty function combined with a neural network to select a subset from a collection of features while maintaining the performance possible with the larger set. The penalty function is related to a mixed-norm function that has proven successful in pruning neural networks. The new function is shown to work on test cases with known redundancy and to be effective in feature selection for practical problems.

While images often contain only one illumination source, objects in the scene are illuminated by varying intensities of that illuminant. We show that the illuminant can be estimated using a few known reflectances within an image taken with a hyperspectral camera. The method relies on projection to a non-convex constraint set, as well as to convex constraint sets. Simulations and tests on actual hyperspectral images show the method is effective.

Many signals and statistical distributions are a mixture of component signals or distributions. Current methods for estimating the proportion of each component assume a parametric form for the components. We introduce nonparametric methods, based on projections onto convex sets, to address the many practical cases where parametric models are not applicable. Comparisons are made with parametric methods and discussed for special cases where both methods can be used.

Pixels in hyperspectral images usually contain spectra from several classifiable objects, so that the recorded pixel is a mixture of the classes. Current methods estimate the proportion of each class using a set of spectral signatures describing only the class means. Since the means are known only by estimation methods, we introduce an approach that also incorporates the variation inherent in this estimation. The total least squares approach using projections onto convex sets (POCS) produces improved performance over simple maximum likelihood methods, even one that also uses the constraint sets and POCS.

Hyperspectral images provide a vast amount of information about a scene. However, much of that information is redundant as the bands are highly correlated. For computational and data compression reasons, it is desired to reduce the dimensionality of the data set while maintaining good performance in image analysis tasks. This work presents a method of dimensionality reduction based on neural networks. A novel penalty function is presented and shown to successfully reduce the number of active neurons, which corresponds to the dimensionality of the data for the task of interest.

A single ADC is often used to digitize several channels. In this application, the channels are sampled sequentially in time. This results in signals that are correlated but are not sampled at the same time. Bandlimited interpolation can be used to obtain signals with the same sampling times. However, methods that were recently developed for digital cameras can be used to achieve resolution beyond the Nyquist limit of the sampling rate of a single channel. This work demonstrates the effectiveness of this method on stereo signals and shows it to be robust to estimations of the modelling parameters.

With the proliferation of digital cameras, more consumers are faced with the problem of making color corrections to their pictures, while most picture editors allow some white point, or illuminant, correction and some enhancements, these methods work on the image, as a whole rather than on specific regions or colors. This work describes a simple method, that allows the user the ability to correct specific colors in specific locations in a picture. It is shown that relatively few sample colors are needed to produce a well-behaved interpolation in three-dimensional color spaces. A quantitative measure of performance is obtained by using the method to correct for illumination.

Many researchers are working on various aspects of color imaging. However, it is apparent from the papers published that it is difficult for many of them to produce high quality color reproductions. While our previous work outlined the steps needed to produce calibrated color images, the problem of creating the programs to implement the process locally seems to be a serious problem. To surmount this final barrier, we have developed a web site that has the MATLAB programs necessary to characterize printers and produce high quality images.

Digital color cameras sample the continuous color spectrum using three or more filters; however, each pixel represents a sample of only one of the color bands. This arrangement is called a mosaic. To produce a full-resolution color image, the recorded image must be processed to estimate the values of the pixels for all the other color bands. This restoration process is often called demosaicking. This paper uses stacked notation to represent the mosaicked image capture and derives the minimum mean square error (MMSE) estimator for the demosaicked image. By making common assumptions, the restoration can be computed in a cost-effective manner. Extensions to the linear method are proposed to allow adaptive behavior.

To demonstrate the performance of color image processing algorithms, it is desirable to be able to accurately display color images in archival publications. In poster presentations, the authors have substantial control of the printing process, although little control of the illumination. For journal publication, the authors must rely on professional intermediaries (printers) to accurately reproduce their results. Our previous work describes requirements for accurately rendering images using your own equipment. This paper discusses the problems of dealing with intermediaries and offers suggestions for improved communication and rendering.

Digital color cameras sample the continuous color spectrum using three or more filters; however, each pixel represents a sample of only one of the color bands. This arrangement is called a mosaic. To produce a full resolution color image, the recorded image must be processed to estimate the values of the pixels for all the other color bands. This restoration process is called demosaicking. This paper uses stacked notation to represent the mosaicked image capture and derives the minimum mean square error estimator for the demosaicked image. By making common assumptions, the restoration can be computed in a cost effective manner. This allows the user to apply most of the common adaptations that have been used in non-mosaicked sampled image processing to produce a variety of improved algorithms.

A colorimetric approach to restoration of digital images is presented. Assumptions are made to simplify the general problem to obtain a more computable form. Two methods are developed, using Karhunen-Loeve transformation and independent restoration schemes from earlier works, to solve the estimation problem in color image processing using multidimensional restoration. A comparison of the methods is presented including the effects of parameters of interest to desktop scanners and digital cameras. The results for the SNRs and blurs studied indicate that more than three color channels produces a slight numerical gain and modest visual gain.

The concentration of most image processing courses is on the various algorithms used to alter an input image or data to produce a desired output image. Little effort is expended on teaching the appropriate display methods that are required to accurately demonstrate the effectiveness of the processing algorithms under investigation. This paper reviews the fundamentals of image display that every student should know before displaying the homework and project results that are assigned in those courses.

To demonstrate the performance of color image processing algorithms, it is desirable to be able to accurately display color images in archival publications. Our previous work (see IEEE Trans. Image Proc., vol.8, no.12, Dec. 1999), described requirements for accurately rendering images using your own equipment. This paper discusses the problems of dealing with intermediaries and offers suggestions for improved communication and rendering.

The mathematical formulation of calibrating color scanners is presented. The mapping from scanned values to colorimetric values is inherently nonlinear. Calibration required approximating this nonlinear mapping. Neural networks are particularly suited to this task. Performance using an artificial neural network generated LUT is compared to that achieved by other commonly used methods.

For part I, see ibid., p.143-50. This paper is the second of two companion papers. The foundations of the proposed method of heuristic constraint enforcement on membership functions for knowledge extraction from a fuzzy/neural architecture was given in Part I. Part II develops methods for forming constraint sets using the constraints and techniques for finding acceptable solutions that conform to all available a priori information Moreover, methods of integration of enforcement methods into the training of the fuzzy-neural architecture are discussed. The proposed technique is illustrated on a fuzzy-AND classification problem and a motor fault detection problem. The results indicate that heuristic constraint enforcement on membership functions leads to extraction of heuristically acceptable membership functions in the input and output spaces. Although the method is described on a specific fuzzy/neural architecture, it is applicable to any realization of a fuzzy inference system, including adaptive and/or static fuzzy inference systems.

Using fuzzy/neural architectures to extract heuristic information from systems has received increasing attention. A number of fuzzy/neural architectures and knowledge extraction methods have been proposed. Knowledge extraction from systems where the existing knowledge limited is a difficult task. One of the reasons is that there is no ideal rulebase, which can be used to validate the extracted rules. In most of the cases, using output error measures to validate extracted rules is not sufficient as extracted knowledge may not make heuristic sense, even if the output error may meet the specified criteria. The paper proposes a novel method for enforcing heuristic constraints on membership functions for rule extraction from a fuzzy/neural architecture. The proposed method not only ensures that the final membership functions conform to a priori heuristic knowledge, but also reduces the domain of search of the training and improves convergence speed. Although the method is described on a specific fuzzy/neural architecture, it is applicable to other realizations, including adaptive or static fuzzy inference systems. The foundations of the proposed method are given in Part I. The techniques for implementation and integration into the training are given in Part II, together with applications.

The mathematical formulation of calibrating color image reproduction and recording devices is presented. This formulation provides a foundation for future research in areas of characterization of devices and display of color images. The importance of calibration is demonstrated by real examples. The procedure outlined in this paper should become standard for displaying color images for the image processing community.

The conventional two-stage training algorithm of the fuzzy/neural architecture called FALCON may not provide accurate results for certain type of problems, due to the implicit assumption of independence that this training makes about parameters of the underlying fuzzy inference system. In this correspondence, a training scheme is proposed for this fuzzy/neural architecture, which is based on line search methods that have long been used in iterative optimization problems. This scheme involves synchronous update of the parameters of the architecture corresponding to input and output space partitions and rules defining the underlying mapping; the magnitude and direction of the update at each iteration is determined using the Armijo rule. In our motor fault detection study case, the mutual update algorithm arrived at the steady-state error of the conventional FALCON training algorithm as twice as fast and produced a lower steady-state error by an order of magnitude.

A colorimetric approach to restoration of digital images is presented. Assumptions are made to simplify the general problem to obtain a more computable form. Two methods are developed using Karhunen-Loeve transformation and independent restoration schemes to solve the estimation problem in color image processing using multidimensional restoration. A comparison of the methods is presented including the results obtained in CIELAB values and visual images. The results for the SNR and blurs studied indicate that more than three color channels produces only a slight gain.

The mathematical formulation of calibrating color image reproduction and recording devices is presented. This formulation provides a foundation for future research in areas of characterization of devices and display of color images. The procedure outlined in this paper should become standard for displaying color images for the image processing community.

To a significant degree, multimedia applications derive their effectiveness from the use of color graphics, images, and video. However, the requirements for accurate color reproduction and for the preservation of this information across display and print devices that have very different characteristics and may be geographically apart are often not clearly understood. This paper describes the basics of color science, color input and output devices, color management, and calibration that help in defining and meeting these requirements.

In this correspondence, the problem of designing color scanning filters for multi-illuminant color recording is considered. The filter transmittances are determined from a minimum-mean-squared orthogonal tristimulus error criterion that minimizes the color error in estimates obtained from noisy recorded data. Nonnegativity constraints essential for physical realizability are imposed on the filter transmittances. In order to demonstrate the significant improvements obtained, the resulting filters are compared with suboptimal filters reported in earlier literature.

The CIE color matching functions, which are the foundation of computational color, are constructed and tabulated from experimental data by using various interpolations and smoothing. This work shows how the exact form of the mathematical operations used to construct the tabulated values can produce a bias in the computation of tristimulus values when used with sampled data obtained from various measuring instruments. The practical limitations caused by the bias are discussed.

This paper surveys current technology and research in the area of digital color imaging. In order to establish the background and lay down terminology, fundamental concepts of color perception and measurement are first presented using vector-space notation and terminology. Present-day color recording and reproduction systems are reviewed along with the common mathematical models used for representing these devices. Algorithms for processing color images for display and communication are surveyed, and a forecast of research trends is attempted. An extensive bibliography is provided.

In the design and evaluation of color scanners and cameras, it is useful to have a single figure of merit that closely agrees with perceived color accuracy. In the past, several measures of goodness for color scanning filters have been proposed to fulfil such a requirement. Most of the proposed measures have had shortcomings in that they are either based on error metrics in color spaces that are not perceptually uniform, or in that they do not take into account the effects of measurement noise. An extension of the most promising measure, based on linearized CIELAB space, is proposed to obtain a new figure of merit that has a high degree of perceptual relevance and also accounts for the varying noise performance of different filters. The paper also provides a common framework for the different figures of merit and a comprehensive comparison of their computational complexity and reliability.

The restoration of a signal degraded by a stochastic impulse response is formulated as a problem with uncertainties in both the measurements and the impulse response. The method of total least squares, and variants thereof, are effective techniques for solving this class of problems. However, unlike set theoretic estimation schemes, these methods do not allow the incorporation of other a priori information in the estimate. In this correspondence, two new sets motivated by total least squares are introduced for set theoretic estimation. The convexity of these sets is established and the projection operators onto these sets are given. Through simulations, the advantages of the new technique over conventional and older set theoretic schemes for restoration are demonstrated.

The problem of the design of color scanning filters is addressed in this paper. The problem is posed within the framework of the vector space approach to color systems. The measure of the goodness of a set of color scanning filters presented in earlier work is used as an optimization criterion to design color scanning filters modeled in terms of known, smooth, nonnegative functions. The best filters are then trimmed using the gradient of the mean square DeltaE(ab) error to obtain filters with a lower value of perceptual error. The results obtained demonstrate the utility of the method.

The problem of the sensitivity analysis of color scanning filters is addressed in this paper. The second differential of the mean square DeltaE(ab) error provides a means of calculating the sensitivity of the mean square DeltaE(ab) error to filter fabrication errors. Tolerances on the allowable change in the mean square DeltaE(ab) error are used to define bounds on the filter fabrication errors at all wavelengths and at single wavelengths.

In image-restoration problems involving a known blur, set-theoretic estimation provides an effective framework for incorporation of both noise statistics and a priori information. However, the sets formulated for use with known blurs are not suitable for situations involving unknown stochastic blurs. In this paper, new sets based on an error in variables criterion are developed, which are more appropriate for restoration of uncertain blurs. The conditions for convexity of these sets are rigorously established. Through 1-D simulations, the set-theoretic restoration scheme utilizing these sets is compared with the stochastic MMSE filter and with set-theoretic schemes for stochastic blurs developed earlier.

Digital signal processing tools are used to determine the proper sampling of color spectra and the effect of sampling on the accuracy of derived properties such as CIE tristimulus values and color rendering indexes. It is found that 10 nm sampling is adequate for most applications, but not for more exacting textile and paint matching applications. Special methods are proposed to treat the cases of color signals with delta function components such as fluorescent lights.

The senior level digital signal processing (DSP) course at North Carolina State University is designed to teach basic methods of describing and analyzing digital signals and systems. In order to reinforce this approach, the laboratory is designed to demonstrate DSP concepts with actual signals and systems. The lab requires no programming but gives the student the opportunity to see the application of theory by manipulating and analyzing real signals. The basis for the lab is a dual channel, multiple scope software package that allows the student simultaneous viewing of time domain and frequency domain signals.

A comparison is presented between recommended CIE interpolation and extrapolation methods and those derived from signal processing methods. While the DSP based methods are superior in estimating tri-stimulus values, the difference in CIEL*a*b* values is slight.

The effect of noise on the number of effective channels (color filters) used to record a color image is investigated. Transmittances of color filters are calculated that minimize the mean square error that occurs when estimating, from the recorded data, the colors in the image under a collection of viewing illuminants. Since the results indicate that a significant improvement in color correction accuracy is achieved by using four channels, there is good reason to consider using four-tuples for representation of colorimetric information.

Fluorescent lamps are widely used in the office environment and in common desktop scanners. These lamps are characterized by the nearly monochromatic emission lines present in their radiant spectrum. Due to the presence of spectral lines special care is required in the computation of tristimulus values under these illuminants. Accurate computation of the tristimulus values can be performed digitally by modeling the radiance as the sum of a continuous spectrum emitted by the phosphors and weighted impulses corresponding to the emission lines. The paper considers a scheme for estimating the continuous spectrum and the strengths of the impulses from measurements of the spectrum with band limited sensors. The impact of noise in measured data on the accuracy of the final color computation is also considered.>

The paper discusses the sampling of color spectra and its effect on the accuracy of derived properties such as CIE tristimulus values and color rendering indices. The effect of aliasing and common mathematical operations are discussed.>

Fluorescent lamps are the most common lighting source for desktop publishing and standard viewing conditions. In order to predict the appearance of reflective material viewed under fluorescent lamps, the CIE tristimulus values must be computed. While these values are readily computed for most smoothly varying reflectances by using a simple summation, the presence of line spectra in the fluorescent lamps requires special treatment. This paper presents a method for the accurate computation of the tristimulus values. The effect of noise on the measurement is also considered.>

The quality of color correction is dependent on the filters used to scan the image. This paper introduces a method of selecting the color filters using a priori information about the viewing illuminants. Color correction results using the derived filters are compared with color correction results using filters that are optimal for individual viewing and recording illuminants. The comparison is performed using the CIE PEL (L*a*b*) perceptual color difference measure. Applications of this work are found in the design of scanners, copiers, and television systems.

The estimation of the point spread function (PSF) for blur identification, often a necessary first step in the restoration of real images, method is presented. The PSF estimate is chosen from a collection of candidate PSFs, which may be constructed using a parametric model or from experimental measurements. The PSF estimate is selected to provide the best match between the restoration residual power spectrum and its expected value, derived under the assumption that the candidate PSF is equal to the true PSF. Several distance measures were studied to determine which one provides the best match. The a priori knowledge required is the noise variance and the original image spectrum. The estimation of these statistics is discussed, and the sensitivity of the method to the estimates is examined analytically and by simulations. The method successfully identified blurs in both synthetically and optically blurred images.

Point spread function (PSF) models derived from physical optics provide a more accurate representation of real blurs than simpler models based on geometrical optics. However, the physical PSF models do not always result in a significantly better restoration, due to the coarse sampling of the recording device and insufficiently high signal-to-noise ratio (SNR) levels. Low recording resolutions result in aliasing errors in the PSF and suboptimal restorations. A high-resolution representation of the PSF where aliasing errors are minimized is used to obtain improved restorations. The SNR is the parameter which ultimately limits the restoration quality and determines the need for an accurate PSF model. As a rule of thumb, the geometrical PSF can be used in place of the physical PSF without significant loss in restoration quality when the SNR is less than 30 dB.

In order to reproduce perceived color accurately the three bands of a color image must be obtained using sensors whose relative spectral sensitivity satisfies certain constraints. These constraints, the design of filters which satisfy these constraints, and the effect of inaccuracies in the sensors' response are discussed. The mathematical techniques used for the error analysis have not been used previously in color scanning filter design. The results of this study are applicable to most color systems, including television, lithography, copiers and printers.>

Sequential imaging cameras are designed to record objects in motion. When the speed of the objects exceeds the temporal resolution of the shutter, the image is blurred. Because objects in a scene are often moving in different directions at different speeds, the degradation of a recorded image may be characterized by a space-variant point spread function (PSF). The sequential nature of such images can be used to determine the relative motion of various parts of the image. This information can be used to estimate the space-variant PSF. A modification of the Landweber iteration is developed to utilize the space-variant PSF to produce an estimate of the original image.

A new blur identification method is proposed which estimates the point spread function (PSF) parameters by comparing the power spectrum of the Wiener restoration residual with its expected value, derived under the assumption that the parameter values tested are correct. The parameter values for which there is the closest match between the residual statistics are chosen as the estimates of the true parameters. The method has successfully identified blur parameters in both synthetically and in-camera blurred images.>

The reproduction of color images often requires color correction. The original image may have been recorded under one illumination while the reproduction is to be viewed under another or made to appear as if it were recorded under another. Since it is often the case that the original illumination is unknown to the image scientist, it is necessary to estimate. Two methods are presented for estimating the illuminant. The sensitivity of the methods to various assumptions is discussed.>

In the last decade, many researchers have devoted considerable effort to the problem of image restoration. However, no recent study has been undertaken for a comparative evaluation of these techniques under conditions where a user may have different kinds of a priori information about the ideal image. To this effect, we briefly survey some recent techniques and compare the performance of a linear space-invariant (LSI) maximum a posteriori (MAP) filter, an LSI reduced update Kalman filter (RUKF), an edge-adaptive RUKF, and an adaptive convex-type constraint-based restoration implemented via the method of projection onto convex sets (POCS). The mean square errors resulting from the LSI algorithms are compared with that of the finite impulse response Wiener filter, which is the theoretical limit in this case. We also compare the results visually in terms of their sharpness and the appearance of artifacts. As expected, the space-variant restoration methods which are adaptive to local image properties obtain the best results.

Two methods for the synthesis of set theoretic estimates are presented. The first is a generalization of the method of successive projections onto closed and convex subsets of Hilbert spaces to approximately compact subsets of metric spaces. The second is based on a stochastic search in the solution space. These methods allow greater flexibility with regard to the incorporation of prior knowledge, thereby extending the scope of set theoretic estimation. Applications to digital signal processing problems are discussed.>

Constraints are developed based on prototype images and used in set-theoretic image restoration. A prototype can be obtained as a result of applying a predetermined operator to the observed image. In this case, the operator and the bound, which limits the variation of the restored image from the prototype, are the two defining quantities of a prototype constraint. General guidelines for rigorously estimating the defining bound of a prototype constraint under certain simplifying conditions are discussed. Two examples of prototype constraints are provided and used in the context of projections onto convex sets. The resulting restorations show significant improvement over the Wiener restorations in reducing the restoration artifacts.>

A description is given of how information pertaining to an arbitrary absolute moment of the noise process can be used in a general set-theoretic estimation framework. It is shown that for each such piece of a priori information, a set can be constructed in the solution space by constraining the corresponding sample statistics of the estimation residual to lie within some acceptable distance from the expected value. The geometrical and topological properties of these sets are investigated. The benefits of the simultaneous use of several such sets with regard to the synthesis of better set-theoretic estimates are discussed. Applications to signal restoration/reconstruction, speech prediction, spectral estimation, and radar signal processing are discussed.>

The use of a priori information and its effect on multiband image restoration are considered. The Wiener solution that takes into account the statistical correlations between image bands is shown to be extremely sensitive to between-channel correlation estimates. In fact, the Wiener restoration using the cross correlations, estimated from a prototype image similar to the original, may give worse results than the Wiener restoration obtained by simply ignoring the cross correlations and independently restoring the channels. With the aim of obtaining a more robust algorithm, a unified set-theoretic framework that allows the simultaneous use of single and multiband a priori information is developed. A number of convex constraint sets are provided for use in a convex projections restoration algorithm.>

The authors investigate the application of set-theoretic estimation methods to the design of linear-predictive-coding (LPC) digital filters. The constraints involved in the design are represented by sets in an abstract space. Any member of their intersection satisfies all the design specifications and is called feasible. Two sets are considered: the set of stable filters and the set of filters which minimize the mean-square prediction error in an environment where the statistics of the observed data are unknown. These two sets are described analytically and the problem of obtaining a feasible LPC filter is addressed. Experimental results are also presented.>

The performance is compared of a linear space-invariant (LSI) maximum a posteriori filter, an LSI reduced update Kalman filter (RUKF), an edge-adaptive RUKF, and an adaptive convex-type constraint-based restoration implemented via the method of projection onto convex sets. The finite impulse response Wiener filter is taken as a benchmark in this comparison. In image restoration, the LSI techniques are found to have some important drawbacks, such as producing ringing artifacts. As expected, the space-variant restoration methods which are adaptive to local image properties provide the best results.>

A theoretical bound on the improvement possible due to knowledge of signal points, for the case of a Gaussian signal in Gaussian noise, has been calculated. Wiener and projections-onto-convex-sets restorations have been computed both with and without knowledge of the known points. The estimation errors are compared for different noise levels and blurs, and different numbers of known points.>

Adaptive LMS (least mean squares) filter are applied to cancel harmonic noise. Simulations were done using actual noise recorded at a distribution power substation. Two implementation methods are discussed. Using the characteristic properties of the noise, a constrained filter is proposed which greatly reduces computation without reducing its effectiveness. It is shown that both constrained and unconstrained adaptive noise cancellation filters can be used effectively. For either case, significant improvement in the error rate is obtained.>

This paper presents a technique for restoring images which have been degraded by a stochastic point spread function (psf). In the past, the restoration of such images has been approached in terms of averages without considering the variations of the psf. It will be shown that the integration of the additional uncertainties caused by the stochastic psf can be used to obtain better estimates. These uncertainties can be included to the restoration scheme in a very flexible manner through the use of the Projection Onto Convex Sets (POCS) method. Finally, the benefits of the method will be illustrated through simulations.

The minimum mean square error estimate for the deconvolution problem of a Gaussian signal in Gaussian noise is shown to be feasible in the sense of being inside closed convex sets defined by the noise statistics. It is pointed out that there is some a priori knowledge which is not satisfied by the Wiener solution but the set formed by this information is not convex.

Iterative tomographic reconstruction methods have been developed which can enforce various constraints on the reconstructed image An important step in these methods is the reprojection of the reconstructed image. A common disadvantage of these methods is they fail to converge due to the accumulation of the reprojection errors. In this paper the errors generated by such reprojection schemes are investigated and bounds for these errors are derived. The approach in deriving the error bounds is probabilistic and the resulting bounds are much smaller than the previously derived maximum bounds.

Tomographic image reconstruction using limited projection data requires incorporation of all available a priori information in the reconstruction process. This necessitates the use of transformations between projection and image spaces. The consistency of these transformations is important in elevating the confidence in the solution. It is also observed that better reconstructions can be obtained through consistent transformations.

The equivalence of three fast fixed order reeursive least squares (RLS] algorithms is shown. The FAEST and FTF algorithms are derived by eliminating redundancies in the fast Kalman algorithm. Exact equivalence is obtained by careful selection of the initial conditions. This equivalence suggests a new rescue variable which can perform no worse than previous ones and can test other symptoms of divergence as well.

The fuzzy set deconvolution technique provides increased flexibility in incorporating a priori information. This method makes it possible to model partially defined information as well as exact knowledge and it has generated successful results when the conventional techniques have failed.

The problem of obtaining the optimal initial conditions and pulse values is discussed. If the pulse positions are available then these optimal values can be obtained by minimizing the mean square error between the original signal and the reconstructed signal at the receiver. The result is obtained by solving a large but simple system of linear equations. The optimal values improve the signal-to-noise ratio 3-5 dB when compared with a multipulse algorithm which operates on data at the transmitter.

One of the sources of degradation in LPC-synthesized speech is the mechanical quality due to a single impulse excitation per pitch period. This paper presents a simple method for extracting the amplitudes and locations of a multiple impulse excitation model. These multipulse parameters are obtained very easily from the autoregressive (LPC) residual. Additionally, a method is developed which allows a more accurate recomputation of the autoregressive coefficients based upon incorporating the multipulse excitation.

The method of projection onto convex sets is extended to the problem of deconvolution in the presence of noise. A collection of convex sets is defined by using properties of the noise and of the ideal signal. The ideal signal is then a member of the intersection of these convex sets. A solution to the deconvolution problem is to choose a member of this intersection. Such a member is obtained by successive projections onto convex sets. If the intersection is small, then any member of the intersection should be a good estimate. One and two dimensional results have shown that this method is effective in producing estimates that are superior to conventional methods when sufficient a priori knowledge is available to define the convex sets.

A relationship is shown between the usual formulation of constrained iterative restoration and restoration by successive projections onto convex sets. When used with a reasonable convergence criterion, this relationship characterizes the restoration as the point closest to the initial estimate which satisfies the convergence criterion. Experimental work is presented to demonstrate the effects of the choice of the initial estimate.

Many iterative signal restoration methods have been shown to converge in a mathematical sense but lack a practical criterion for halting the iterative process. The residual signal can be used to define such a criterion. The results of applying this criterion show a definite advantage over the simple method of examining successive iterations.

Sparse delta function series occur as data in many chemical analysis and seismic methods. This original data is often sufficiently degraded by the recording instrument response that the individual delta function peaks are difficult to distinguish and measure. A method, which has been used to measure these peaks, is to fit a parameterized model by a nonlinear least squares fitting algorithm. The deconvolution approaches described here have the advantage of not requiring a parameterized point spread function, nor do they expect a fixed number of peaks. Two new methods will be presented. The maximum power technique will be reviewed. A maximum a posteriori technique will be introduced. Results on both simulated and real data by the two methods will be presented. The characteristics of the data can determine which method gives superior results.

An improved numerical solution method for maximum a posteriori image restoration is presented. Results of the use of this method are shown to be superior to previous MAP restorations and equal or better than some common linear restorations. A natural convergence criterion is defined and shown to be a good indicator of restoration quality. The effects of the parameters of the MAP restorations are discussed.

The mathematical description of the algorithm presented in a previous paper and a more efficient software implementation is given.

Previous work on sectional methods in image processing is extended to the processing of degradations produced by space variant point spread functions.

Evidence is reviewed suggesting that a Laplacian probability density function constitutes a more valid model for high-pass filtered imagery than the Gaussian model postulated in earlier work. In addition, it is shown that this discrepancy does not either seriously weaken the applicability of this class of images to a major image restoration method or challenge any other basic conclusions of the previous work.

Signal deconvolution is a problem commonly found in digital signal processing. If the recorded data is a nonlinear transformation of the degraded data, then linear techniques for deconvolution are not applicable. Herein we review the nonlinear Bayesian estimate for deconvolution and show that it may be implemented in a sectioned form for processing on-going data streams.