A wavelet approach to detect enriched regions and explore epigenomic landscapes

Heavy-Tailed Noise Suppression and Derivative Wavelet Scalogram for Detecting DNA Copy Number Aberrations

Most existing array comparative genomic hybridization (array CGH) data processing methods and evaluation models assumed that the probability density function (pdf) of noise in array CGH data is a Gaussian distribution. However, in practice, such noise distribution is peaky and heavy-tailed. Therefore, a Gaussian pdf is not adequate to approximate the noise in array CGH data and hence introduces wrong detections of chromosomal aberrations and leads misunderstanding on disease pathogenesis. A more accurate and sufficient model of noise in array CGH data is necessary and beneficial to the detection of DNA copy number variations. We analyze the real array CGH data from different platforms and show that the distribution of noise in array CGH data is fitted very well by generalized Gaussian distribution (GGD). Based on our new noise model, we propose a novel array CGH processing method combining the advantages of both the smoothing and segmentation approaches. The new method uses generalized Gaussian bivariate shrinkage function and one-directional derivative wavelet scalogram in generalized Gaussian noise. In the smoothing step, with the new generalized Gaussian noise model, we derive the heavy-tailed noise suppression algorithm in stationary wavelet domain. In the segmentation step, the 1D Gaussian derivative wavelet scalogram is employed to detect break points. Both real and simulated array CGH data with different noises (such as Gaussian noise, GGD noise, and real noise) are used in our experiments. We demonstrate that our new method outperforms other state-of-the-art methods, in terms of both root mean squared errors and receiver operating characteristic curves.

Application of Time-Frequency Domain Transform to Three-Dimensional Interpolation of Medical Images

Medical image three-dimensional (3D) interpolation is an important means to improve the image effect in 3D reconstruction. In image processing, the time-frequency domain transform is an efficient method. In this article, several time-frequency domain transform methods are applied and compared in 3D interpolation. And a Sobel edge detection and 3D matching interpolation method based on wavelet transform is proposed. We combine wavelet transform, traditional matching interpolation methods, and Sobel edge detection together in our algorithm. What is more, the characteristics of wavelet transform and Sobel operator are used. They deal with the sub-images of wavelet decomposition separately. Sobel edge detection 3D matching interpolation method is used in low-frequency sub-images under the circumstances of ensuring high frequency undistorted. Through wavelet reconstruction, it can get the target interpolation image. In this article, we make 3D interpolation of the real computed tomography (CT) images. Compared with other interpolation methods, our proposed method is verified to be effective and superior.

A stationary wavelet entropy-based clustering approach accurately predicts gene expression

Studying epigenetic landscapes is important to understand the condition for gene regulation. Clustering is a useful approach to study epigenetic landscapes by grouping genes based on their epigenetic conditions. However, classical clustering approaches that often use a representative value of the signals in a fixed-sized window do not fully use the information written in the epigenetic landscapes. Clustering approaches to maximize the information of the epigenetic signals are necessary for better understanding gene regulatory environments. For effective clustering of multidimensional epigenetic signals, we developed a method called Dewer, which uses the entropy of stationary wavelet of epigenetic signals inside enriched regions for gene clustering. Interestingly, the gene expression levels were highly correlated with the entropy levels of epigenetic signals. Dewer separates genes better than a window-based approach in the assessment using gene expression and achieved a correlation coefficient above 0.9 without using any training procedure. Our results show that the changes of the epigenetic signals are useful to study gene regulation.