3D medical volume segmentation using hybrid multiresolution statistical approaches

This article is available through the Brunel Open Access Publishing Fund. Copyright © 2010 S AlZu’bi and A Amira.3D volume segmentation is the process of partitioning voxels into 3D regions (subvolumes) that represent meaningful physical entities which are more meaningful and easier to analyze and usable in future applications. Multiresolution Analysis (MRA) enables the preservation of an image according to certain levels of resolution or blurring. Because of multiresolution quality, wavelets have been deployed in image compression, denoising, and classification. This paper focuses on the implementation of efficient medical volume segmentation techniques. Multiresolution analysis including 3D wavelet and ridgelet has been used for feature extraction which can be modeled using Hidden Markov Models (HMMs) to segment the volume slices. A comparison study has been carried out to evaluate 2D and 3D techniques which reveals that 3D methodologies can accurately detect the Region Of Interest (ROI). Automatic segmentation has been achieved using HMMs where the ROI is detected accurately but suffers a long computation time for its calculations

The curvelet transform for image denoising

We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of a` trous wavelet filters. Our philosophy throughout is that transforms should be overcomplete, rather than critically sampled. We apply these digital transforms to the denoising of some standard images embedded in white noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state of the art" techniques based on wavelets, including thresholding of decimated or undecimated wavelet transforms and also including tree-based Bayesian posterior mean methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems. The empirical results reported here are in encouraging agreement

Wavelets and Imaging Informatics: A Review of the Literature

AbstractModern medicine is a field that has been revolutionized by the emergence of computer and imaging technology. It is increasingly difficult, however, to manage the ever-growing enormous amount of medical imaging information available in digital formats. Numerous techniques have been developed to make the imaging information more easily accessible and to perform analysis automatically. Among these techniques, wavelet transforms have proven prominently useful not only for biomedical imaging but also for signal and image processing in general. Wavelet transforms decompose a signal into frequency bands, the width of which are determined by a dyadic scheme. This particular way of dividing frequency bands matches the statistical properties of most images very well. During the past decade, there has been active research in applying wavelets to various aspects of imaging informatics, including compression, enhancements, analysis, classification, and retrieval. This review represents a survey of the most significant practical and theoretical advances in the field of wavelet-based imaging informatics

A Wavelet Transform Module for a Speech Recognition Virtual Machine

This work explores the trade-offs between time and frequency information during the feature extraction process of an automatic speech recognition (ASR) system using wavelet transform (WT) features instead of Mel-frequency cepstral coefficients (MFCCs) and the benefits of combining the WTs and the MFCCs as inputs to an ASR system. A virtual machine from the Speech Recognition Virtual Kitchen resource (www.speechkitchen.org) is used as the context for implementing a wavelet signal processing module in a speech recognition system. Contributions include a comparison of MFCCs and WT features on small and large vocabulary tasks, application of combined MFCC and WT features on a noisy environment task, and the implementation of an expanded signal processing module in an existing recognition system. The updated virtual machine, which allows straightforward comparisons of signal processing approaches, is available for research and education purposes

WARP: Wavelets with adaptive recursive partitioning for multi-dimensional data

Effective identification of asymmetric and local features in images and other data observed on multi-dimensional grids plays a critical role in a wide range of applications including biomedical and natural image processing. Moreover, the ever increasing amount of image data, in terms of both the resolution per image and the number of images processed per application, requires algorithms and methods for such applications to be computationally efficient. We develop a new probabilistic framework for multi-dimensional data to overcome these challenges through incorporating data adaptivity into discrete wavelet transforms, thereby allowing them to adapt to the geometric structure of the data while maintaining the linear computational scalability. By exploiting a connection between the local directionality of wavelet transforms and recursive dyadic partitioning on the grid points of the observation, we obtain the desired adaptivity through adding to the traditional Bayesian wavelet regression framework an additional layer of Bayesian modeling on the space of recursive partitions over the grid points. We derive the corresponding inference recipe in the form of a recursive representation of the exact posterior, and develop a class of efficient recursive message passing algorithms for achieving exact Bayesian inference with a computational complexity linear in the resolution and sample size of the images. While our framework is applicable to a range of problems including multi-dimensional signal processing, compression, and structural learning, we illustrate its work and evaluate its performance in the context of 2D and 3D image reconstruction using real images from the ImageNet database. We also apply the framework to analyze a data set from retinal optical coherence tomography

Hyperanalytic denoising

A new threshold rule for the estimation of a deterministic image immersed in noise is proposed. The full estimation procedure is based on a separable wavelet decomposition of the observed image, and the estimation is improved by introducing the new threshold to estimate the decomposition coefficients. The observed wavelet coefficients are thresholded, using the magnitudes of wavelet transforms of a small number of "replicates" of the image. The "replicates" are calculated by extending the image into a vector-valued hyperanalytic signal. More than one hyperanalytic signal may be chosen, and either the hypercomplex or Riesz transforms are used, to calculate this object. The deterministic and stochastic properties of the observed wavelet coefficients of the hyperanalytic signal, at a fixed scale and position index, are determined. A "universal" threshold is calculated for the proposed procedure. An expression for the risk of an individual coefficient is derived. The risk is calculated explicitly when the "universal" threshold is used and is shown to be less than the risk of "universal" hard thresholding, under certain conditions. The proposed method is implemented and the derived theoretical risk reductions substantiated

Image Denoising Based on Dilated Singularity Prior

In order to preserve singularities in denoising, we propose a new scheme by adding dilated singularity prior to noisy images. The singularities are detected by canny operator firstly and then dilated using mathematical morphology for finding pixels “near” singularities instead of “on” singularities. The denoising results for pixels near singularities are obtained by nonlocal means in spatial domain to preserve singularities while the denoising results for pixels in smooth regions are obtained by EM algorithm constrained by a mask formed by downsampled spatial image with dilated singularity prior to suiting the sizes of the subbands of wavelets. The final denoised results are got by combining the above two results. Experimental results show that the scheme can preserve singularity well with relatively high PSNR and good visual quality

Medical image denoising using convolutional denoising autoencoders

Image denoising is an important pre-processing step in medical image analysis. Different algorithms have been proposed in past three decades with varying denoising performances. More recently, having outperformed all conventional methods, deep learning based models have shown a great promise. These methods are however limited for requirement of large training sample size and high computational costs. In this paper we show that using small sample size, denoising autoencoders constructed using convolutional layers can be used for efficient denoising of medical images. Heterogeneous images can be combined to boost sample size for increased denoising performance. Simplest of networks can reconstruct images with corruption levels so high that noise and signal are not differentiable to human eye.Comment: To appear: 6 pages, paper to be published at the Fourth Workshop on Data Mining in Biomedical Informatics and Healthcare at ICDM, 201

Enhanced Speckle Filters For Sonar Images Using Stationary Wavelets And Hybrid Inter- And Intra Scale Wavelet Coefficient Dependency

The quality of Sonar images are often reduced by the presence of speckle noise. The presence of speckle noise leads to incorrect analysis and has to be handled carefully. In this paper, an improved non-parametric statistical wavelet denoising method is presented. The algorithm uses a stationary wavelet transformation to derive the wavelet coefficients, from which edge and non-edge wavelet coefficients are identified. Further to improve the time complexity, only homogenous regions with respect to coefficients of neighbors are considered. This method uses an ant colony classification technique. A hybrid method that exploits both inter-scale and intra-scale dependencies between wavelet coefficients is also proposed. The experimental results show that the proposed method is efficient in terms of reduction in speckle noise and speed and can be efficiently used by various sonar imaging systems