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PubMed2006

Optimization of partition-based Weighted Sum filters and their application to image denoising.

Partition-based Weighted Sum (P-WS) filtering is an effective method for processing nonstationary signals, especially those with regularly occurring structures, such as images. P-WS filters were originally formulated as Hard-partition Weighted Sum (HP-WS) filters and were successfully applied to image denoising. This formulation relied on intuitive arguments to generate the filter class. Here we present a statistical analysis that justifies the use of weighted sum filters after observation space partitioning. Unfortunately, the HP-WS filters are nondifferentiable and an analytical solution for their global optimization is therefore difficult to obtain. A two-stage suboptimal training procedure has been reported in the literature, but prior to this research no evaluation on the optimality of this approach has been reported. Here, a Genetic Algorithm (GA) HP-WS optimization procedure is developed that, in simulations, shows that the simpler two-stage training procedure yields near optimal results. Also developed in this paper are Soft-partition Weighted Sum (SP-WS) filters. The SP-WS filters utilize soft, or fuzzy, partitions that yield a differentiable filtering operation, enabling the development of gradient-based optimization procedures. Image denoising simulation results are presented comparing HP-WS and SP-WS filters, their optimization procedures, and wavelet-based image denoising. These results show that P-WS filters, in general, outperform traditional and wavelet-based image filters, and SP-WS filters utilizing soft partitioning not only allow for simple optimization, but also yields improved performance.

Algorithms↗
PubMed2003

[Application of wavelet translation-PLS to simultaneous determination of Co, Ni and Zn].

The optimum conditions of the colour reaction of Cobalt, Nickel and Zinc with 5-Br-PADAP were established in the presence of the sensitizer/solubilizer CPB. The absorbances of the reaction system Co-Ni-Zn- (5-Br-PADAP) -CPB were measured in the spectral range of 530-590 nm at every 2 nm intervals. A chemometric method of data treatment was studied. Through the comparative study of data treatment by PLS method and by PLS after wavelet transformation, it was found that the recovery of determination is significantly improved by using the latter method.

Algorithms↗
PubMed1997

Multiresolution statistical analysis of high-resolution digital mammograms.

A multiresolution statistical method for identifying clinically normal tissue in digitized mammograms is used to construct an algorithm for separating normal regions from potentially abnormal regions; that is, small regions that may contain isolated calcifications. This is the initial phase of the development of a general method for the automatic recognition of normal mammograms. The first step is to decompose the image with a wavelet expansion that yields a sum of independent images, each containing different levels of image detail. When calcifications are present, there is strong empirical evidence that only some of the image components are necessary for the purpose of detecting a deviation from normal. The underlying statistic for each of the selected expansion components can be modeled with a simple parametric probability distribution function. This function serves as an instrument for the development of a statistical test that allows for the recognition of normal tissue regions. The distribution function depends on only one parameter, and this parameter itself has an underlying statistical distribution. The values of this parameter define a summary statistic that can be used to set detection error rates. Once the summary statistic is determined, spatial filters that are matched to resolution are applied independently to each selected expansion image. Regions of the image that correlate with the normal statistical model are discarded and regions in disagreement (suspicious areas) are flagged. These results are combined to produce a detection output image consisting only of suspicious areas. This type of detection output is amenable to further processing that may ultimately lead to a fully automated algorithm for the identification of normal mammograms.

Algorithms↗
PubMed2005

EEG phase synchrony differences across visual perception conditions may depend on recording and analysis methods.

OBJECTIVE: (1) To investigate the neural synchrony hypothesis by examining if there was more synchrony for upright than inverted Mooney faces, replicating a previous study; (2) to investigate whether inverted stimuli evoke neural synchrony by comparing them to a new scrambled control condition, less likely to produce face perception. METHODS: Multichannel EEG was recorded via nose reference while participants viewed upright, inverted, and scrambled Mooney face stimuli. Gamma-range spectral power and inter-electrode phase synchrony were calculated via a wavelet-based method for upright stimuli perceived as faces and inverted/scrambled stimuli perceived as non-faces. RESULTS: When the frequency of interest was selected from the upright condition exhibiting maximal spectral power responses (as in the previous study) greater phase synchrony was found in the upright than inverted/scrambled conditions. However, substantial synchrony was present in all conditions, suggesting that choosing the frequency of interest from the upright condition only may have been biased. In addition, artifacts related to nose reference contamination by micro-saccades were found to be differentially present across experimental conditions in the raw EEG. When frequency of interest was selected instead from each experimental condition and the data were transformed to a laplacian 'reference free' derivation, the between-condition phase synchrony differences disappeared. Spectral power differences were robust to the change in reference, but not the combined changes in reference and frequency selection criteria. CONCLUSIONS: Synchrony differences between face/non-face perceptions depend upon frequency selection and recording reference. Optimal selection of these parameters abolishes differential synchrony between conditions. SIGNIFICANCE: Neural synchrony is present not just for face percepts for upright stimuli, but also for non-face percepts achieved for inverted/scrambled Mooney stimuli.

Adult↗
PubMed2005

Comparative analysis of algorithms for identifying amplifications and deletions in array CGH data.

MOTIVATION: Array Comparative Genomic Hybridization (CGH) can reveal chromosomal aberrations in the genomic DNA. These amplifications and deletions at the DNA level are important in the pathogenesis of cancer and other diseases. While a large number of approaches have been proposed for analyzing the large array CGH datasets, the relative merits of these methods in practice are not clear. RESULTS: We compare 11 different algorithms for analyzing array CGH data. These include both segment detection methods and smoothing methods, based on diverse techniques such as mixture models, Hidden Markov Models, maximum likelihood, regression, wavelets and genetic algorithms. We compute the Receiver Operating Characteristic (ROC) curves using simulated data to quantify sensitivity and specificity for various levels of signal-to-noise ratio and different sizes of abnormalities. We also characterize their performance on chromosomal regions of interest in a real dataset obtained from patients with Glioblastoma Multiforme. While comparisons of this type are difficult due to possibly sub-optimal choice of parameters in the methods, they nevertheless reveal general characteristics that are helpful to the biological investigator.

Algorithms↗
PubMed2006

Wavelet basis selection and feature extraction for shift invariant ultrasound foreign body classification.

This paper proposes a novel technique for automatic ultrasound non-destructive foreign body (FB) detection and classification. A signal registration process is introduced to eliminate shift variations commonly encountered in ultrasound signals. Information theory based methods are then developed for wavelet basis selection and feature extraction to facilitate robust FB classification. Probabilistic neural networks are used for FB classification. Experimental results confirm that the wavelet basis selected by the proposed method improves the FB classification accuracy. It is concluded that low order wavelet bases have better ability to distinguish classes with great similarities than their higher order counterparts, while the reverse is true for more divergent classes.

Algorithms↗
PubMedDate not supplied

Classification of the myoelectric signal using time-frequency based representations.

An accurate and computationally efficient means of classifying surface myoelectric signal patterns has been the subject of considerable research effort in recent years. Effective feature extraction is crucial to reliable classification and, in the quest to improve the accuracy of transient myoelectric signal pattern classification, an ensemble of time-frequency based representations are proposed. It is shown that feature sets based upon the short-time Fourier transform, the wavelet transform, and the wavelet packet transform provide an effective representation for classification, provided that they are subject to an appropriate form of dimensionality reduction.

Action Potentials↗
PubMed2004

Computationally efficient wavelet affine invariant functions for shape recognition.

An affine invariant function for object recognition is constructed from wavelet coefficients of the object boundary. In previous works, undecimated dyadic wavelet transform was used to construct affine invariant functions. In this paper, an algorithm based on decimated wavelet transform is developed to compute an affine invariant function. As a result computational complexity is reduced without decreasing recognition performance. Experimental results are presented.

Algorithms↗
PubMed2003

Wavelet-based compression of medical images: filter-bank selection and evaluation.

Wavelet-based image coding algorithms (lossy and lossless) use a fixed perfect reconstruction filter-bank built into the algorithm for coding and decoding of images. However, no systematic study has been performed to evaluate the coding performance of wavelet filters on medical images. We evaluated the best types of filters suitable for medical images in providing low bit rate and low computational complexity. In this study a variety of wavelet filters are used to compress and decompress computed tomography (CT) brain and abdomen images. We applied two-dimensional wavelet decomposition, quantization and reconstruction using several families of filter banks to a set of CT images. Discreet Wavelet Transform (DWT), which provides efficient framework of multi-resolution frequency was used. Compression was accomplished by applying threshold values to the wavelet coefficients. The statistical indices such as mean square error (MSE), maximum absolute error (MAE) and peak signal-to-noise ratio (PSNR) were used to quantify the effect of wavelet compression of selected images. The code was written using the wavelet and image processing toolbox of the MATLAB (version 6.1). This results show that no specific wavelet filter performs uniformly better than others except for the case of Daubechies and bi-orthogonal filters which are the best among all. MAE values achieved by these filters were 5 x 10(-14) to 12 x 10(-14) for both CT brain and abdomen images at different decomposition levels. This indicated that using these filters a very small error (approximately 7 x 10(-14)) can be achieved between original and the filtered image. The PSNR values obtained were higher for the brain than the abdomen images. For both the lossy and lossless compression, the 'most appropriate' wavelet filter should be chosen adaptively depending on the statistical properties of the image being coded to achieve higher compression ratio.

Algorithms↗
PubMed2004

Influence of MRI acquisition protocols and image intensity normalization methods on texture classification.

Texture analysis methods quantify the spatial variations in gray level values within an image and thus can provide useful information on the structures observed. However, they are sensitive to acquisition conditions due to the use of different protocols and to intra- and interscanner variations in the case of MRI. The influence was studied of two protocols and four different conditions of normalization of gray levels on the discrimination power of texture analysis methods applied to soft cheeses. Thirty-two samples of soft cheese were chosen at two different ripening periods (16 young and 16 old samples) in order to obtain two different microscopic structures of the protein gel. Proton density and T(2)-weighted MR images were acquired using a spin echo sequence on a 0.2 T scanner. Gray levels were normalized according to four methods: original gray levels, same maximum for all images, same mean for all images, and dynamics limited to micro +/- 3sigma. Regions of interest were automatically defined, and texture descriptors were then computed for the co-occurrence matrix, run length matrix, gradient matrix, autoregressive model, and wavelet transform. The features with the lowest probability of error and average correlation coefficient were selected and used for classification with 1-nearest neighbor (1-NN) classifier. The best results were obtained when using the limitation of dynamics to micro +/- 3sigma, which enhanced the differences between the two classes. The results demonstrated the influence of the normalization method and of the acquisition protocol on the effectiveness of the classification and also on the parameters selected for classification. These results indicate the need to evaluate sensitivity to MR acquisition protocols and to gray level normalization methods when texture analysis is required.

Cheese↗
PubMed2001

Myocardial rapid velocity distribution.

Myocardial motion exhibits frequency components of up to 100 Hz, as found by a phased tracking method. To simultaneously measure the rapid and minute velocity signals at multiple points along the surface of the left ventricle (LV), in this study, conventional ultrasonic diagnosis equipment was modified to allow 10 scan lines from a sector scanner to be arbitrarily selected in real-time for analysis. By considering the maximum value of the velocity in the heart wall and the maximum depth from the chest surface, the number of transmission directions of the ultrasonic pulses should be carefully confirmed to be 10 to avoid aliasing, which is much less than the number employed in conventional tissue Doppler imaging (TDI). By applying the system, the velocity signals at about 240 points in the heart walls were simultaneously measured for three healthy volunteers. During a short period of 35 ms around end-diastole, the velocity signals varied spatially in the heart wall. At the end of systole, in the wavelets near the base of the interventricular septum (IVS), the slow pulse continued for about 30 ms, just before the radiation timing of the second heart sound. Then, a steep pulse occurred just at the timing of the closure of the aortic valve. The steep pulse at the base preceded that at the apex by several ms. By Fourier transforming each wavelet, the spatial distribution of the phase of the steep pulse components were clearly displayed. By applying the measurement method to two patients with aortic stenosis (AS), irregular vibration signals, which correspond to the murmur of the heart sound, could be directly detected during the ejection period. In conventional TDI, only the large slow movements due to the heartbeat are displayed, but these rapid and minute velocity components cannot be displayed. In this study, moreover, the phase components were detected for the first time from each of the velocity signals simultaneously measured at multiple points along the 10 scan lines. This measurement and method of analysis offer potential for new diagnostic techniques in cardiac dysfunction.

Aged↗
PubMed2005

The use of stationarity and nonstationarity in the detection and analysis of neural oscillations.

Using available signal (i.e., spectral and time-frequency) analysis methods, it can be difficult to detect neural oscillations because of their continuously changing properties (i.e., nonstationarities) and the noise in which they are embedded. Here, we introduce fractally scaled envelope modulation (FSEM) estimation which is sensitive specifically to the changing properties of oscillatory activity. FSEM utilizes the fractal characteristic of wavelet transforms to produce a compact, two-dimensional representation of time series data where signal components at each frequency are made directly comparable according to the spectral distribution of their envelope modulations. This allows the straightforward identification of neural oscillations and other signal components with an envelope structure different from noise. For stable oscillations, we demonstrate how partition-referenced spectral estimation (PRSE) removes the noise slope from spectral estimates, yielding a level estimate where only peaks signifying the presence of oscillatory activity remain. The functionality of these methods is demonstrated with simulations and by analyzing MEG data from human auditory brain areas. FSEM uncovered oscillations in the 9- to 12-Hz and 15- to 18-Hz ranges whereas traditional spectral estimates were able to detect oscillations only in the former range. FSEM further showed that the oscillations exhibited envelope modulations spanning 3-7 s. Thus, FSEM effectively reveals oscillations undetectable with spectral estimates and allows the use of EEG and MEG for studying cognitive processes when the common approach of stimulus time-locked averaging of the measured signal is unfeasible.

Acoustic Stimulation↗
PubMed2001

From 1/f noise to multifractal cascades in heartbeat dynamics.

We explore the degree to which concepts developed in statistical physics can be usefully applied to physiological signals. We illustrate the problems related to physiologic signal analysis with representative examples of human heartbeat dynamics under healthy and pathologic conditions. We first review recent progress based on two analysis methods, power spectrum and detrended fluctuation analysis, used to quantify long-range power-law correlations in noisy heartbeat fluctuations. The finding of power-law correlations indicates presence of scale-invariant, fractal structures in the human heartbeat. These fractal structures are represented by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales. We then describe very recent work that quantifies multifractal features in these cascades, and the discovery that the multifractal structure of healthy dynamics is lost with congestive heart failure. The analytic tools we discuss may be used on a wide range of physiologic signals. (c) 2001 American Institute of Physics.

Journal Article↗
PubMed2001

Determination of aorta failure with the application of FFT, AR and wavelet methods to Doppler technique.

In this study, Doppler signals recorded from the output of aorta valve of 24 patients were transferred to a personal computer (PC) by using a 16-bit sound card. Doppler difference frequencies were recorded from each of the patients, and then analyzed using fast Fourier transform, autoregressive and wavelet transform analyzer to obtain their sonograms. These sonograms are then used to compare with the applied methods in terms of medical evaluation.

Aortic Valve Insufficiency↗
PubMedDate not supplied

Wavelet-based histogram equalization enhancement of gastric sonogram images.

The gray levels of gastric sonogram images are usually concentrated at the zero end of the spectrum, making the image too low in contrast and too dark for the naked eye. Though histogram equalization can enhance the contrast by redistributing the gray levels, it has the drawback that it reduces the information in the processed image. In this paper, a wavelet-based enhancement algorithm post-processor is used to further enhance the image and compensate for the information loss during histogram equalization. Experimental results show that the wavelet-based enhancement algorithm can enhance the contrast and significantly increase the informational entropy of the image. Because the combination of the histogram equalization and wavelet approach can dramatically increase the contrast and maintain information rate in gastric sonograms, it has the potential to improve clinical diagnosis and research.

Algorithms↗
PubMed2006

Hidden Markov models for wavelet-based blind source separation.

In this paper, we consider the problem of blind source separation in the wavelet domain. We propose a Bayesian estimation framework for the problem where different models of the wavelet coefficients are considered: the independent Gaussian mixture model, the hidden Markov tree model, and the contextual hidden Markov field model. For each of the three models, we give expressions of the posterior laws and propose appropriate Markov chain Monte Carlo algorithms in order to perform unsupervised joint blind separation of the sources and estimation of the mixing matrix and hyper parameters of the problem. Indeed, in order to achieve an efficient joint separation and denoising procedures in the case of high noise level in the data, a slight modification of the exposed models is presented: the Bernoulli-Gaussian mixture model, which is equivalent to a hard thresholding rule in denoising problems. A number of simulations are presented in order to highlight the performances of the aforementioned approach: 1) in both high and low signal-to-noise ratios and 2) comparing the results with respect to the choice of the wavelet basis decomposition.

Algorithms↗
PubMed2006

Multiresolution MAP despeckling of SAR images based on locally adaptive generalized Gaussian pdf modeling.

In this paper, a new despeckling method based on undecimated wavelet decomposition and maximum a posteriori MIAP) estimation is proposed. Such a method relies on the assumption that the probability density function (pdf) of each wavelet coefficient is generalized Gaussian (GG). The major novelty of the proposed approach is that the parameters of the GG pdf are taken to be space-varying within each wavelet frame. Thus, they may be adjusted to spatial image context, not only to scale and orientation. Since the MAP equation to be solved is a function of the parameters of the assumed pdf model, the variance and shape factor of the GG function are derived from the theoretical moments, which depend on the moments and joint moments of the observed noisy signal and on the statistics of speckle. The solution of the MAP equation yields the MAP estimate of the wavelet coefficients of the noise-free image. The restored SAR image is synthesized from such coefficients. Experimental results, carried out on both synthetic speckled images and true SAR images, demonstrate that MAP filtering can be successfully applied to SAR images represented in the shift-invariant wavelet domain, without resorting to a logarithmic transformation.

Algorithms↗
PubMed2005

Wavelet coding of volumetric medical images for high throughput and operability.

This paper presents a new three-dimensional (3-D) wavelet-based scalable lossless coding scheme for compression of volumetric medical images. Aiming to improve the productivity of radiologists and the cost-effectiveness of the system, we strive to achieve high decoder throughput, random access to coded data volume, progressive transmission, and high compression ratio in a balanced design approach. These desirable functionalities are realized by a modified 3-D dyadic wavelet transform tailored to volumetric medical images and an optimized Rice code of very low complexity.

Algorithms↗