An P. N. Vo

A study of relative phase in complex wavelet domain: Property, statistics and applications in texture image retrieval and segmentation

In this paper, we develop a new approach which exploits the probabilistic properties from the phase information of 2-D complex wavelet coefficients for image modeling. Instead of directly using phases of complex wavelet coefficients, we demonstrate why relative phases should be used. The definition, properties and statistics of relative phases of complex coefficients are studied in detail. We proposed von Mises and wrapped Cauchy for the probability density function (pdf) of relative phases in the complex wavelet domain. The maximum-likelihood method is used to estimate two parameters of von Mises and wrapped Cauchy. We demonstrate that the von Mises and wrapped Cauchy fit well with real data obtained from various real images including texture images as well as standard images. The von Mises and wrapped Cauchy models are compared, and the simulation results show that the wrapped Cauchy fits well with the peaky and heavy-tailed pdf of relative phases and the von Mises fits well with the pdf which is in Gaussian shape. For most of the test images, the wrapped Cauchy model is more accurate than the von Mises model, when images are decomposed by different complex wavelet transforms including dual-tree complex wavelet (DTCWT), pyramidal dual-tree directional filter bank (PDTDFB) and uniform discrete curvelet transform (UDCT). Moreover, the relative phase is applied to obtain new features for texture image retrieval and segmentation applications. Instead of using only real or magnitude coefficients, the new approach uses a feature in which phase information is incorporated, yielding a higher accuracy in texture image retrieval as well as in segmentation. The relative phase information which is complementary to the magnitude is a promising approach in image processing.

Using Phase and Magnitude Information of the Complex Directional Filter Bank for Texture Image Retrieval

This paper discusses how to utilize both magnitude and phase information obtained from the complex directional filter bank (CDFB) for the purpose of texture image retrieval. The relative phase, which is the difference of phases between adjacent CDFB coefficients, has a linear relationship with the angle of dominant orientation within a subband. This information is incorporated to form a new feature vector called CDFB-RP. Texture retrieval performance of the proposed CDFB-RP is compared to those of the conventional transforms including the Gabor wavelet, the contourlet transform, the steerable pyramid and the CDFB. With the same number of features, the CDFB-RP method outperforms all other transforms in texture image retrieval, while keeping lower complexity and computational time.

Vonn distribution of relative phase for statistical image modeling in complex wavelet domain

With the assumptions of Gaussian as well as Gaussian scale mixture models for images in wavelet domain, marginal and joint distributions for phases of complex wavelet coefficients are studied in detail. From these hypotheses, we then derive a relative phase probability density function, which is called Vonn distribution, in complex wavelet domain. The maximum-likelihood method is proposed to estimate two Vonn distribution parameters. We demonstrate that the Vonn distribution fits well with behaviors of relative phases from various real images including texture images as well as standard images. The Vonn distribution is compared with other standard circular distributions including von Mises and wrapped Cauchy. The simulation results, in which images are decomposed by various complex wavelet transforms, show that the Vonn distribution is more accurate than other conventional distributions. Moreover, the Vonn model is applied to texture image retrieval application and improves retrieval accuracy.

Complex Gaussian Scale Mixtures of Complex Wavelet Coefficients

In this paper, we propose the complex Gaussian scale mixture (CGSM) to model the complex wavelet coefficients as an extension of the Gaussian scale mixture (GSM), which is for real-valued random variables to the complex case. Along with some related propositions and miscellaneous results, we present the probability density functions of the magnitude and phase of the complex random variable. Specifically, we present the closed forms of the probability density function (pdf) of the magnitude for the case of complex generalized Gaussian distribution and the phase pdf for the general case. Subsequently, the pdf of the relative phase is derived. The CGSM is then applied to image denoising using the Bayes least-square estimator in several complex transform domains. The experimental results show that using the CGSM of complex wavelet coefficients visually improves the quality of denoised images from the real case.

Mass spectrometry data processing using zero-crossing lines in multi-scale of Gaussian derivative wavelet

Motivation: Peaks are the key information in mass spectrometry (MS) which has been increasingly used to discover diseases-related proteomic patterns. Peak detection is an essential step for MS-based proteomic data analysis. Recently, several peak detection algorithms have been proposed. However, in these algorithms, there are three major deficiencies: (i) because the noise is often removed, the true signal could also be removed; (ii) baseline removal step may get rid of true peaks and create new false peaks; (iii) in peak quantification step, a threshold of signal-to-noise ratio (SNR) is usually used to remove false peaks; however, noise estimations in SNR calculation are often inaccurate in either time or wavelet domain. In this article, we propose new algorithms to solve these problems. First, we use bivariate shrinkage estimator in stationary wavelet domain to avoid removing true peaks in denoising step. Second, without baseline removal, zero-crossing lines in multi-scale of derivative Gaussian wavelets are investigated with mixture of Gaussian to estimate discriminative parameters of peaks. Third, in quantification step, the frequency, SD, height and rank of peaks are used to detect both high and small energy peaks with robustness to noise. Results: We propose a novel Gaussian Derivative Wavelet (GDWavelet) method to more accurately detect true peaks with a lower false discovery rate than existing methods. The proposed GDWavelet method has been performed on the real Surface-Enhanced Laser Desorption/Ionization Time-Of-Flight (SELDI-TOF) spectrum with known polypeptide positions and on two synthetic data with Gaussian and real noise. All experimental results demonstrate that our method outperforms other commonly used methods. The standard receiver operating characteristic (ROC) curves are used to evaluate the experimental results. Availability: http://ranger.uta.edu/∼heng/MS/GDWavelet.html or http://www.naaan.org/nhanguyen/archive.htm Contact: heng@uta.edu

Stationary wavelet packet transform and dependent laplacian bivariate shrinkage estimator for array-CGH data smoothing.

Array-based comparative genomic hybridization (aCGH) has merged as a highly efficient technique for the detection of chromosomal imbalances. Characteristics of these DNA copy number aberrations provide the insights into cancer, and they are useful for the diagnostic and therapy strategies. In this article, we propose a statistical bivariate model for aCGH data in the stationary wavelet packet transform (SWPT) and apply this bivariate shrinkage estimator into the aCGH smoothing study. Because our new dependent Laplacian bivariate shrinkage estimator covers the dependency between wavelet coefficients and the shift invariant SWPT results include both low- and high-frequency information, our dependent Laplacian bivariate shrinkage estimator based SWPT method (named as SWPT-LaBi) has fundamental advantages to solve aCGH data smoothing problem compared to other methods. In our experiments, two standard evaluation methods, the Root Mean Squared Error (RMSE) and the Receiver Operating Characteristic (ROC) curve, are calculated to demonstrate the performance of our method. In all experimental results, our SWPT-LaBi method outperforms the previous most commonly used aCGH smoothing algorithms on both synthetic data and real data. Meantime, we also propose a new synthetic data generation method for aCGH smoothing algorithms evaluation. In our new data model, the noise from real aCGH data is extracted and used to improve synthetic data generation.

PEAK DETECTION IN MASS SPECTROMETRY BY GABOR FILTERS AND ENVELOPE ANALYSIS

Mass Spectrometry (MS) is increasingly being used to discover diseases-related proteomic patterns. The peak detection step is one of the most important steps in the typical analysis of MS data. Recently, many new algorithms have been proposed to increase true position rate with low false discovery rate in peak detection. Most of them follow two approaches: one is the denoising approach and the other is the decomposing approach. In the previous studies, the decomposition of MS data method shows more potential than the first one. In this paper, we propose two novel methods, named GaborLocal and GaborEnvelop, both of which can detect more true peaks with a lower false discovery rate than previous methods. We employ the method of Gaussian local maxima to detect peaks, because it is robust to noise in signals. A new approach, peak rank, is defined for the first time to identify peaks instead of using the signal-to-noise ratio. Meanwhile, the Gabor filter is used to amplify important information and compress noise in the raw MS signal. Moreover, we also propose the envelope analysis to improve the quantification of peaks and remove more false peaks. The proposed methods have been performed on the real SELDI-TOF spectrum with known polypeptide positions. The experimental results demonstrate that our methods outperform other commonly used methods in the Receiver Operating Characteristic (ROC) curve.

Solenoid and non-solenoid protein recognition using stationary wavelet packet transform

Motivation: Solenoid proteins are emerging as a protein class with properties intermediate between structured and intrinsically unstructured proteins. Containing repeating structural units, solenoid proteins are expected to share sequence similarities. However, in many cases, the sequence similarities are weak and non-detectable. Moreover, solenoids can be degenerated and widely vary in the number of units. So that it is difficult to detect them. Recently, several solenoid repeats detection methods have been proposed, such as self-alignment of the sequence, spectral analysis and discrete Fourier transform of sequence. Although these methods have shown good performance on certain data sets, they often fail to detect repeats with weak similarities. In this article, we propose a new approach to recognize solenoid repeats and non-solenoid proteins using stationary wavelet packet transform (SWPT). Our method associates with three advantages: (i) naturally representing five main factors of protein structure and properties by wavelet analysis technique; (ii) extracting novel wavelet features that can capture hidden components from solenoid sequence similarities and distinguish them from global proteins; (iii) obtaining statistics features that capture repeating motifs of solenoid proteins. Results: Our method analyzes the characteristics of amino acid sequence in both spectral and temporal domains using SWPT. Both global and local information of proteins are captured by SWPT coefficients. We obtain and integrate wavelet-based features and statistics-based features of amino acid sequence to improve the classification task. Our proposed method is evaluated by comparing to state-of-the-art methods such as HHrepID and REPETITA. The experimental results show that our algorithm consistently outperforms them in areas under ROC curve. At the same false positive rate, the sensitivity of our WAVELET method is higher than other methods. Availability: http://www.naaan.org/anvo/Software/Software.htm Contact: anphuocnhu.vo@mavs.uta.edu

Statistical image modeling using von Mises distribution in the complex directional wavelet domain

In this paper, a new statistical model is proposed for modeling the nature images in the transform domain. We demonstrate that the von Mises distribution (VM) fits accurately the behaviors of relative phases in the complex directional wavelet subband from different nature images. Moreover, a new image feature based on the VM model is proposed for texture image retrieval application. The VM based feature yields higher retrieval accuracy compared to the energy features and the relative phase features. In addition to magnitude information typically used in many other feature extraction methods, the VM based phase information is also incorporated to further improve the performance.

Image Denoising using Shiftable Directional Pyramid and Scale Mixtures of Complex Gaussians

In this paper, a modified version of the complex directional pyramid (PDTDFB) is proposed. Unlike the previous approach, the new FB provides approximately tight-frame decomposition. We introduced the complex Gaussian scale mixture (CGSM) for modeling the distribution of complex directional wavelet coefficients. The statistical model is then used to obtain the denoised coefficients from the noisy image decomposition by Bayes least squares estimator. Performance of the denoised images using the PDTDFB is compared to the conventional transforms including the orthogonal wavelet, the contourlet and the steerable pyramid. The experiments show that the PDTDFB could achieve higher quality image denoising than the wavelet and the contourlet with the hard thresholding method, and is comparable to the steerable pyramid in terms of mean squared error (MSE) and perceptual image quality (SSIM) with the Bayes least squares estimator.