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The Fourier-Series Method For Inverting Transforms Of Probability Distributions
, 1991
"... This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourier-series method are remar ..."
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Cited by 211 (52 self)
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This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourier-series method are remarkably easy to use, requiring programs of less than fifty lines. The Fourier-series method can be interpreted as numerically integrating a standard inversion integral by means of the trapezoidal rule. The same formula is obtained by using the Fourier series of an associated periodic function constructed by aliasing; this explains the name of the method. This Fourier analysis applies to the inversion problem because the Fourier coefficients are just values of the transform. The mathematical centerpiece of the Fourier-series method is the Poisson summation formula, which identifies the discretization error associated with the trapezoidal rule and thus helps bound it. The greatest difficulty is approximately calculating the infinite series obtained from the inversion integral. Within this framework, lattice cdf's can be calculated from generating functions by finite sums without truncation. For other cdf's, an appropriate truncation of the infinite series can be determined from the transform based on estimates or bounds. For Laplace transforms, the numerical integration can be made to produce a nearly alternating series, so that the convergence can be accelerated by techniques such as Euler summation. Alternatively, the cdf can be perturbed slightly by convolution smoothing or windowing to produce a truncation error bound independent of the original cdf. Although error bounds can be determined, an effective approach is to use two different methods without elaborate error analysis. For this...
Interpolation revisited
- IEEE Transactions on Medical Imaging
, 2000
"... Abstract—Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are not interpolating. By opposition to ..."
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Cited by 198 (33 self)
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Abstract—Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are not interpolating. By opposition to traditional interpolation, we call their use generalized interpolation; they involve a prefiltering step when correctly applied. We explain why the approximation order inherent in any basis function is important to limit interpolation artifacts. The decomposition theorem states that any basis function endowed with approximation order can be expressed as the convolution of a B-spline of the same order with another function that has none. This motivates the use of splines and spline-based functions as a tunable way to keep artifacts in check without any significant cost penalty. We discuss implementation and performance issues, and we provide experimental evidence to support our claims. Index Terms—Approximation constant, approximation order, B-splines, Fourier error kernel, maximal order and minimal support (Moms), piecewise-polynomials. I.
Survey: Interpolation Methods in Medical Image Processing
- IEEE Transactions on Medical Imaging
, 1999
"... Abstract — Image interpolation techniques often are required in medical imaging for image generation (e.g., discrete back projection for inverse Radon transform) and processing such as compression or resampling. Since the ideal interpolation function spatially is unlimited, several interpolation ker ..."
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Cited by 161 (2 self)
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Abstract — Image interpolation techniques often are required in medical imaging for image generation (e.g., discrete back projection for inverse Radon transform) and processing such as compression or resampling. Since the ideal interpolation function spatially is unlimited, several interpolation kernels of finite size have been introduced. This paper compares 1) truncated and windowed sinc; 2) nearest neighbor; 3) linear; 4) quadratic; 5) cubic B-spline; 6) cubic; g) Lagrange; and 7) Gaussian interpolation and approximation techniques with kernel sizes from 1 2 1upto 8 2 8. The comparison is done by: 1) spatial and Fourier analyses; 2) computational complexity as well as runtime evaluations; and 3) qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing. For local and Fourier analyses, a standardized notation is introduced
An overview of text-independent speaker recognition: from features to supervectors
, 2009
"... This paper gives an overview of automatic speaker recognition technology, with an emphasis on text-independent recognition. Speaker recognition has been studied actively for several decades. We give an overview of both the classical and the state-of-the-art methods. We start with the fundamentals of ..."
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Cited by 156 (37 self)
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This paper gives an overview of automatic speaker recognition technology, with an emphasis on text-independent recognition. Speaker recognition has been studied actively for several decades. We give an overview of both the classical and the state-of-the-art methods. We start with the fundamentals of automatic speaker recognition, concerning feature extraction and speaker modeling. We elaborate advanced computational techniques to address robustness and session variability. The recent progress from vectors towards supervectors opens up a new area of exploration and represents a technology trend. We also provide an overview of this recent development and discuss the evaluation methodology of speaker recognition systems. We conclude the paper with discussion on future directions.
SoundSense: Scalable Sound Sensing for People-Centric Applications on Mobile Phones
"... Top end mobile phones include a number of specialized (e.g., accelerometer, compass, GPS) and general purpose sensors (e.g., microphone, camera) that enable new people-centric sensing applications. Perhaps the most ubiquitous and unexploited sensor on mobile phones is the microphone – a powerful sen ..."
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Cited by 139 (10 self)
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Top end mobile phones include a number of specialized (e.g., accelerometer, compass, GPS) and general purpose sensors (e.g., microphone, camera) that enable new people-centric sensing applications. Perhaps the most ubiquitous and unexploited sensor on mobile phones is the microphone – a powerful sensor that is capable of making sophisticated inferences about human activity, location, and social events from sound. In this paper, we exploit this untapped sensor not in the context of human communications but as an enabler of new sensing applications. We propose SoundSense, a scalable framework for modeling sound events on mobile phones. SoundSense is implemented on the Apple iPhone and represents the first general purpose sound sensing system specifically designed to work on resource limited phones. The architecture and algorithms are designed for scalability and SoundSense uses a combination of supervised and unsupervised learning techniques to classify both general sound types (e.g., music, voice) and discover novel sound events specific to individual users. The system runs solely on the mobile phone with no back-end interactions. Through implementation and evaluation of two proof of concept peoplecentric sensing applications, we demostrate that SoundSense is capable of recognizing meaningful sound events that occur in users ’ everyday lives. Categories and Subject Descriptors
A chronology of interpolation: From ancient astronomy to modern signal and image processing
- Proceedings of the IEEE
, 2002
"... This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently used in signal and image processing into histo ..."
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Cited by 105 (0 self)
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This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently used in signal and image processing into historical perspective. A summary of the insights and recommendations that follow from relatively recent theoretical as well as experimental studies concludes the presentation. Keywords—Approximation, convolution-based interpolation, history, image processing, polynomial interpolation, signal processing, splines. “It is an extremely useful thing to have knowledge of the true origins of memorable discoveries, especially those that have been found not by accident but by dint of meditation. It is not so much that thereby history may attribute to each man his own discoveries and others should be encouraged to earn like commendation, as that the art of making discoveries should be extended by considering noteworthy examples of it. ” 1 I.
Image Interpolation and Resampling
- HANDBOOK OF MEDICAL IMAGING, PROCESSING AND ANALYSIS
, 2000
"... This chapter presents a survey of interpolation and resampling techniques in the context of exact, separable interpolation of regularly sampled data. In this context, the traditional view of interpolation is to represent an arbitrary continuous function as a discrete sum of weighted and shifted syn ..."
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Cited by 81 (11 self)
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This chapter presents a survey of interpolation and resampling techniques in the context of exact, separable interpolation of regularly sampled data. In this context, the traditional view of interpolation is to represent an arbitrary continuous function as a discrete sum of weighted and shifted synthesis functions—in other words, a mixed convolution equation. An important issue is the choice of adequate synthesis functions that satisfy interpolation properties. Examples of finite-support ones are the square pulse (nearest-neighbor interpolation), the hat function (linear interpolation), the cubic Keys' function, and various truncated or windowed versions of the sinc function. On the other hand, splines provide examples of infinite-support interpolation functions that can be realized exactly at a finite, surprisingly small computational cost. We discuss implementation issues and illustrate the performance of each synthesis function. We also highlight several artifacts that may arise when performing interpolation, such as ringing, aliasing, blocking and blurring. We explain why the approximation order inherent in the synthesis function is important to limit these interpolation artifacts, which motivates the use of splines as a tunable way to keep them in check without any significant cost penalty.
MOMS: Maximal-Order Interpolation of Minimal Support
- IEEE Trans. Image Process
, 2001
"... We consider the problem of interpolating a signal using a linear combination of shifted versions of a compactly-supported basis function ( ). We first give the expression of the 's that have minimal support for a given accuracy (also known as "approximation order"). This class of func ..."
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Cited by 74 (27 self)
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We consider the problem of interpolating a signal using a linear combination of shifted versions of a compactly-supported basis function ( ). We first give the expression of the 's that have minimal support for a given accuracy (also known as "approximation order"). This class of functions, which we call maximal -order-minimal-support functions (MOMS) is made of linear combinations of the B-spline of same order and of its derivatives.
Quantitative evaluation of convolution-based methods for medical image interpolation
- Medical Image Analysis
, 2001
"... Abstract—Interpolation is required in a variety of medical image processing applications. Although many interpolation techniques are known from the literature, evaluations of these techniques for the specific task of applying geometrical transformations to medical images are still lacking. In this p ..."
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Cited by 58 (2 self)
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Abstract—Interpolation is required in a variety of medical image processing applications. Although many interpolation techniques are known from the literature, evaluations of these techniques for the specific task of applying geometrical transformations to medical images are still lacking. In this paper we present such an evaluation. We consider convolution-based interpolation methods and rigid transformations (rotations and translations). A large number of sincapproximating kernels are evaluated, including piecewise polynomial kernels and a large number of windowed sinc kernels, with spatial supports ranging from two to ten grid intervals. In the evaluation we use images from a wide variety of medical image modalities. The results show that spline interpolation is to be preferred over all other methods, both for its accuracy and its relatively low computational cost. Keywords—Convolution-based interpolation, spline interpolation, piecewise polynomial kernels, windowed sinc kernels, geometrical transformation, medical images, quantitative evaluation. 1
