analysis of a nonsmooth optimization approach to robust estimation in this paper we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitrarily large errors this is a fundamental problem in many estimation related applications such as fault detection state estimation in lossy networks hybrid system identification robust estimation etc the problem is hard because it exhibits some intrinsic combinatorial features therefore obtaining an effective solution necessitates relaxations that are both solvable at a reasonable cost and effective in the sense that they can return the true parameter vector the current paper discusses a nonsmooth convex optimization approach and provides a new analysis of its behavior in particular it is shown that under appropriate conditions on the data an exact estimate can be recovered from data corrupted by a large even infinite number of gross errors

high breakdown point and high efficiency robust estimates for regression a class of robust estimates for the linear model is introduced these estimates called mm estimates have simultaneously the following properties i they are highly efficient when the errors have a normal distribution and ii their breakdown point is 0 5 the mm estimates are defined by a three stage procedure in the first stage an initial regression estimate is computed which is consistent robust and with high breakdown point but not necessarily efficient in the second stage an m estimate of the errors scale is computed using residuals based on the initial estimate finally in the third stage an m estimate of the regression parameters based on a proper redescending psi function is computed consistency and asymptotical normality of the mm estimates assuming random carriers are proved a convergent iterative numerical algorithm is given finally the asymptotic biases under contamination of optimal bounded influence estimates and mm estimates are compared

segmentation of range images as the search for geometric parametric models segmentation of range images has long been considered in computer vision as an important but extremely difficult problem in this paper we present a new paradigm for the segmentation of range images into piecewise continuous surfaces data aggregation is performed via model recovery in terms of variable order bi variate polynomials using iterative regression model recovery is initiated independently in regularly placed seed regions in the image all the recovered models are potential candidates for the final description of the data selection of the models is defined as a quadratic boolean problem and the solution is sought by the wta winner takes all technique which turns out to be a good compromise between the speed of computation and the accuracy of the solution the overall efficiency of the method is achieved by combining model recovery and model selection in an iterative way partial recovery of the models is followed by the selection optimization procedure and only the best models are allowed to develop further

on the unification of line processes outlier rejection and robust statistics with applications in early vision the modeling of spatial discontinuities for problems such as surface recovery segmentation image reconstruction and optical flow has been intensely studied in computer vision while line process models of discontinuities have received a great deal of attention there has been recent interest in the use of robust statistical techniques to account for discontinuities this paper unifies the two approaches to achieve this we generalize the notion of a line process to that of an analog outlier process and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics we also characterize a class of robust statistical problems for which an equivalent outlier process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier process formulation we show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier process formulation these results indicate that the outlier process approach provides a general framework which subsumes the traditional line process approaches as well as a wide class of robust estimation problems examples in surface reconstruction image segmentation and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited an appendix provides a catalog of common robust error norms and their equivalent outlier process formulations

dithered a d conversion of smooth non bandlimited signals the classical method for sampling a smooth non bandlimited signal requires a lowpass anti aliasing filter in applications like distributed sampling where sampling and quantization operations precede filtering aliasing error is inevitable motivated by such applications the sampling of smooth and bounded non bandlimited signals whose spectra have a finite absolute first moment without the use of an analog anti alias lowpass filter is studied in a centralized setup upper bounds for the distortion rate function are derived by first upper bounding the distortion with a linear combination of errors due to aliasing and quantization and then balancing their contributions by selecting an appropriate reconstruction bandwidth for a class of dithered sampling methods it is shown that a lower quantizer precision can be traded for a higher sampling rate without affecting the realizable high rate asymptotic distortion rate characteristics these results are applied to signals with exponentially and polynomially decaying spectral characteristics and truncated bandlimited signals to uncover the realizable distortion rate characteristics for these signal classes

distributed source coding using syndromes discus design and construction we address the problem of compressing correlated distributed sources i e correlated sources which are not co located or which cannot cooperate to directly exploit their correlation we consider the related problem of compressing a source which is correlated with another source that is available only at the decoder this problem has been studied in the information theory literature under the name of the slepian wolf 1973 source coding problem for the lossless coding case and as rate distortion with side information for the lossy coding case we provide a constructive practical framework based on algebraic trellis codes dubbed as distributed source coding using syndromes discus that can be applicable in a variety of settings simulation results are presented for source coding of independent and identically distributed i i d gaussian sources with side information available at the decoder in the form of a noisy version of the source to be coded our results reveal the promise of this approach using trellis based quantization and coset construction the performance of the proposed approach is 2 5 db from the wyner ziv 1976 bound

segmentation through variable order surface fitting the solution of the segmentation problem requires a mechanism for partitioning the image array into low level entities based on a model of the underlying image structure a piecewise smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete noiseless image reconstruction based on the extracted functions and regions surface curvature sign labeling provides an initial coarse image segmentation which is refined by an iterative region growing method based on variable order surface fitting experimental results show the algorithm s performance on six range images and three intensity images

analysis of sparse regularization based robust regression approaches regression in the presence of outliers is an inherently combinatorial problem however compressive sensing theory suggests that certain combinatorial optimization problems can be exactly solved using polynomial time algorithms motivated by this connection several research groups have proposed polynomial time algorithms for robust regression in this paper we specifically address the traditional robust regression problem where the number of observations is more than the number of unknown regression parameters and the structure of the regressor matrix is defined by the training dataset and hence it may not satisfy properties such as restricted isometry property or incoherence we derive the precise conditions under which the sparse regularization l0 and l1 norm approaches solve the robust regression problem we show that the smallest principal angle between the regressor subspace and all k dimensional outlier subspaces is the fundamental quantity that determines the performance of these algorithms in terms of this angle we provide an estimate of the number of outliers the sparse regularization based approaches can handle we then empirically evaluate the sparse l1 norm regularization approach against other traditional robust regression algorithms to identify accurate and efficient algorithms for high dimensional regression problems

a boosting approach to exploit instance correlations for multi instance classification we propose a boosting approach for multi instance mi classification l p norm is integrated to localize the witness instances and formulate the bag scores from classifier outputs the contributions are twofold first a flexible and concise model for boosting is proposed by the l p norm localization and exponential loss optimization the scores for bag level classification are directly fused from the instance feature space without probabilistic assumptions second gradient and newton descent optimizations are applied to derive the weak learners for boosting in particular the instance correlations are exploited by fitting the weights and newton updates for the weak learner construction the final boosted classifiers are the sums of iteratively chosen weak learners experiments demonstrate that the proposed l p norm localized boosting approach significantly improves the mi classification performance compared with the state of the art the approach achieves the highest mi classification accuracy on 7 10 benchmark data sets

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

soft decision decoding using punctured codes let a q ary linear n k code be used over a memoryless channel we design a soft decision decoding algorithm that tries to locate a few most probable error patterns on a shorter length s spl isin k n first we take s cyclically consecutive positions starting from any initial point then we cut the subinterval of length s into two parts and examine t most plausible error patterns on either part to obtain codewords of a punctured s k code we try to match the syndromes of both parts finally the designed codewords of an s k code are re encoded to find the most probable codeword on the full length n for any long linear code the decoding error probability of this algorithm can be made arbitrarily close to the probability of its maximum likelihood ml decoding given sufficiently large t by optimizing s we prove that this near ml decoding can be achieved by using only t spl ap q sup n k k n k error patterns for most long linear codes this optimization also gives about t re encoded codewords as a result we obtain the lowest complexity order of q sup n k k n k known to date for near ml decoding for codes of rate 1 2 the new bound grows as a cubic root of the general trellis complexity q sup min n k k for short blocks of length 63 the algorithm reduces the complexity of the trellis design by a few decimal orders

robust detection of straight and circular road segments in noisy aerial images this paper treats the problem of detecting straight or circular pieces of road in noisy low resolution aerial images it first uses a local operator to detect pixels whose neighborhoods are line like and then applies robust estimation techniques to find sets of such pixels that lie on or near straight or circular loci an unbiased ordinary least squares estimator cannot handle outlying data even for straight loci on the other hand conventional robust techniques for fitting circular arcs are severely affected by digitization effects and the fact that circular road segments are typically short and shallow we therefore introduce an estimator that is both robust and statistically efficient we also present a simple ad hoc technique that achieves comparable results and can handle road segments that are either straight or circular

on a class of optimization based robust estimators in this paper we consider the problem of estimating a parameter matrix from observations which are affected by two types of noise components i a sparse noise sequence which whenever nonzero can have arbitrarily large amplitude ii and a dense and bounded noise sequence of moderate amount this is termed a robust regression problem to tackle it a quite general optimization based framework is proposed and analyzed when only the sparse noise is present a sufficient bound is derived on the number of nonzero elements in the sparse noise sequence that can be accommodated by the estimator while still returning the true parameter matrix while almost all the restricted isometry based bounds from the literature are not verifiable our bound can be easily computed through solving a convex optimization problem moreover empirical evidence tends to suggest that it is generally tight if in addition to the sparse noise sequence the training data are affected by a bounded dense noise we derive an upper bound on the estimation error

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

on three dimensional surface reconstruction methods a survey is presented of some of the surface reconstruction methods that can be found in the literature the focus is on a small recent and important subset of the published reconstruction techniques the techniques are classified based on the surface representation used implicit versus explicit functions a study is made of the important aspects of the surface reconstruction techniques one aspect is the viewpoint invariance of the methods this is an important property if object recognition is the ultimate objective the robustness of the various methods is examined it is determined whether the parameter estimates are biased and the sensitivity to obscuration is addressed the latter two aspects are particularly important for fitting functions in the implicit form a detailed description is given of a parametric reconstruction method for three dimensional object surfaces that involves numeric grid generation techniques and variational principle formulations this technique is invariant to rigid motion in dimensional space

robust parameter estimation in computer vision estimation techniques in computer vision applications must estimate accurate model parameters despite small scale noise in the data occasional large scale measurement errors outliers and measurements from multiple populations in the same data set increasingly robust estimation techniques some borrowed from the statistics literature and others described in the computer vision literature have been used in solving these parameter estimation problems ideally these techniques should effectively ignore the outliers and measurements from other populations treating them as outliers when estimating the parameters of a single population two frequently used techniques are least median of squares lms p j rousseeuw j amer statist assoc 79 1984 pp 871 880 and m estimators robust statistics the approach based on influence functions f r hampel et al john wiley 1986 robust statistics p j huber john wiley 1981 lms handles large fractions of outliers up to the theoretical limit of 50 for estimators invariant to affine changes to the data but has low statistical efficiency m estimators have higher statistical efficiency but tolerate much lower percentages of outliers unless properly initialized while robust estimators have been used in a variety of computer vision applications three are considered here in analysis of range images images containing depth or x y z measurements at each pixel instead of intensity measurements robust estimators have been used successfully to estimate surface model parameters in small image regions in stereo and motion analysis they have been used to estimate parameters of what is called the fundamental matrix which characterizes the relative imaging geometry of two cameras imaging the same scene recently robust estimators have been applied to estimating a quadratic image to image transformation model necessary to create a composite mosaic image from a series of images of the human retina in each case a straightforward application of standard robust estimators is insufficient and carefully developed extensions are used to solve the problem

matching 3 d models to 2 d images we consider the problem of analytically characterizing the set of all 2 d images that a group of 3 d features may produce and demonstrate that this is a useful thing to do our results apply for simple point features and point features with associated orientation vectors when we model projection as a 3 d to 2 d affine transformation we show how to represent the set of images that a group of 3 d points produces with two lines 1 d subspaces one in each of two orthogonal high dimensional spaces where a single image group corresponds to one point in each space the images of groups of oriented point features can be represented by a 2 d hyperbolic surface in a single high dimensional space the problem of matching an image to models is essentially reduced to the problem of matching a point to simple geometric structures moreover we show that these are the simplest and lowest dimensional representations possible for these cases we demonstrate the value of this way of approaching matching by applying our results to a variety of vision problems in particular we use this result to build a space efficient indexing system that performs 3 d to 2 d matching by table lookup this system is analytically built and accessed accounts for the effects of sensing error and is tested on real images we also derive new results concerning the existence of invariants and non accidental properties in this domain finally we show that oriented points present unexpected difficulties indexing requires fundamentally more space with oriented than with simple points we must use more images in a motion sequence to determine the affine structure of oriented points and the linear combinations result does not hold for oriented points

consistent estimation of continuous time signals from nonlinear transformations of noisy samples a signal cannot in general be reconstructed from its sign i e from its hard limited version however by the deliberate addition of noise to samples of the signal prior to hard limiting it is shown that the signal can be estimated consistently from its hard limited noisy samples as the sampling rate tends to infinity in fact such estimates are shown to converge with probability one to the signal and to be asymptotically normal although the estimates are in general nonlinear they can be made linear by a proper choice of the noise distribution these rather unexpected results hold for all bounded and uniformly continuous signals in addition to the hard limiter such results are also established for certain monotonic and nonmonotonic nonlinearities

on simple oversampled a d conversion in l sup 2 r the accuracy of oversampled analog to digital a d conversion the dependence of accuracy on the sampling interval spl tau and on the bit rate r are characteristics fundamental to a d conversion but not completely understood these characteristics are studied for oversampled a d conversion of band limited signals in l sup 2 r we show that the digital sequence obtained in the process of oversampled a d conversion describes the corresponding analog signal with an error which tends to zero as spl tau sup 2 in energy provided that the quantization threshold crossings of the signal constitute a sequence of stable sampling in the respective space of band limited functions further we show that the sequence of quantized samples can be represented in a manner which requires only a logarithmic increase in the bit rate with the sampling frequency r o log spl tau and hence that the error of oversampled a d conversion actually exhibits an exponential decay in the bit rate as the sampling interval tends to zero

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

bias in robust estimation caused by discontinuities and multiple structures when fitting models to data containing multiple structures such as when fitting surface patches to data taken from a neighborhood that includes a range discontinuity robust estimators must tolerate both gross outliers and pseudo outliers pseudo outliers are outliers to the structure of interest but inliers to a different structure they differ from gross outliers because of their coherence such data occurs frequently in computer vision problems including motion estimation model fitting and range data analysis the focus in this paper is the problem of fitting surfaces near discontinuities in range data to characterize the performance of least median of the squares least trimmed squares m estimators hough transforms ransac and minpran on this type of data the pseudo outlier bias metric is developed using techniques from the robust statistics literature and it is used to study the error in robust fits caused by distributions modeling various types of discontinuities the results show each robust estimator to be biased at small but substantial discontinuities they also show the circumstances under which different estimators are most effective most importantly the results imply present estimators should be used with care and new estimators should be developed

single bit oversampled a d conversion with exponential accuracy in the bit rate a scheme for simple oversampled analog to digital a d conversion using single bit quantization is presented the scheme is based on recording positions of zero crossings of the input signal added to a deterministic dither function this information can be represented in a manner such that the bit rate increases only logarithmically with the oversampling factor r the input band limited signal can be reconstructed from this information locally with o 1 r pointwise error resulting in an exponentially decaying distortion rate characteristic in the course of studying the accuracy of the proposed a d conversion scheme some new results are established about reconstruction of band limited signals from irregular samples using linear combination of functions with fast decay schemes for local interpolation of band limited signals from quantized irregular samples are also proposed

oversampled sigma delta modulation oversampled sigma delta modulation has been proposed as a practical implementation for high rate analog to digital conversion because of its simplicity and its robustness against circuit imperfections to date mathematical developments of the basic properties of such systems have been based either on simplified continuous time approximate models or on linearized discrete time models where the quantizer is replaced by an additive white uniform noise source in this paper we rigorously derive several basic properties of a simple discrete time single integrator loop sigma delta modulator with an accumulate and dump demodulator the derivation does not require any assumptions on the correlation or distribution of the quantizer error and hence involves no linearization of the nonlinear system but it does show that when the input is constant the state sequence of the integrator in the encoder loop can be modeled exactly as a linear system in an appropriate space two basic properties are developed 1 the behavior of the sigma delta quantizer when driven by a constant input and its relation to uniform quantization and 2 the rate distortion tradeoffs between the oversampling ratio and the average mean squared quantization error

deterministic analysis of oversampled a d conversion and decoding improvement based on consistent estimates discusses the deterministic analysis of oversampled a d conversion adc the properties derivable from such an analysis and the consequences on reconstruction using nonlinear decoding given a band limited input x producing a quantized version c the authors consider the set of all input signals that are band limited and produce c they call any element of this set a consistent estimate of x regardless of the type of encoder simple predictive or noise shaping they show that this set is convex and as a consequence any nonconsistent estimate can be improved they also show that the classical linear decoding estimates are not necessarily consistent numerical tests performed on simple adc single loop and multiloop spl sigma spl delta modulation show that consistent estimates yield a mean square error mse that decreases asymptotically with the oversampling ratio faster than the linear decoding mse by approximately 3 db octave this implies an asymptotic mse of the order of spl oscr r sup spl minus 2n 2 instead of spl oscr r sup spl minus 2n 1 in linear decoding where r is the oversampling ratio and n the order of the modulator methods of improvement of nonconsistent estimates based on the deterministic knowledge of the quantized signal are proposed for simple adc predictive adc single loop and multiloop spl sigma spl delta modulation

fundamental distortion limits of analog to digital compression representing a continuous time signal by a set of samples is a classical problem in signal processing we study this problem under the additional constraint that the samples are quantized or compressed in a lossy manner under a limited bitrate budget to this end we consider a combined sampling and source coding problem in which an analog stationary gaussian signal is reconstructed from its encoded samples these samples are obtained by a set of bounded linear functionals of the continuous time path with a limitation on the average number of samples per unit time given in this setting we provide a full characterization of the minimal distortion in terms of the sampling frequency the bitrate and the signal s spectrum assuming that the signal s energy is not uniformly distributed over its spectral support we show that for each compression bitrate there exists a critical sampling frequency smaller than the nyquist rate such that the distortion in signal reconstruction when sampling at this frequency is minimal our results can be seen as an extension of the classical sampling theorem for bandlimited random processes in the sense that they describe the minimal amount of excess distortion in the reconstruction due to lossy compression of the samples and provide the minimal sampling frequency required in order to achieve this distortion finally we compare the fundamental limits in the combined source coding and sampling problem to the performance of pulse code modulation where each sample is quantized by a scalar quantizer using a fixed number of bits

additive logistic regression a statistical view of boosting boosting is one of the most important recent developments in classification methodology boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced for many classification algorithms this simple strategy results in dramatic improvements in performance we show that this seemingly mysterious phenomenon can be understood in terms of well known statistical principles namely additive modeling and maximum likelihood for the two class problem boosting can be viewed as an approximation to additive modeling on the logistic scale using maximum bernoulli likelihood as a criterion we develop more direct approximations and show that they exhibit nearly identical results to boosting direct multiclass generalizations based on multinomial likelihood are derived that exhibit performance comparable to other recently proposed multiclass generalizations of boosting in most situations and far superior in some we suggest a minor modification to boosting that can reduce computation often by factors of 10 to 50 finally we apply these insights to produce an alternative formulation of boosting decision trees this approach based on best first truncated tree induction often leads to better performance and can provide interpretable descriptions of the aggregate decision rule it is also much faster computationally making it more suitable to large scale data mining applications

learning sparse kernel classifiers for multi instance classification we propose a direct approach to learning sparse kernel classifiers for multi instance mi classification to improve efficiency while maintaining predictive accuracy the proposed method builds on a convex formulation for mi classification by considering the average score of individual instances for bag level prediction in contrast existing formulations used the maximum score of individual instances in each bag which leads to nonconvex optimization problems based on the convex mi framework we formulate a sparse kernel learning algorithm by imposing additional constraints on the objective function to enforce the maximum number of expansions allowed in the prediction function the formulated sparse learning problem for the mi classification is convex with respect to the classifier weights therefore we can employ an effective optimization strategy to solve the optimization problem that involves the joint learning of both the classifier and the expansion vectors in addition the proposed formulation can explicitly control the complexity of the prediction model while still maintaining competitive predictive performance experimental results on benchmark data sets demonstrate that our proposed approach is effective in building very sparse kernel classifiers while achieving comparable performance to the state of the art mi classifiers

solving the multiple instance problem with axis parallel rectangles the multiple instance problem arises in tasks where the training examples are ambiguous a single example object may have many alternative feature vectors instances that describe it and yet only one of those feature vectors may be responsible for the observed classification of the object this paper describes and compares three kinds of algorithms that learn axis parallel rectangles to solve the multiple instance problem algorithms that ignore the multiple instance problem perform very poorly an algorithm that directly confronts the multiple instance problem by attempting to identify which feature vectors are responsible for the observed classifications performs best giving 89 correct predictions on a musk odor prediction task the paper also illustrates the use of artificial data to debug and compare these algorithms

the development and comparison of robust methodsfor estimating the fundamental matrix this paper has two goals the first is to develop a variety of robust methods for the computation of the fundamental matrix the calibration free representation of camera motion the methods are drawn from the principal categories of robust estimators viz case deletion diagnostics m estimators and random sampling and the paper develops the theory required to apply them to non linear orthogonal regression problems although a considerable amount of interest has focussed on the application of robust estimation in computer vision the relative merits of the many individual methods are unknown leaving the potential practitioner to guess at their value the second goal is therefore to compare and judge the methods comparative tests are carried out using correspondences generated both synthetically in a statistically controlled fashion and from feature matching in real imagery in contrast with previously reported methods the goodness of fit to the synthetic observations is judged not in terms of the fit to the observations per se but in terms of fit to the ground truth a variety of error measures are examined the experiments allow a statistically satisfying and quasi optimal method to be synthesized which is shown to be stable with up to 50 percent outlier contamination and may still be used if there are more than 50 percent outliers performance bounds are established for the method and a variety of robust methods to estimate the standard deviation of the error and covariance matrix of the parameters are examined the results of the comparison have broad applicability to vision algorithms where the input data are corrupted not only by noise but also by gross outliers

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

the reconstruction of analog signals from the sign of their noisy samples the reconstruction of a continuous time signal s t from the sign of its deliberately contaminated samples is considered sequential generally nonlinear estimates of s t are established and their performance is studied error bounds and convergence rates are derived the signal s t need not be band limited the convergence rates obtained here are faster than those obtained previously for nonsequential estimates the degradation in the reconstruction of the signal due to transmission over a noisy channel is also investigated and bounds on the additional error are obtained

a d conversion with imperfect quantizers this paper analyzes mathematically the effect of quantizer threshold imperfection commonly encountered in the circuit implementation of analog to digital a d converters such as pulse code modulation pcm and sigma delta sigmadelta modulation sigmadelta modulation which is based on coarse quantization of oversampled redundant samples of a signal enjoys a type of self correction property for quantizer threshold errors bias that is not shared by pcm although classical sigmadelta modulation is inferior to pcm in the rate distortion sense this robustness feature is believed to be one of the reasons why sigmadelta modulation is preferred over pcm in a d converters with imperfect quantizers motivated by these facts other encoders are constructed in this paper that use redundancy to obtain a similar self correction property but that achieve higher order accuracy relative to bit rate compared to classical sigmadelta more precisely two different types of encoders are introduced that exhibit exponential accuracy in the bit rate in contrast to the polynomial type accuracy of classical sigmadelta while possessing the self correction property

information rates of densely sampled data distributed vector quantization and scalar quantization with transforms for gaussian sources this paper establishes rates attainable by several lossy schemes for coding a continuous parameter source to a specified mean squared error distortion based on sampling at asymptotically large rates first a densely sampled spatiotemporal stationary gaussian source is distributively encoded the berger tung bound to the distributed rate distortion function and three convergence theorems are used to obtain an upper bound expressed in terms of the source spectral density to the smallest attainable rate at asymptotically large sampling rates the bound is tighter than that recently obtained by kashyap both indicate that with ideal distributed lossy coding dense sensor networks can efficiently sense and convey a field in contrast to the negative result obtained by marco for encoders based on scalar quantization and slepian wolf distributed lossless coding the second scheme is transform coding with scalar coefficient quantization a new generalized transform coding analysis as well as the aforementioned convergence theorems is used to find the smallest attainable rate at asymptotically large sampling rates in terms of the source spectral density and the operational rate distortion function of the family of quantizers which in contrast to previous analyses need not be convex the result shows that when a transform is used scalar quantization need not cause the poor performance found by marco as a corollary the final result pursues an approach originally proposed by berger to show that the inverse water pouring formula for the rate distortion function can be attained at high sampling rates by transform coding with ideal vector quantization to encode the coefficients also established in the paper are relations between operational rate distortion and distortion rate functions for a continuous parameter source and those for the discrete parameter source that results from sampling

high resolution distributed sampling of bandlimited fields with low precision sensors the problem of sampling a discrete time sequence of spatially bandlimited fields with a bounded dynamic range in a distributed communication constrained processing environment is studied a central unit having access to the data gathered by a dense network of low precision sensors is required to reconstruct the field snapshots to maximum accuracy both deterministic and stochastic field models are considered for stochastic fields results are established in the almost sure sense the feasibility of having a flexible tradeoff between the oversampling rate sensor density and the analog to digital converter adc precision while achieving an exponential accuracy in the number of bits per nyquist interval per snapshot is demonstrated this exposes an underlying conservation of bits principle the bit budget per nyquist interval per snapshot the rate can be distributed along the amplitude axis sensor precision and space sensor density in an almost arbitrary discrete valued manner while retaining the same exponential distortion rate characteristics

sampling and reconstruction of spatial fields using mobile sensors spatial sampling is traditionally studied in a static setting where static sensors scattered around space take measurements of the spatial field at their locations in this paper we study the emerging paradigm of sampling and reconstructing spatial fields using sensors that move through space we show that mobile sensing offers some unique advantages over static sensing in sensing bandlimited spatial fields since a moving sensor encounters such a spatial field along its path as a time domain signal a time domain anti aliasing filter can be employed prior to sampling the signal received at the sensor such a filtering procedure when used by a configuration of sensors moving at constant speeds along equispaced parallel lines leads to a complete suppression of spatial aliasing in the direction of motion of the sensors we analytically quantify the advantage of using such a sampling scheme over a static sampling scheme by computing the reduction in sampling noise due to the filter we also analyze the effects of nonuniform sensor speeds on the reconstruction accuracy using simulation examples we demonstrate the advantages of mobile sampling over static sampling in practical problems we extend our analysis to sampling and reconstruction schemes for monitoring time varying bandlimited fields using mobile sensors we demonstrate that in some situations we require a lower density of sensors when using a mobile sensing scheme instead of the conventional static sensing scheme the exact advantage is quantified for a problem of sampling and reconstructing an audio field

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

computing least median of squares regression lines and guided topological sweep abstract given a set of data points pi xi yi for 1 i n the least median of squares regression line is a line y ax b for which the median of the squared residuals is a minimum over all choices of a and b an algorithm is described that computes such a line in o n 2 time and o n memory space thus improving previous upper bounds on the problem this algorithm is an application of a general method built on top of the topological sweep of line arrangements

reduction of the mse in r times oversampled a d conversion o 1 r to o 1 r sup 2 in oversampled analog to digital conversion the usual reconstruction method using lowpass filtering leads to a mean squared error mse inversely proportional to the oversampling ratio r the authors prove under certain assumptions and with periodic analog input signals that optimal reconstruction achieves an mse with an oversampling ratio dependence order of at least o 1 r sup 2 that is an mse slope of spl minus 6 db per octave of oversampling is obtained rather than the conventional spl minus 3 db octave slope of classical schemes