ll filters a new class of order statistic filters the ll filters are introduced to generate the order statistic filters l filters and the nonrecursive linear or finite duration impulse response fir filters such estimators are particularly effective filtering signals that do not necessarily follow gaussian distributions they can be designed to restore one dimensional or multidimensional signals corrupted by noise of impulsive type such filters are appealing since they are suitable for being made robust against the presence of spurious outliers in the data

decision based order statistic filters the authors propose two adaptive order statistic filters which generate outputs based on the results of hypothesis tests to reduce edge shifting of the median filter a modified median filter mmf is proposed first a hypothesis test is applied to detect the edge location then whenever an edge is detected the mmf generates the output by modifying the median output based on a comparison of median value to the current input value the mmf can retain more fine details than the median filter with the same window size as well as reduce the output mean square error which is caused mainly by edge shifting to suppress nonimpulsive noise as well as impulsive noise an l type structure is combined with the mmf the proposed filter generates the output by using asymmetric alpha trimming on the mmf output in addition to noise suppression it can enhance the gradient of blurred edges provided that the size of the window is greater than the transition width of the blurred edges experimental results for one and two dimensional signals are presented

an adaptive order statistic noise filter for gamma corrected image sequences original video signals are often corrupted by a certain amount of noise originating from the camera electronics as a result of the gamma correction in cameras the observed noise is signal dependent we present a spatio temporal order statistic os noise filter that takes into account the gamma correction in the camera the calculation of the filter coefficients requires higher order order statistics hoos of the noise process we make use of a range test rt to determine locally from which neighboring signal values an estimate should be formed the noise filter that we arrive at is adaptive and computationally efficient

high stability awfm filter for signal restoration and its hardware design abstract an adaptive weighted fuzzy mean awfm filter with high stability is proposed for signal restoration in this paper awfm is an extension of weighted fuzzy mean wfm filter by linking a fuzzy detector and a dynamic selection procedure to wfm in order to overcome the drawback of wfm in fine signal preservation the fuzzy detector detects the amplitude of impulse noise which will be used as the argument of the dynamic selection procedure by referring to two fuzzy intervals and the wfm filtered outputs then the dynamic selection procedure applies four heuristic decision rules to determine the final filtering output awfm not only preserves the high performance of wfm on removing heavy additive impulse noise but also improves the performance of wfm on light additive impulse noise moreover it results in a high stability on the full range of noise occurrence probability compared with the other filters awfm exhibits better performance in the criteria of mean absolute error mae and mean square error mse on the subjective evaluation of those filtered images awfm also results in a higher quality of global restoration for the dedicated hardware implementation the kernel of awfm filter wfm is synthesized with the generic lr fuzzy cells which realize high speed fuzzy inference the hardware complexity is much simpler than the conventional median filter and simulation result exhibits that up to 6 6m pixels per second can be filtered by a wfm filter with small chip area

balanced projectives and axiom 3 abstract a global definition of k nice subgroup is formulated which generalizes both the notion of a nice subgroup in the context of torsion groups and the notion of a k nice submodule used in a recent study of p local balanced projective groups it is shown analogous to hill s treatment of totally projective p groups that the global balanced projective groups of warfield are precisely those mixed abelian groups that satisfy the third axiom of countability for k nice subgroups a variety of equivalent characterizations of balanced projectives are derived by methods independent of the uniqueness and existence theorems previously established for these groups

short term temporal integration evidence for the influence of peripheral compression thresholds for a 6 5 khz sinusoidal signal temporally centered in a 400 ms broadband noise masker were measured as a function of signal duration for normally hearing listeners and listeners with cochlear hearing loss over a range of masker levels for the normally hearing listeners the slope of the function relating signal threshold to signal duration integration function was steeper at medium masker levels than at low or high levels by a factor of nearly 2 for signal durations between 2 and 10 ms while no significant effect of level was found for signal durations of 20 ms and more no effect of stimulus level was found for the hearing impaired listeners at any signal duration for signal durations greater than 10 ms consistent with many previous studies the slope of the integration function was shallower for the hearing impaired listeners than for the normally hearing listeners however for shorter durations there was no significant difference in slope between the results from the hearing impaired listeners and those from the normally hearing listeners in the high and low level masker conditions a model incorporating a compressive nonlinearity representing the effect of basilar membrane bm compression and a short term temporal integrator postulated to be a more central process can account well for changes in the short term integration function with level if it is assumed that the compression is greater at medium levels than at low or high levels by a factor of about 4 this is in reasonable agreement with physiological measurements of bm compression and with previous psychophysical estimates

temporal integration and compression near absolute threshold in normal and impaired ears the decrease in absolute threshold with increasing stimulus duration often referred to as temporal integration is greater for listeners with normal hearing than for listeners with sensorineural hearing loss it has been suggested that the difference is related to reduced basilar membrane bm compression in the impaired group the present experiment tested this hypothesis by comparing temporal integration and bm compression in normal and impaired ears at low levels absolute thresholds were measured for 4 24 and 44 ms pure tone signals with frequencies f s of 2 and 4 khz the difference between the absolute thresholds for the 4 and 24 ms signals was used as a measure of temporal integration compression near threshold was estimated by measuring the level of a 100 ms off frequency 0 45f s pure tone forward masker required to mask a 44 ms pure tone signal presented at sensation levels of 5 and 10 db there was a significant negative correlation between amount of temporal integration and absolute threshold however there was no correlation between absolute threshold and compression at low levels both normal and impaired ears showed a nearly linear response the results suggest that the differences in integration between normal and impaired ears cannot be explained by differences in bm compression

analytical expressions for the envelope correlation of certain narrow band stimuli analytical solutions are presented for the correlation between the envelopes of certain narrow band stimuli which are typically used in binaural research these stimuli are either the sum of an in phase masker and an out of phase signal or they are two partially correlated noises because an envelope has a nonzero mean the solutions differ depending on whether the envelope correlation is expressed as the normalized cross correlation or as the normalized cross covariance pearson product moment correlation the envelope correlation depends on the statistics of the masker and the signal whereas the waveform correlation depends on neither this influence only disappears for the normalized envelope cross correlation provided that the correlation is close to one in this case the normalized envelope cross correlation is equal to the square root of the waveform correlation the results for two partially correlated noise bands are also of relevance for experiments dealing with monaural envelope discrimination and comodulation masking release

effects of level and frequency on the detection of decrements and increments in sinusoids thresholds for the detection of decrements in level of sinusoidal signals were measured as a function of decrement duration level 25 40 55 and 70 db spl and frequency 250 1000 and 4000 hz in eleven normally hearing subjects thresholds for detecting a brief increment in level were also measured the sinusoids were presented in a background noise intended to mask spectral splatter associated with the decrement or increment performance tended to worsen with decreasing frequency for all decrement durations and for increment detection performance also worsened with decreasing level the results were analyzed using a model consisting of a compressive nonlinearity a sliding temporal integrator and a decision device the analysis indicated that the worsening in performance with decreasing frequency and decreasing level can be attributed partly to increases in the equivalent rectangular duration erd of the temporal integrator but mainly to changes in the efficiency of the detection process following the temporal integrator at lower frequencies and levels a larger change is required at the output of the integrator for threshold to be reached at each frequency the erd was relatively invariant with level for levels more than about 20 db above the absolute threshold

parametric generalized linear system based on the notion of the t norm by using the triangular norm we propose two methods for the construction of generalized linear systems and show new insights into the relationship between typical systems using the hamacher and frank t norm we propose a parametric log ratio model which is a generalization of the log ratio model and is more flexible in algorithmic development we develop a generalized linear contrast enhancement algorithm based on the proposed parametric log ratio model we show that the performance of the proposed algorithm is effective and robust for different types of images

butler groups of infinite rank ii a torsion free abelian group g is called a butler group if bext g t 0 for any torsion group t we show that every butler group g of cardinality ltl is a b2 group i e g is a union of a smooth ascending chain of pure subgroups g0 where g ga b0 b 0 a butler group of finite rank assuming the validity of the continuum hypothesis ch we show that every butler group of cardinality not exceeding n is a b2 group moreover we are able to prove that the derived functor bext2 a t 0 for any torsion group t and any torsion free a with jai this implies that under ch all balanced subgroups of completely decomposable groups of cardinality nt are b2 groups

relations between intelligibility of narrow band speech and auditory functions both in the 1 khz frequency region relations between perception of suprathreshold speech and auditory functions were examined in 24 hearing impaired listeners and 12 normal hearing listeners the speech intelligibility index sii was used to account for audibility the auditory functions included detection efficiency temporal and spectral resolution temporal and spectral integration and discrimination of intensity frequency rhythm and spectro temporal shape all auditory functions were measured at 1 khz speech intelligibility was assessed with the speech reception threshold srt in quiet and in noise and with the speech reception bandwidth threshold srbt previously developed for investigating speech perception in a limited frequency region around 1 khz the results showed that the elevated srt in quiet could be explained on the basis of audibility audibility could only partly account for the elevated srt values in noise and the deviant srbt values suggesting that suprathreshold deficits affected intelligibility in these conditions sii predictions for the srbt improved significantly by including the individually measured upward spread of masking in the sii model reduced spectral resolution reduced temporal resolution and reduced frequency discrimination appeared to be related to speech perception deficits loss of peripheral compression appeared to have the smallest effect on the intelligibility of suprathreshold speech

detection and intensity discrimination of gaussian shaped tone pulses as a function of duration j acoust soc am 105 3425 3435 1999 proposed that the auditory system partitions the spectro temporal domain into frequency time f t windows and that the characteristics of these windows could be explored by measuring intensity discrimination for gaussian shaped tone pulses presented just above their detection threshold in noise they reasoned that for a long duration tone pulse the auditory representation would be maximally compact in the frequency domain but would spread across several f t windows in the time domain for a very short duration tone pulse the auditory representation would be maximally compact in the time domain but would spread across several f t windows in the frequency domain there should be some intermediate duration at which the auditory representation is compact in both the time and frequency domains and for which intensity discrimination performance should worsen due to the limited opportunity for multiple looks their data for signal frequencies of 1 and 4 khz were consistent with this expectation intensity discrimination was poorest at a duration of about 3 5 ms at 1 khz and 1 ms at 4 khz durations are specified between 6 8 db down points on the envelope this experiment attempted to replicate those results and to extend them to a wider range of frequencies and levels intensity discrimination of gaussian shaped tone pulses was measured at three levels 10 db above absolute threshold or above masked threshold in a pink noise with a spectrum level of either 15 or 40 db at 1 khz the signal frequency was 0 25 khz durations from 2 to 320 ms 1 khz durations from 0 5 to 80 ms or 4 khz durations from 0 1 to 20 ms three normally hearing subjects were tested at 1 and 4 khz performance was poorest overall for the 15 db pink noise level and thresholds showed a peak at intermediate durations about 3 5 ms at 1 khz and 1 ms at 4 khz such peaks were still apparent but smaller in the no noise condition and were almost absent at the higher noise level for the 0 25 khz signal frequency peaks were not observed consistently at any level although two subjects showed small peaks for durations around 10 ms an explanation is offered for the results in terms of the level and frequency dependence of basilar membrane input output functions

effects of degradation of intensity time or frequency content on speech intelligibility for normal hearing and hearing impaired listeners many hearing impaired listeners suffer from distorted auditory processing capabilities this study examines which aspects of auditory coding i e intensity time or frequency are distorted and how this affects speech perception the distortion sensitivity model is used the effect of distorted auditory coding of a speech signal is simulated by an artificial distortion and the sensitivity of speech intelligibility to this artificial distortion is compared for normal hearing and hearing impaired listeners stimuli speech plus noise are wavelet coded using a complex sinusoidal carrier with a gaussian envelope 14 octave bandwidth intensity information is distorted by multiplying the modulus of each wavelet coefficient by a random factor temporal and spectral information are distorted by randomly shifting the wavelet positions along the temporal or spectral axis respectively measured were 1 detection thresholds for each type of distortion and 2 speech reception thresholds for various degrees

the normalized interaural correlation accounting for nospi thresholds obtained with gaussian and low noise masking noise recently j acoust soc am 103 2578 2589 1998 and j acoust soc am 103 2573 2577 1998 independently reported that greater masking of interaurally phase reversed s tones was produced by diotic low noise noise than by diotic gaussian noise based on quantitative analyses eddins and barber suggested that their results could not be accounted for by assuming that listeners judgments were based on constant criterion changes in the normalized interaural correlation produced by adding the s signal to the diotic masker in particular they showed that a model like the one previously employed by j acoust soc am 100 3774 3784 1996 predicted an ordering of thresholds between the conditions of interest that was opposite to that observed bernstein and trahiotis computed the normalized interaural correlation subsequent to half wave square law rectification and low pass filtering the parameters of which were chosen to mimic peripheral auditory processing in this report it is demonstrat

torsion free groups in this paper we introduce the class of torsion free k groups and the notion of a knice subgroup torsion free k groups form a class of groups more extensive than the separable groups of baer but they enjoy many of the same closure properties we establish a role for knice subgroups of torsion free groups analogous to that played by nice subgroups in the study of torsion groups for example among the torsion free groups the balanced projectives are characterized by the fact that they satisfy the third axiom of countability with respect to knice subgroups separable groups are characterized as those torsion free k groups with the property that all finite rank pure knice subgroups are direct summands the introduction of these new classes of groups and subgroups is based on a preliminary study of the interplay between primitive elements and valuated coproducts as a by product of our investigation new proofs are obtained for many classical results on separable groups our techniques lead naturally to the discovery that a balanced subgroup of a completely decomposable group is itself completely decomposable provided the corresponding quotient is a separable group of cardinality not exceeding 81 that is separable groups of cardinality 81 have balanced projective dimension

efficient realizations of two dimensional quadratic digital filters realization structures of two dimensional finite support quadratic digital filters which are based on matrix decomposition are introduced the resulting structures consist generally of a number of parallel branches which operate simultaneously and independently on a common input array by proper decomposition of the coefficient matrix each parallel branch can be realized by a two dimensional finite impulse response digital filter in cascade with a squaring operator the lower upper triangular decomposition and the singular value lower upper decomposition is used in order to arrive at efficient structures with computational and hardware advantages

detection of partially filled gaps in noise and the temporal modulation transfer function results of experiments on the detection of silent intervals or gaps in broadband noise are reported for normal hearing listeners in some preliminary experiments a gap threshold of about 2 ms was measured this value was independent of the duration of the noise burst variation of the noise level on each presentation or the temporal position of the gap within the noise burst in the main experiments the thresholds for partial decrements in the noise waveform as well as brief increments were determined as predicted by a model that assumes a single fixed peak to valley detection ratio thresholds for increments are slightly higher than thresholds for decrements when the signal is measured as the change in rms noise level a first order model describes the temporal properties of the auditory system as a low pass filter with a 7 to 8 ms time constant temporal modulation transfer functions were determined for the same subjects and the estimated temporal parameters agreed well with those estimated from the gap detection data more detailed modeling was carried out by simulating viemeister s three stage temporal model simulations using an initial stage bandwidth of 4000 hz and a 3 ms time constant for the low pass filter generate data that are very similar to those obtained from human subjects in both modulation and gap detection

temporal masking functions for listeners with real and simulated hearing loss a functional simulation of hearing loss was evaluated in its ability to reproduce the temporal masking functions for eight listeners with mild to severe sensorineural hearing loss each audiometric loss was simulated in a group of age matched normal hearing listeners through a combination of spectrally shaped masking noise and multi band expansion temporal masking functions were obtained in both groups of listeners using a forward masking paradigm in which the level of a 110 ms masker required to just mask a 10 ms fixed level probe 5 10 db sl was measured as a function of the time delay between the masker offset and probe onset at each of four probe frequencies 500 1000 2000 and 4000 hz temporal masking functions were obtained using maskers that were 0 55 1 0 and 1 15 times the probe frequency the slopes and y intercepts of the masking functions were not significantly different for listeners with real and simulated hearing loss the y intercepts were positively correlated with level of hearing loss while the slopes were negatively correlated the ratio of the slopes obtained with the low frequency maskers relative to the on frequency maskers was similar for both groups of listeners and indicated a smaller compressive effect than that observed in normal hearing listeners

additivity of masking in normally hearing and hearing impaired subjects the effects of combining two equally effective maskers were studied in normally hearing and elderly hearing impaired subjects the additivity of nonsimultaneous masking was investigated by measuring thresholds for a brief 4 khz signal in the presence of a broadband noise forward masker a backward masker and a combination of both for the normally hearing subjects combining two equally effective nonsimultaneous maskers resulted in up to a 15 db greater increase in threshold than the 3 db predicted by an energy summation model excess masking however the hearing impaired subjects showed little or no excess masking the difference between the two groups is consistent with a theory linking excess masking to the compressive transfer function measured on the basilar membrane bm in the hearing impaired subjects the transfer function is more linear accounting for the lack of excess masking the additivity of simultaneous masking was investigated by measuring thresholds for a 100 ms 4 khz signal in the presence of either a 400 ms broadband noise masker or a 400 ms sinusoidal masker at the same frequency as the signal and then combining two equally effective maskers a noise and a tone the maximum amount of excess masking 3 to 4 db was similar across the two groups of subjects consistent with an explanation based on the use of different detection cues for the tonal and noise maskers it is argued that while peripheral compression may underlie excess masking for pairs of nonsimultaneous maskers it is unlikely that in simultaneous masking where the maskers are close in frequency to the signal the two maskers are compressed individually before their effects are combined it is further suggested that bm nonlinearity may underlie the effects of the upward spread of masking and the nonlinear growth of forward masking as well as accounting for the additivity of simultaneous masking when the masker frequencies are well below that of the signal

geometric methods for spectral analysis this paper explores a geometric framework for modeling nonstationary but slowly varying time series based on the assumption that short windowed power spectra capture their spectral character and that energy transference in the frequency domain has a physical significance the framework relies on certain notions of transportation distance and their respective geodesics to model possible nonparametric changes in the power spectral density with respect to time we discuss the relevance of this framework to applications in spectral tracking spectral averaging and speech morphing

multilevel nonlinear filters for edge detection and noise suppression two new classes of multilevel nonlinear filters are introduced for simultaneous edge detection and noise suppression which the authors call a nested median filter median averaging filter nmf maf pair and a delayed decision filter embedded median trimmed filter ddf emtf pair median filters and median related filter cause an edge shift in the presence of an impulse near the edge the proposed filters reduce such edge shifting while suppressing impulsive as well as nonimpulsive noise it is shown that at the noisy edge point the nmf and the ddf are substantially superior both theoretically and experimentally to the median filter the spl alpha tm filter and the stm filter in two respects 1 the output bias error and 2 the output mean square error it is also shown that in the noisy homogeneous region nonedge point the bias errors of the maf are zero and the output mean square errors of the maf are substantially close to those of the optimized single level filters the averager the median filter and the min max filter under gaussian laplacian and uniform noise respectively test results confirm that the nmf maf pair and the ddf emtf structure are each robust in preserving sharp edges inhibiting edge shifting and suppressing a wide variety of noise

a comparison of threshold estimation methods in children 6 11 years of age estimating detection threshold for auditory stimuli in children can be problematic because of lapses in attention and the time limits usually imposed by scheduling restrictions or fatigue data reported here were collected to compare the stability of threshold estimation procedures in testing children ages 6 to 11 in a three alternative forced choice paradigm stimuli consisted of a 1 khz tonal signal and a gaussian noise masker bandpass filtered between 500 2000 hz and presented at 25 db spectrum level the signal was either presented for 400 ms in the presence of a continuous masker simultaneous masking or for 10 ms just prior to a 400 ms masker backward masking for each masking paradigm the 79 correct threshold was assessed via each of three procedures 3 down 1 up adaptive staircase levitt maximum likelihood estimation mle and method of constant stimuli percent correct was measured at the end of the study for a signal 10 db above the previously determined threshold in order to estimate the most appropriate psychometric function asymptote for fitting data collected via the method of constant stimuli both the mle and levitt procedures produced equally stable threshold estimates for both conditions and age groups this was the case despite considerable variability in backward masking thresholds

a behavioral measure of basilar membrane nonlinearity in listeners with normal and impaired hearing this paper examines the possibility of estimating basilar membrane bm nonlinearity using a psychophysical technique the level of a forward masker required to mask a brief signal was measured for conditions where the masker was either at or one octave below the signal frequency the level of the forward masker at masked threshold provided an indirect measure of the bm response to the signal as follows consistent with physiological studies it was assumed that the bm responds linearly to frequencies well below the characteristic frequency cf thus the ratio of the slopes of the masking functions between a masker at the signal frequency and a masker well below the signal frequency should provide an estimate of bm compression at cf results obtained from normally hearing listeners were in quantitative agreement with physiological estimates of bm compression furthermore differences between normally hearing listeners and listeners with cochlear hearing impairment were consistent with the physiological effects of damage to the cochlea the results support the hypothesis that bm nonlinearity governs the nonlinear growth of the upward spread of masking and suggest that this technique provides a straightforward method for estimating bm nonlinearity in humans

nonlinear ultrasonic image processing based on signal adaptive filters and self organizing neural networks two approaches for ultrasonic image processing are examined first signal adaptive maximum likelihood saml filters are proposed for ultrasonic speckle removal it is shown that in the case of displayed ultrasound us image data the maximum likelihood ml estimator of the original noiseless signal closely resembles the l sub 2 mean which has been proven earlier to be the ml estimator of the original signal in us b mode data thus the design of signal adaptive l sub 2 mean filters is treated for us b mode data and displayed us image data as well secondly the segmentation of ultrasonic images using self organizing neural networks nn is investigated a modification of the learning vector quantizer l sub 2 lvq is proposed in such a way that the weight vectors of the output neurons correspond to the l sub 2 mean instead of the sample arithmetic mean of the input observations the convergence in the mean and in the mean square of the proposed l sub 2 lvq nn are studied l sub 2 lvq is combined with signal adaptive filtering in order to allow preservation of image edges and details as well as maximum speckle reduction in homogeneous regions

nonlinear mean filters in image processing the use of nonlinear means in image processing is introduced the properties of these means in the presence of different types of noise are investigated it is shown that nonlinear filters based on these means behave well for both additive and impulse noise their performance in the presence of signal dependent noise is satisfactory they preserve the edges better than linear filters and they reject the noise better than median filters

isotype submodules of p local balanced projective groups by giving necessary and sufficient conditions for two isotype submodules of a p local balanced projective group to be equivalent we are able to introduce a general theory of isotype submodules of p local balanced projective groups or ib modules numerous applications of the above result are available particularly for the special class of ib modules introduced by wick known as skt modules we first show that the class of skt modules is closed under direct summands and then we are able to show that if h appears as an isotype submodule of the p local balanced projective group g such that g h is the coproduct of countably generated torsion groups then h is an skt module finally we show that ib modules satisfy general structural properties such as transitivity full transitivity and the equivalence of p high

level dependence of auditory filters in nonsimultaneous masking as a function of frequency auditory filter bandwidths were measured using nonsimultaneous masking as a function of signal level between 10 and 35db sl for signal frequencies of 1 2 4 and 6khz the brief sinusoidal signal was presented in a temporal gap within a spectrally notched noise two groups of normal hearing subjects were tested one using a fixed masker level and adaptively varying signal level the other using a fixed signal level and adaptively varying masker level in both cases auditory filters were derived by assuming a constant filter shape for a given signal level the filter parameters derived from the two paradigms were not significantly different at 1khz the equivalent rectangular bandwidth erb decreased as the signal level increased from 10to20db sl after which it remained roughly constant in contrast at 6khz the erb increased consistently with signal levels from 10to35db sl the results at 2 and 4khz were intermediate showing no consistent change in erb with signal level overall the results sugge

temporal integration at 6 khz as a function of masker bandwidth thresholds were measured for a 6 khz sinusoidal signal presented within a 500 ms masker the masker was either a bandpass gaussian noise of varying bandwidth or a sinusoid of the same frequency as the signal the spectrum level of the noise masker was kept constant at 20 db spl and the level of the sinusoidal masker was 40 db spl thresholds for signal durations between 2 and 300 ms were measured for masker bandwidths ranging from 60 to 12 000 hz the masker was spectrally centered around 6 khz for masker bandwidths less than 600 hz the slope of the temporal integration function decreased with decreasing masker bandwidth the results are not consistent with current models of temporal integration or temporal resolution it is suggested that the results at narrow bandwidths can be understood in terms of changes in the power spectrum of the stimulus envelope or modulation spectrum according to this view the onset and offset ramps of the signal introduce detectable high frequency components into the modulation spectrum which provide a salient cue in narrowband maskers for broadband maskers these high frequency components are masked by the inherent rapid fluctuations in the masker envelope additionally for signal durations between 7 and 80 ms signal thresholds decreased by up to 5 db as the masker bandwidth increased from 1200 to 12 000 hz the mechanisms underlying this effect are not yet fully understood

the balanced projective dimension of p local abelian groups abstract by generalizing hill s theorem giving a necessary and sufficient condition for an isotype subgroup of a totally projective p group to be itself totally projective we are able to give a condition which will determine the balanced projective dimension of an arbitrary p local abelian group when that dimension is finite we rely on our recent third axiom of countability characterization for p local balanced projectives and are able to carry over almost routinely the arguments given recently by fuchs and hill which were used to determine the balanced projective dimension of an arbitrary abelian p group we are then able to prove that the balanced projective dimension of any countable p local abelian group and of any p local warfieid group is less than or equal to 1

enhancement of chest radiographs with gradient operators reference is made to the sobel and roberts gradient operators used to enhance image edges overall the sobel operator was found to be superior to the roberts operator in edge enhancement a theoretical explanation for the superior performance of the sobel operator was developed based on the concept of analyzing the x and y sobel masks as linear filters by applying pill box gaussian or median filtering prior to applying a gradient operator noise was reduced the pill box and gaussian filters were more computationally efficient than the median filter with approximately equal effectiveness in noise reduction

determination of means by invariance abstract if m is a mean on r n and m f x 1 f x 2 f x n f m x 1 x 2 x n then we say that m is invariant under f the problem is to find a class of functions that by invariance determines a mean uniquely we focus on the geometric mean which can be transformed to obtain results for other means

axiom 3 modules by introducing the concept of a knice submodule a refinement of the notion of nice subgroup we are able to formulate a version of the third axiom of countability appropriate to the study of plocal mixed groups in the spirit of the well known characterization of totally projective pgroups our axiom 3 modules in fact form a class of zp modules encompassing the totally projectives in the torsion case for which we prove a uniqueness theorem and establish closure under direct summands indeed axiom 3 modules turn out to be precisely the previously classified warfield modules but with the added power of the third axiom of countability characterization we derive numerous new results including the resolution of a long standing problem of warfield and theorems in the vein of familiar criteria due to kulikov and pontryagin

a nonlinear derivative scheme applied to edge detection this paper presents a nonlinear derivative approach to addressing the problem of discrete edge detection this edge detection scheme is based on the nonlinear combination of two polarized derivatives its main property is a favorable signal to noise ratio snr at a very low computation cost and without any regularization a 2d extension of the method is presented and the benefits of the 2d localization are discussed the performance of the localization and snr are compared to that obtained using classical edge detection schemes tests of the regularized versions and a theoretical estimation of the snr improvement complete this work

pure subgroups of torsion free groups in this paper we show that certain new notions of purity stronger than the classical concept are relevant to the study of torsion free abelian groups in particular implications of purity a concept introduced in one of our recent papers are investigated we settle an open question posed by nongxa by proving that the union of an ascending countable sequence of pure subgroups is completely decomposable provided the subgroups are this result is false for ordinary purity the principal result of the paper however deals with e purity a concept stronger than purity but weaker than the usual notion of strong purity our main theorem which has a number of corollaries including the recent result of nongxa that strongly pure subgroups of separable groups are again separable states that a e pure subgroup of a k group is itself a k group among other results is the negative resolution of the conjecture valid in the countable case that a strongly pure subgroup of a completely decomposable group is again completely decomposable

lum filters a class of rank order based filters for smoothing and sharpening a new class of rank order based filters called lower upper middle lum filters is introduced the output of these filters is determined by comparing a lower and an upper order statistic to the middle sample in the filter window these filters can be designed for smoothing and sharpening or outlier rejection the level of smoothing done by the filter can range from no smoothing to that of the median filter this flexibility allows the lum filter to be designed to best balance the tradeoffs between noise smoothing and signal detail preservation lum filters for enhancing edge gradients can be designed to be insensitive to low levels of additive noise and to remove impulsive noise furthermore lum filters do not cause overshoot or undershoot some statistical and deterministic properties of the lum filters are developed and a number of experimental results are presented to illustrate the performance these experiments include applications to 1d signals and to images

effects of compression and onset offset asynchronies on the detection of one tone in the presence of another the weaker of two temporally overlapping complex tones can be easier to hear when the tones are asynchronous than when they are synchronous this study explored how the use of fast and slow five channel amplitude compression as might be used in hearing aids affected the ability to use onset and offset asynchronies to detect one signal complex tone when another masking complex tone was presented almost simultaneously a 2 1 compression ratio was used with normal hearing subjects and individual compression ratios and gains recommended by the cam2 hearing aid fitting method were used for hearing impaired subjects when the signal started before the masker there was a benefit of compression for both normal hearing and hearing impaired subjects when the signal finished after the masker there was a benefit of fast compression for the normal hearing subjects but no benefit for most of the hearing impaired subjects except when the offset asynchrony was relatively large 100 ms the benefit of compression probably occurred because the compression improved the effective signal to masker ratio hence reducing backward and forward masking this apparently outweighed potential deleterious effects of distortions in envelope shape and the introduction of partially correlated envelopes of the signal and masker

moving window based double haar wavelet transform for image processing image denoising is a lively research field the classical nonlinear filters used for image denoising such as median filter are based on a local analysis of the pixels within a moving window recently the research of image denoising has been focused on the wavelet domain compared to the classical nonlinear filters it is based on a global multiscale analysis of images apparently the wavelet transform can be embedded in a moving window thus a moving window based local multiscale analysis is obtained in this paper based on the haar wavelet a class of nonorthogonal multichannel filter bank with its corresponding wavelet shrinkage called lee shrinkage is derived as a special case of this filter bank the double haar wavelet transform is introduced examples show that it is suitable for a moving window based local multiscale analysis used for image denoising edge detection and edge enhancement

on and off frequency compression estimated using a new version of the additivity of forward masking technique on and off frequency compression at the 4000 and 8000 hz cochlear places were estimated using a new version of the additivity of forward masking afm technique that measures the effects of combining two non overlapping forward maskers instead of measuring signal thresholds to estimate compression of the signal as in the original afm technique the decrease in masker threshold in the combined masker condition compared to the individual masker conditions is used to estimate compression of the masker at the signal place by varying masker frequency it is possible to estimate off frequency compression the maskers were 500 hz wide bands of noise and the signal was a brief pure tone compression at different levels was estimated using different overall signal levels or different masker signal intervals it was shown that the new afm technique and the original afm technique produce consistent results considerable compression was observed for maskers well below the signal frequency suggesting that the assumption of off frequency linearity used in other techniques may not be valid reducing the duration of the first masker from 200 to 20 ms reduced the compression exponent in some cases suggesting a possible influence of olivocochlear efferent activity

interaural fluctuations and the detection of interaural incoherence iv the effect of compression on stimulus statistics the purpose of this experiment was to determine whether the normalized interaural cross correlation cc model or a model based on interaural phase and level differences can better describe incoherence detection data the ability to detect interaural incoherence in three sets of reproducible dichotic noises was tested in six listeners the first set contained noises with a constrained value of the cc and the cc including signal compression the second set contained noises with a constrained value of the cc including signal compression the third set contained noises with constrained values in the fluctuations in the interaural differences modeling showed that neither the cc model nor the model using the interaural differences could account for the data in any set examination of the statistical properties of the stimuli showed that including compression before the calculation of the interaural cc causes a substantial correlation of this metric to the fluctuations in the interaural phase difference this finding implies that it may be more difficult to discriminate between the common types of binaural models than previously thought

forward masking adaptation or integration the aim of this study was to attempt to distinguish between neural adaptation and persistence or temporal integration as possible explanations of forward masking thresholds were measured for a sinusoidal signal as a function of signal duration for conditions where the delay between the masker offset and the signal offset the offset offset interval was fixed the masker was a 200 ms broadband noise presented at a spectrum level of 40 db re 20 pa and the signal was a 4 khz sinusoid gated with 2 ms ramps the offset offset interval was fixed at various durations between 4 and 102 ms and signal thresholds were measured for a range of signal durations at each interval a substantial decrease in thresholds was observed with increasing duration for signal durations up to about 20 ms at short offset offset intervals the amount of temporal integration exceeded that normally found in quiet the results were simulated using models of temporal integration the temporal window model and adaptation for both models the inclusion of a peripheral nonlinearity similar to that observed physiologically in studies of the basilar membrane was essential in producing a good fit to the data both models were about equally successful in accounting for the present data however the temporal window model provided a somewhat better account of similar data from a simultaneous masking experiment using the same parameters this suggests that the linear time invariant properties of the temporal window approach are appropriate for modeling forward masking overall the results confirm that forward masking can be described in terms of peripheral nonlinearity followed by linear temporal integration at higher levels in the auditory system however the difference in predictions between the adaptation and integration models is relatively small meaning that influence of adaptation cannot be ruled out

comparing different estimates of cochlear compression in listeners with normal and impaired hearing a loss of cochlear compression may underlie many of the difficulties experienced by hearing impaired listeners two behavioral forward masking paradigms that have been used to estimate the magnitude of cochlear compression are growth of masking gom and temporal masking tm the aim of this study was to determine whether these two measures produce within subjects results that are consistent across a range of signal frequencies and if so to compare them in terms of reliability or efficiency gom and tm functions were measured in a group of five normal hearing and five hearing impaired listeners at signal frequencies of 1000 2000 and 4000 hz compression values were derived from the masking data and confidence intervals were constructed around these estimates both measures produced comparable estimates of compression but both measures have distinct advantages and disadvantages so that the more appropriate measure depends on factors such as the frequency region of interest and the degree of hearing loss because of the long testing times needed neither measure is suitable for clinical use in its current form

axiomatic characterization of nonlinear homomorphic means one important problem in mathematics and statistics is to formulate a mean from a set of data various definitions of mean have been studied to represent in some sense an average of data the applications of these means involve all the fields of science and technology with nonlinear filtering being a primary example in the area of image processing 1 3 the goal of this work is to axiomatically investigate the rationale for a large class of means which is referred to as quasi arithmetic mean 4 nonlinear homomorphic mean or nonlinear homomorphic filter 3

switching bilateral filter with a texture noise detector for universal noise removal in this paper we propose a switching bilateral filter sbf with a texture and noise detector for universal noise removal operation was carried out in two stages detection followed by filtering for detection we propose the sorted quadrant median vector sqmv scheme which includes important features such as edge or texture information this information is utilized to allocate a reference median from sqmv which is in turn compared with a current pixel to classify it as impulse noise gaussian noise or noise free the sbf removes both gaussian and impulse noise without adding another weighting function the range filter inside the bilateral filter switches between the gaussian and impulse modes depending upon the noise classification result simulation results show that our noise detector has a high noise detection rate as well as a high classification rate for salt and pepper uniform impulse noise and mixed impulse noise unlike most other impulse noise filters the proposed sbf achieves high peak signal to noise ratio and great image quality by efficiently removing both types of mixed noise salt and pepper with uniform noise and salt and pepper with gaussian noise in addition the computational complexity of sbf is significantly less than that of other mixed noise filters

detail preserving ranked order based filters for image processing the theoretical analysis of multistage median filters is developed it is shown that multistage median filters are a combination of max median and min median filters since multistage median filters belong to the class of two dimensional stack filters they have threshold decomposition attributes making their theoretical analysis simple statistical threshold decomposition is applied to derive the statistical characteristics of these filters and the results are used to evaluate the performance of these two types of multistage filters finally a quantitative and qualitative comparison of the multistage filters and of other efficient detail preserving filters is presented the comparisons are made using the mean squared error and the mean absolute error criteria

interaural fluctuations and the detection of interaural incoherence iii narrowband experiments and binaural models in the first two articles of this series reproducible noises with a fixed value of interaural coherence 0 992 were used to study the human ability to detect interaural incoherence it was found that incoherence detection is strongly correlated with fluctuations in interaural differences especially for narrow noise bandwidths but it remained unclear what function of the fluctuations best agrees with detection data in the present article ten different binaural models were tested against detection data for 14 and 108 hz bandwidths these models included different types of binaural processing independent interaural phase difference interaural level difference lateral position and short term cross correlation several preprocessing transformations of the interaural differences were incorporated compression of binaural cues temporal averaging and envelope weighting for the 14 hz bandwidth data the most successful model postulated that incoherence is detected via fluctuations of interaural phase and interaural level processed by independent centers that model correlated with detectability at r 0 87 that model proved to be more successful than short term cross correlation models incorporating standard physiologically based model features r 0 78 for the 108 hz bandwidth data detection performance varied much less among different waveforms and the data were less able to distinguish between models

a recursive variant of mallows filter class mallows 1980 nonlinear fir filter class includes most of the nonlinear digital filters in wide use today this filter class is defined in terms of five axioms and this paper modifies two of these axioms to obtain a class of symmetric recursive nonlinear filters one of the main points considered in this paper is the consequence of mallows location invariance axiom a2 and general prescriptions are given for both mallows original fir filter class and its recursive extension this representation is also extremely useful in discussing the root sequences of both the recursive and nonrecursive structures since recursive filters can exhibit various forms of instability a number of stability results are presented for this class of filters finally some simple examples are considered that illustrate the potential utility of the results presented

interpolating autoregressive processes a bound on the restoration error an upper bound is obtained for the restoration error variance of a sample restoration method for autoregressive processes that was presented by a j e m janssen et al ibid vol assp 34 p 317 30 apr 1986 the upper bound derived is lower if the autoregressive process has poles close to the unit circle of the complex plane this situation corresponds to a peaky signal spectrum the bound is valid for the case in which one sample is unknown in a realization of an autoregressive process of arbitrary finite order

combination median filter a detail and structure preserving smoothing filter is introduced it is called the combination median filter as it uses directional median multilevel median and median filters to smooth different regions of the image the decision about the region is made by robust dixon s r test which is well known in statistics for outlier detection the threshold value of dixon s test can be kept constant as a result the filtering algorithm operates like a quasi nonadaptive filter and no computation of local statistics is involved some properties of the filter as well as detailed experimental results that demonstrate its superior performance are presented

edge preserving filtering by combining nonlinear mean and median filters a very general class of nonlinear filters called mapping order statistics filters mosfs is introduced a subclass of the mosfs called l sub p mean median filters l sub p mmfs is discussed the l sub p mmf shows better properties in preserving edges and attenuating positive and negative impulse noise simultaneously than do the nonlinear mean filters in the analysis of the deterministic properties of the l sub p mmf the concept of a monotonic trend region is introduced a necessary condition for a signal to be a root signal is given this necessary condition is also valid for the known finite impulse response median hybrid filter

double window hodges lehman d filter and hybrid d median filter for robust image smoothing the double window hodges lehman filter dwd filter and a hybrid d median filter hdm filter for robust image smoothing are proposed an adaptive mixture of the median and the d filter the hdm filter first makes decisions about the presence of edges on the basis of a two way classification of pixels near and around the pixel to be filtered subsequently straightforward d filtering is used in the absence of edges and median filtering is used in the presence of edges the dwd filter uses two windows and d filtering the smaller window is used to preserve the details then the larger window to provide for sufficient smoothing detailed simulation results show that the hdm filter while retaining all the good properties of the dwd filter consistently performs better in terms of signal to noise ratio than the dwd filter and a number of other filters including the median filter the dwd filter is shown to have simpler structure although not necessarily lesser computational complexity

characterizations of warfield groups abstract warfield groups are defined to be direct summands of simply presented abelian groups by introducing a global definition of quasi sequentially nice subgroups we prove some characterizations of warfield groups involving these groups knice subgroups and valuated coproducts furthermore we exhibit a new proof of a characterization of warfield groups in terms of nice subgroups and valuated coproducts

representation of digital image by fuzzy neural network a multilayer feedforward fuzzy neural network fnn by which the predetermined fuzzy system can be realized is constructed to express a given two dimensional 2 d digital image it is shown that such a network is universal approximator the fnn approach provides us with the representation model of the 2 d discrete image in noise environment some given fuzzy numbers are employed to describe gray levels of a digital image and the deviation of corrupted image to its noise free one a class of fuzzy rules for removing impulse noise in degraded image are presented the corresponding fnn may work as a filter which improves the performances of median and rank conditioned rank selection filters especially such a filter may to a greatest extent maintain the fine structure of the image under the minimum mean absolute error criterion the membership functions of fuzzy numbers are adaptively adjusted and an optimal fnn for image representation is derived in noise environment simultaneously some real image examples are systemically analyzed to show that the fnn may result in higher quality global restoration

nonlinear smoothing filters based on rank estimates of location a class of nonlinear filters that are based on the rank estimates r estimates of location parameters in statistical theory is introduced it is shown how moving window rank filters r filters can be defined starting from rank estimates of location these filters utilize the relative ranks of the observations in each window to produce an output value the idea of rank winsorization is extended to that of averaging only observations which lie within small temporal neighborhoods this leads to a definition of the class of generalized wilcoxon gw filters which are parameterized by three parameters namely the degrees of temporal and rank winsorization and the degree of averaging the gw filters can be defined to have desirable characteristics of edge preservation detail retention and impulse rejection in addition to the property of gaussian noise smoothing performance characteristics of these filters are considered through analysis and simulation the filters show that all three well known classes of robust location estimates the l m and r estimates can be applied to nonlinear smoothing of signals

nfir nonlinear filter a nonlinear filter is introduced whose output is nearest in distance to the output of a fir finite impulse response linear phase filter hence it is called the nfir filter after choosing the impulse response of the fir filter properly the nfir filter can clean impulsive noise and preserve edges of signals as a special case of the nfir filter a nearest mean neme filter is derived theoretical analysis shows that the neme filter is better than the median filter in smoothing additive gaussian noise in addition based on the definition of the neme filter a new interpretation of the low pass property of the median filter with window width 3 is described also the performance of the nearest mean filter on a noisy edge is quantitatively compared with that of the median and mean filters

temporal integration of loudness in listeners with hearing losses of primarily cochlear origin to investigate how hearing loss of primarily cochlear origin affects the loudness of brief tones loudness matches between 5 and 200 ms tones were obtained as a function of level for 15 listeners with cochlear impairments and for seven age matched controls three frequencies usually 0 5 1 and 4 khz were tested in each listener using a two interval two alternative forced choice 2i 2afc paradigm with a roving level up down adaptive procedure results for the normal listeners generally were consistent with published data e g j acoust soc am 99 1633 1644 1996 the amount of temporal integration defined as the level difference between equally loud short and long tones varied nonmonotonically with level and was largest at moderate levels no consistent effect of frequency was apparent the impaired listeners varied widely but most showed a clear effect of level on the amount of temporal integration overall their results appear consistent with expectations based on knowledge of the general properties of their loudness growth functions and the equal loudness ratio hypothesis which states that the loudness ratio between equal spl long and brief tones is the same at all spls the impaired listeners amounts of temporal integration at high spls often were larger than normal although it was reduced near threshold when evaluated at equal sls the amount of temporal integration well above threshold usually was in the low end of the normal range two listeners with abrupt high frequency hearing losses slopes 50 db octave showed larger than normal maximal amounts of temporal integration 40 to 50 db this finding is consistent with the shallow loudness functions predicted by our excitation pattern model for impaired listeners in modeling sensorineural hearing loss edited by w jesteadt erlbaum mahwah nj 1997 pp 187 198 loudness functions derived from impaired listeners temporal integration functions indicate that restoration of loudness in listeners with cochlear hearing loss usually will require the same gain whether the sound is short or long

the transitivity of local warfield groups abstract for a fixed prime p let g denote a module over the integers localized at p such a module is often referred to as a p local abelian group following established precedent we say that g is transitive provided that there exists an automorphism of g that maps a onto b whenever a and b are elements of g having the same height sequence however relatively few nontorsion g meet this criterion of transitivity indeed as we show there are four different classes of simply presented p local groups of torsion free rank 3 that are nontransitive in this article we introduce a weaker version of transitivity that allows all local warfield groups summands of simply presented p local groups to qualify as being transitive in this connection we associate with each element of a local warfield group g a new invariant called a type vector and we prove that there is an automorphism of g that maps a onto b if and only if a and b have the same height sequence and the same type vector as an application of this result we are able to determine exactly which local warfield groups are transitive in the classical sense also our results yield an alternate proof of a recent result of files regarding the equivalence of transitivity and full transitivity for local warfield groups finally we give a complete survey of transitivity for local warfield groups of torsion free rank 3

a parametrized family of nonlinear image smoothing filters a parameterized family of nonlinear image smoothers is developed which provides a range of tradeoffs between noise smoothing and edge retention the presentation unifies many approaches to the problem of image smoothing where the estimate of the gray level of a pixel is taken as a nonlinear data dependent weighted sum of the gray levels of the pixel s neighborhood local confidence measures are defined and it is shown how filters based on the sample median the absolute gradient and the sample variance incorporate these confidence measures in their nonlinear weights the notion of localized sample variance is then introduced and shown to constitute a more appropriate confidence measure using the localized sample variances a family of filters termed lv sub n is derived smaller values of n provide better noise removal whereas higher values of n provide better edge preservation experiments indicate that the lv sub 2 member of the family is very efficient for noise removal while the extreme member lv sub infinity is nearly perfect for edge retention a good tradeoff is achieved using n 4 5 or 6 these values give the most aesthetically appealing results and yield lower rms error than those of other filters discussed