Microarray images when contaminated with noise may severely affect the detection and quantification of gene expression. In this paper, we propose to use the complex Gaussian scale mixture (CGSM) model in complex wavelet domain for noise reduction in complementary DNA microarray images. Based on the joint information in the red and green channel microarray images, we model the complex wavelet coefficients of the channel images jointly using the CGSM, and subsequently perform image denoising using Bayes least square estimator in complex wavelet domain. The experimental results show that using the CGSM of complex wavelet coefficients provides better noise reduction of microarray images compared to other complex wavelet-based models.

In this paper, we propose an approximation of the relative phase probability function (RP pdf) and use it to find a non-iterative estimator for the concentration parameter of the pdf. In particular, we approximate the log-likelihood equation which is highly nonlinear by another equation where we can use the proposed pdf's approximation to solve for the estimator. To illustrate the effectiveness of the proposed estimator, the comparisons between the proposed method and the maximum likelihood (ML) estimation method are displayed in terms of both numerical accuracy and computational saving in the estimation. The results show that the proposed method yields a good and comparable estimator with the ML estimator but with less computational time in estimating the parameters from the simulated samples, and also works well in histogram fitting of the relative phase samples of complex wavelet coefficients extracted from several standard test images.

This paper proposes a method to estimate the parameters of the relative phase probability density function (RP pdf) of the complex coefficients when the image is corrupted by additive white Gaussian noise. With the complex Gaussian scale mixture (CGSM) assumption of the clean coefficients, we first introduce the relative phase mixture pdf (RPM pdf) by deriving the pdf of the relative phase of the noisy coefficients. Along with the derived pdf, the estimation method based on the maximum likelihood approach is proposed by exploiting the relationships between the RP pdf's parameters and the complex covariance matrix of the corresponding complex coefficient vector. The experiments using the simulated data and the data extracted from the real images are performed to show the effectiveness of the estimation method. The results show that the proposed method can well estimate the RP pdf's parameters of the clean vector in the case of simulated data and fit well with the histogram of phase samples extracted from the real images.

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.

The uniform discrete curvelet transform (UDCT) is a variant of the discrete curvelet transform with basis function located on a uniform grid. The transform is implemented based on a filter bank structure in the frequency domain. In this paper, we study statistics and dependency analysis of the UDCT coefficients and impose the hidden Markov tree (HMT) model for the UDCT. Finally, the experiment in image denoising is shown as an application of the modeling.

We derive the probability density function (pdf) of the magnitude of complex wavelet coefficients with the assumption that each of the real and imaginary parts is characterized by the generalized Gaussian distribution (GGD) model. The parameter estimation method using maximum likelihood for the derived pdf is presented. The derived pdf fits acceptably well with the actual coefficient magnitude of images. To show the usefulness of the derived pdf, we use it to model the magnitude of complex coefficients of texture images for an application in texture image retrieval. The experimental results show that using the derived magnitude pdf yields higher retrieval rate than using the GGD model to fit with the real part or imaginary part of coefficients, and than using the mean and standard deviation of the magnitude of coefficients.

In this paper, the probability distributions of relative phase are studied. We proposed von Mises and wrapped Cauchy for the probability density function (pdf) of the relative phase in complex wavelet domain. The maximum-likelihood method is used to estimate the 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 natural 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 the relative phase 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, when images are decomposed by different complex wavelet transforms including dual-tree complex wavelet (DTCWT), pyramidal dual-tree directional filter bank (PDTDFB) and a modified version of curvelet.

The derotated phase of a complex wavelet coefficient is defined as the phase of that coefficient minus twice of the phase of its parent coefficient. It was recently introduced and found to be useful in terms of providing more correlation among coefficients near singularities in scale and space. In this paper, we investigate the derotated phase of a complex wavelet coefficient by deriving its probability density function (pdf). We show that the derotated phase can be well approximated by a Gaussian random variable for moderate signal to noise ratio. The simulation results are shown to confirm the consistency between the derived pdf and the derotated phase of the actual coefficients.

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.

Array based comparative genomic hybridization (CGH) is a molecular cytogenetic method for the detection of chromosomal imbalances and it has been extensively used for studying copy number alterations in various cancer types. Our method captures both the intrinsic spatial change of genome hybridization intensities, and the physical distance between adjacent probes along a chromosome which are not uniform. In this paper, we introduce a dual-tree complex wavelet transform method with the bivariate shrinkage estimator into array CGH data smoothing study. We tested the proposed method on both simulated data and real data, and the results demonstrated superior performance of our method in comparison with extant methods.

Array-based comparative genomic hybridization (array CGH) is a highly efficient technique, allowing the simultaneous measurement of genomic DNA copy number at hundreds or thousands of loci and the reliable detection of local one-copy-level variations. Characterization of these DNA copy number changes is important for both the basic understanding of cancer and its diagnosis. In order to develop effective methods to identify aberration regions from array CGH data, many recent research works focus on both smoothing-based and segmentation-based data processing. In this paper, we propose to use the dual-tree complex wavelet transform to smooth the array CGH data. We demonstrate the effectiveness of our approach through theoretic and experimental exploration of a set of array CGH data, including both synthetic data and real data. The comparison results show that our method outperforms the previous approaches.

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.

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.

Searching for an efficient summarization of multi-channel electroencephalogram (EEG) behavior is a challenging signal analysis problem. Recently, parallel factor analysis (PARAFAC) is reported as an efficient tool for extracting features of multi-channel EEG by simultaneously employing space-time-frequency knowledge, i.e. decomposing multi-channel EEG signal into a linear combination of its space-time-frequency feature. However, this decomposition scheme suffers from expensive computational load when applied to either long term or high number of channels EEG signals. In this paper, a reduced computational complexity space-time-frequency model for multi-channel EEG signal is proposed by dividing selected content into segments yielding additional segment signatures. By carefully selecting the number of segments, features extracted from the proposed model are comparable with those from the conventional space-time-frequency model while the time used in computation is reduced by more than 50%. Simulation results show that the proposed model can efficiently extract eye blink artifact from background EEG. Furthermore, classification accuracy when employing the proposed model to brain computer interface (BCI) application is also comparable with the conventional model.

We address the problem of resilient image coding over error-prone networks where packet losses occur. Recent literature highlights the multiple description coding (MDC) as a promising approach to solve this problem. In this paper, we introduce a novel wavelet-based multiple description image coder, referred to as the feature-oriented MDC (FO-MDC). The proposed multiple description (MD) coder exploits the statistics of the wavelet coefficients and identifies the subsets of samples that are sensitive to packet loss. A joint optimization between tree-pruning and quantizer selection in the rate-distortion sense is used in order to allocate more bits to these sensitive coefficients. When compared with the state-of-the-art MD scalar quantization coder, the proposed FO-MDC yields a more efficient central-side distortion tradeoff control mechanism. Furthermore, it proves to be more robust for image transmission even with high packet loss ratios, which makes it suitable for protecting multimedia streams over packet-erasure channels.

This paper presents a novel embedded image coding system based on the pyramidal multidirectional image representation. The multiscale filter bank is a combination of the overcomplete pyramidal directional filter bank at higher scales and the traditional maximally-decimated wavelet filter bank at lower scales, to provide a sparse image representation. The coding algorithm then efficiently clusters the significant coefficients using progressive morphological operations. Context models for arithmetic coding are designed to exploit the intra-band dependency and the correlation existing among the neighboring directional subbands. Experimental results show that the proposed coding algorithm outperforms the current state-of-the-art wavelet based coders, such as JPEG2000, for images with directional features.

This paper presents a shift-invariant complex directional pyramid transform constructed by a dual-tree pyramidal directional filter banks (DFB). The double filter bank framework consists of a shift-invariant Laplacian pyramid and a dual-tree DFB. The two binary tree struc-ture for the (primal and dual) DFBs employed in the structure are identical except for the filter bank employed at the second level of the dual DFB, where special conditions on the phase of the filters are required. It is proven analytically and experimentally that each pair of corresponding directional filters produced by the primal and dual filter banks are symmetric and anti-symmetric, which can be inter-preted as the real and imaginary parts of a complex filter. Therefore, the two subband coefficients can be viewed as the real and imag-inary parts of a complex-valued subband image. It is proven that there is no aliasing in the decimated complex-valued signal, which implies that the system is shift-invariant in the energy sense. In ad-dition, the proposed shift-invariant, multiscale, multidirectional im-age decomposition has two unique characteristics that other shift-invariant decompositions do not possess. First, the directional reso-lution of the image transform can be arbitrarily high. Secondly, the two-dimensional filter bank is implemented in a separable fashion, which makes the entire structure very computational efficient. 1.

An image coding system based on combination of a multiresolution directional decomposition and a morphological dilation algorithm is proposed in this paper. The multiscale filter bank combines the recently introduced non-uniform quincunx directional filter bank at higher scales and the traditional wavelet filter bank at lower scales, to provide a sparse image representation. The coding algorithm then efficiently clusters the significant coefficients using progressive morphological dilation. The remaining scattered significant coefficients are coded with the aid of the Tarp filter. The proposed image coding algorithm achieves better results than the current state-of-the-art wavelet based coders, such as SPIHT and JPEG2000.

In this paper, we introduce a novel wavelet-based multiple description image coder, referred to as the feature-oriented MDC (FO-MDC). The proposed multiple description coders exploit the statistics of the wavelet coefficients, and identify the subsets of samples those are sensitive to packet loss. A joint optimization between tree-pruning and quantizer selection in the rate-distortion sense is used in order to allocate more bits to these sensitive coefficients. When compared with the state-of-the-art multiple description scalar quantization coders, the proposed FO-MDC yields a more efficient central-side distortion tradeoff control mechanism. Furthermore, it proves to be more robust for image transmission even with high packet loss ratios.

In this paper, the shift-invariant complex directional filter bank (CDFB) is proposed for texture image retrieval. By combining the Laplacian pyramid and the CDFB, a new image representation with an overcomplete ratio of less than 8/3 is obtained. The direction subbands' coefficients are used to form a feature vector for classification. Texture retrieval performance of the proposed representation is compared to those of the conventional transforms including the Gabor wavelet, the contourlet and the steerable pyramid. The overcomplete ratio of the proposed complex directional pyramid is about twice that of the contourlet, and is much lower than those of the other two transforms. An experiment shows that the new transform outperforms the steerable pyramid and the contourlet, and is comparable to the Gabor wavelet in texture image retrieval

This paper presents a method for losslessly compressing multi-channel electroencephalogram signals. The Karhunen-Loeve transform is used to exploit the inter-correlation among the EEG channels. The transform is approximated using lifting scheme which results in a reversible realization under finite precision processing. An integer time-frequency transform is applied to further minimize the temporal redundancy

In this paper, lossless audio coding using the integer modified discrete cosine transform (IntMDCT) is discussed. The IntMDCT is constructed as an integer approximation of the MDCT using the lifting scheme and is reversible. The rounding error shape of the IntMDCT is derived. When the spectral energy of the input audio signal is concentrated at the low frequencies, the rounding error spectrum limits the lossless coding performance. A method for shaping the rounding error in the transform domain is presented. This rounding error shaping scheme manipulates the error so that it is below the spectral envelope of the signal at the high frequencies in order to improve the lossless coding performance for the signal. Examples of an error shaping filter design are presented and verified by simulations. An IntMDCT-based lossless coding implementation is carried out to illustrate the use of the error shaping filters

The integer modified discrete cosine transform (IntMDCT), an integer approximation of the MDCT, is a reversible transform realized by the lifting scheme and thus is a useful transform for lossless audio coding. Because of the integer approximation, however, the approximation error appears as a "noise floor" in the transform domain and limits the lossless coding efficiency. In this paper, a theoretical analysis of the approximation error of the IntMDCT is discussed. The result is then used to design a simple test filter applied to each rounding operation of the IntMDCT in such a way that the error spectrum is shaped towards the low frequencies. As a result, especially when the spectral energy of an input signal is concentrated in the low frequency domain, the lossless coding efficiency is improved.

M-channel paraunitary filter banks (PUFBs) can be designed and implemented using either degree-one or order-one dyadic-based factorization. This paper summarizes how regularity of a desired degree is structurally imposed on such factorizations for any number of channels M/spl ges/2 and any phase responses. The regularity conditions are found to be conveniently expressed in terms of recently reported M-channel lifting structures, which allow fast and reversible implementations. Design examples are presented and they outperform previously reported ones in transform-based image coding.

The purpose of this paper is twofold: one is to establish a framework for general biorthogonal filter banks (BOFBs) with structural regularity; the other is to identify the connection between the general structure used here and the one commonly used for linear-phase biorthogonal filter banks (a.k.a. generalized lapped biorthogonal transform or GLBT). The latter also leads naturally to the same reduced number of free parameters as GLBT. We first revisit a minimal structure of BOFBs using order-one dyadic-based building blocks, by which BOFBs with length constraint can be designed. Conditions for filter bank regularity on the dyadic-based structure are derived and specialized to the case of GLBT. Design examples are presented.

Block-matching algorithms (BMA) have been widely adopted for motion estimation (ME) by real-time video coding applications due to its effectiveness and simplicity in implementation. Most fast BMAs are based on the assumption that ME matching error decreases monotonically as the search approaches the position of the global minimum error. The paper measures the contributions to computational cost reduction by different fast BMAs, including four-step search, diamond search, hexagon-based search and the recently proposed adaptive multi-mode search (AMMS). Comparison results show that the AMMS algorithm achieves a significant improvement based on the given mathematical models. Experimental coding results are also presented.

We propose a new formulation of directional filter banks (DFBs). By using a non-uniform and non-separable filter bank, a critically sampled multiresolution directional image representation can be obtained efficiently. The resulting DFB yields non-uniform frequency division which is composed of one lowpass channel with a decimation factor of one-fourth and six highpass directional channels with a decimation factor of one-eighth. It overcomes the limited directional selectivity of separable wavelets and the limited resolution of the conventional DFB. The lowpass channel can be used to obtain multiresolution representation by simply re-iterating the same DFB decomposition. On the other hand, the directional subbands can be further refined by simply applying a two-channel DFB at each highpass channel. A simple design method yielding near orthogonal uniform and non-uniform multidimensional filter banks is discussed, and, finally, a numerical experiment is presented to demonstrate the potential of the new image basis.

This article presents a novel approach in linear-phase finite-impulse response filter design based on cosine modulation. It is shown that the proposed technique is equivalent to a simple mapping between Mth-band filters, i.e., given an Lth-band filter, an Mth-band filter can be obtained by simple calculation where L and M are different integers.

This paper describes an algorithm for systematically finding a multiplierless approximation of transforms where VLSI-friendly binary coefficients of the form k/2nare employed in the approximation. Assuming the cost of binary shifters is negligible in hardware, the total number of binary adders required to approximate the transform is used as the complexity constraint. The proposed algorithm is systematic and fast. It eliminates the need for trial-and-error binary approximations of the coefficients. Specifically, two types of multiplierless approximations of the discrete cosine transform (DCT) are presented to illustrate the algorithm.

In this paper, we develop the generalized discrete fractional Fourier transform (GDFRFT) by factorizing the generalized discrete Fourier transform (GDFT) matrix. Specifically, the eigenvalues and eigenvectors are presented and then used to define the GDFRFT. It is shown that the GDFRFT may be obtained by simple similarity transformations of the conventional DFRFT if the time and frequency shifting indexes are integers. Fast and efficient structures are presented and integer structures are also discussed.

This letter describes an algorithm for systematically finding a multiplierless approximation of transforms by replacing floating-point multipliers with VLSI-friendly binary coefficients of the form k/2/sup n/. Assuming the cost of hardware binary shifters is negligible, the total number of binary adders employed to approximate the transform can be regarded as an index of complexity. Because the new algorithm is more systematic and faster than trial-and-error binary approximations with adder constraint, it is a much more efficient design tool. Furthermore, the algorithm is not limited to a specific transform; various approximations of the discrete cosine transform are presented as examples of its versatility.

The concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has properties that it is an integer-to-integer mapping, power-adaptable and also reversible. A lifting scheme is used to approximate complex multiplications appearing in the FFT lattice structures. Split-radix FFT is used to illustrate the approach for the case of 2/sup N/-point FFT. The transform can be implemented by using only bit shifts and additions but no multiplication. While preserving the reversibility, the IntFFT is shown experimentally to yield the same accuracy as the FxpFFT when their coefficients are quantized to a certain number of bits. Complexity of the IntFFT is shown to be much lower than that of the FxpFFT in terms of the numbers of additions and shifts.

This paper describes the implementation of the integer discrete cosine transform (IntDCT) using the Walsh-Hadamard transform and the lifting scheme. The implementation is in the forms of shifts and adds, and all internal nodes have finite precision. A general-purpose scheme of 8-pt IntDCT with complexity of 45 adds and 18 shifts is proposed which gives comparable performance to the floating-point DCT (FloatDCT). For this particular scheme with 8-bit input, perfect reconstruction (PR) is preserved even when all the internal nodes are limited to 16-bit words, rendering the Pentium MMX optimization possible. Implementation has been done to incorporate the proposed IntDCT into the H.263+ coder, and the resulting system performs equally well as the original. Further extension to the MPEG coder is straightforward. The proposed IntDCT is reversible, with a low level of power consumption, and is very suitable for source coding, and communication, etc. in a mobile environment.

This paper presents a systematic and computable method for choosing the regularization parameter appearing in Tikhonov-type regularization based on non-quadratic regularizers. First, we extend the notion of the L-curve, originally defined for quadratically regularized problems, to the case of non-quadratic functions. We then associate the optimal value of the regularization parameter for these non-quadratic problems with the corner of the resulting generalized L-curve. We identify the corner of this L-curve as the point of tangency between a straight line of arbitrary slope and the L-curve. This definition results in a corresponding algebraic equation which the optimal regularization parameter must satisfy. This algebraic equation naturally leads to an iterative algorithm for the optimal value of the regularization parameter. The convergence of this iterative algorithm is established. Simulation results confirm that the proposed method yields values of the regularization parameters that result in good reconstructions for non-quadratic problems.

This paper presents an approach for image and video scaling using multirate signal processing. The main objective is to scale images with an arbitrary rational scaling ratio without visible aliasing or distortion artifact. The approach can be applied to grey scale images, color images and video signals in both spatial domain and time domain. Cosine modulation is used to minimize the required on-chip memory since only a prototype filter is stored with some cosine modulation factors. The filters are shown to have comparable regularity for each scaling factor. An efficient structure is proposed for limited bit length filter coefficients which has no imaging artifact after the filter coefficients are quantized. Simulations on still image and video scaling are presented.