Probability, random variables and stochastic processes

doi:10.1109/TASSP.1985.1164715

Journal Article•DOI•

Probability, random variables and stochastic processes

J. Proakis¹•Institutions (1)

01 Dec 1985-IEEE Transactions on Acoustics, Speech, and Signal Processing (IEEE)-Vol. 33, Iss: 6, pp 1637-1637

About: This article is published in IEEE Transactions on Acoustics, Speech, and Signal Processing.The article was published on 1985-12-01. It has received 6899 citations till now. The article focuses on the topics: Entropy (information theory) & Stochastic process.

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A wavelet tour of signal processing

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Stéphane Mallat

01 Jan 1998

TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.

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Abstract: Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

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17,693 citations

Journal Article•DOI•

An information-maximization approach to blind separation and blind deconvolution

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Anthony J. Bell¹, Terrence J. Sejnowski¹•Institutions (1)

University of California, San Diego¹

01 Nov 1995-Neural Computation

TL;DR: It is suggested that information maximization provides a unifying framework for problems in "blind" signal processing and dependencies of information transfer on time delays are derived.

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Abstract: We derive a new self-organizing learning algorithm that maximizes the information transferred in a network of nonlinear units. The algorithm does not assume any knowledge of the input distributions, and is defined here for the zero-noise limit. Under these conditions, information maximization has extra properties not found in the linear case (Linsker 1989). The nonlinearities in the transfer function are able to pick up higher-order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation. This enables the network to separate statistically independent components in the inputs: a higher-order generalization of principal components analysis. We apply the network to the source separation (or cocktail party) problem, successfully separating unknown mixtures of up to 10 speakers. We also show that a variant on the network architecture is able to perform blind deconvolution (cancellation of unknown echoes and reverberation in a speech signal). Finally, we derive dependencies of information transfer on time delays. We suggest that information maximization provides a unifying framework for problems in "blind" signal processing.

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9,157 citations

Cites background or methods from "Probability, random variables and s..."

...15-93): H(y1; y2) = H(y1) +H(y2) I(y1; y2): (35) Maximising this joint entropy consists of maximising the individual entropies while minimising the mutual information, I(y1; y2), shared between the two....
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...The algorithm presented in section 2 is a stochastic gradient ascent algorithmwhich maximises the joint entropy in (35)....
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Proceedings Article•DOI•

Bilateral filtering for gray and color images

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Carlo Tomasi¹, Roberto Manduchi²•Institutions (2)

Stanford University¹, Apple Inc.²

04 Jan 1998

TL;DR: In contrast with filters that operate on the three bands of a color image separately, a bilateral filter can enforce the perceptual metric underlying the CIE-Lab color space, and smooth colors and preserve edges in a way that is tuned to human perception.

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Abstract: Bilateral filtering smooths images while preserving edges, by means of a nonlinear combination of nearby image values. The method is noniterative, local, and simple. It combines gray levels or colors based on both their geometric closeness and their photometric similarity, and prefers near values to distant values in both domain and range. In contrast with filters that operate on the three bands of a color image separately, a bilateral filter can enforce the perceptual metric underlying the CIE-Lab color space, and smooth colors and preserve edges in a way that is tuned to human perception. Also, in contrast with standard filtering, bilateral filtering produces no phantom colors along edges in color images, and reduces phantom colors where they appear in the original image.

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8,738 citations

Cites background from "Probability, random variables and s..."

...Although formal and quantitative explanations of this weight fall-off can be given [11], the intuitionis that images typically vary slowly over space, so near pixels are likely to have similar values, and it is therefore appropriate to average them together....
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Journal Article•DOI•

Independent component analysis: algorithms and applications

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Aapo Hyvärinen¹, Erkki Oja¹•Institutions (1)

Helsinki University of Technology¹

01 May 2000-Neural Networks

TL;DR: The basic theory and applications of ICA are presented, and the goal is to find a linear representation of non-Gaussian data so that the components are statistically independent, or as independent as possible.

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8,231 citations

Cites background or methods from "Probability, random variables and s..."

...The term log |detW| in the likelihood comes from the classic rule for (linearly) transforming random variables and their densities (Papoulis, 1991): In general, for any random vector x with density px and for any matrixW, the density of y=Wx is given by px(Wx)|detW|....
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...A typical example is the uniform distibution in eq....
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...The differential entropy H of a random vector y with density f (y) is defined as (Cover and Thomas, 1991; Papoulis, 1991): H(y) = − ∫ f (y) log f (y)dy....
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...For a proof, see e.g. (Cover and Thomas, 1991; Papoulis, 1991)....
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...To avoid the problems encountered with the preceding approximations of negentropy, new approximations were developed in (Hyvärinen, 1998b)....
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Journal Article•DOI•

Permanent scatterers in SAR interferometry

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Alessandro Ferretti¹, Claudio Prati¹, Fabio Rocca¹•Institutions (1)

Polytechnic University of Milan¹

01 Jan 2001-IEEE Transactions on Geoscience and Remote Sensing

TL;DR: The authors present a complete procedure for the identification and exploitation of stable natural reflectors or permanent scatterers (PSs) starting from long temporal series of interferometric SAR images.

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Abstract: Temporal and geometrical decorrelation often prevents SAR interferometry from being an operational tool for surface deformation monitoring and topographic profile reconstruction. Moreover, atmospheric disturbances can strongly compromise the accuracy of the results. The authors present a complete procedure for the identification and exploitation of stable natural reflectors or permanent scatterers (PSs) starting from long temporal series of interferometric SAR images. When, as it often happens, the dimension of the PS is smaller than the resolution cell, the coherence is good even for interferograms with baselines larger than the decorrelation one, and all the available images of the ESA ERS data set can be successfully exploited. On these pixels, submeter DEM accuracy and millimetric terrain motion detection can be achieved, since atmospheric phase screen (APS) contributions can be estimated and removed. Examples are then shown of small motion measurements, DEM refinement, and APS estimation and removal in the case of a sliding area in Ancona, Italy. ERS data have been used.

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3,963 citations

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Probability, random variables and stochastic processes

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