Blind Curvelet based Denoising of Seismic Surveys in Coherent and Incoherent Noise Environments

The localized nature of curvelet functions, together with their frequency and dip characteristics, makes the curvelet transform an excellent choice for processing seismic data. In this work, a denoising method is proposed based on a combination of the curvelet transform and a whitening filter along with procedure for noise variance estimation. The whitening filter is added to get the best performance of the curvelet transform under coherent and incoherent correlated noise cases, and furthermore, it simplifies the noise estimation method and makes it easy to use the standard threshold methodology without digging into the curvelet domain. The proposed method is tested on pseudo-synthetic data by adding noise to real noise-less data set of the Netherlands offshore F3 block and on the field data set from east Texas, USA, containing ground roll noise. Our experimental results show that the proposed algorithm can achieve the best results under all types of noises (incoherent or uncorrelated or random, and coherent noise)

Extreme Value Analysis of Empirical Frame Coefficients and Implications for Denoising by Soft-Thresholding

Denoising by frame thresholding is one of the most basic and efficient methods for recovering a discrete signal or image from data that are corrupted by additive Gaussian white noise. The basic idea is to select a frame of analyzing elements that separates the data in few large coefficients due to the signal and many small coefficients mainly due to the noise \epsilon_n. Removing all data coefficients being in magnitude below a certain threshold yields a reconstruction of the original signal. In order to properly balance the amount of noise to be removed and the relevant signal features to be kept, a precise understanding of the statistical properties of thresholding is important. For that purpose we derive the asymptotic distribution of max_{\omega \in \Omega_n} || for a wide class of redundant frames (\phi_\omega^n: \omega \in \Omega_n}. Based on our theoretical results we give a rationale for universal extreme value thresholding techniques yielding asymptotically sharp confidence regions and smoothness estimates corresponding to prescribed significance levels. The results cover many frames used in imaging and signal recovery applications, such as redundant wavelet systems, curvelet frames, or unions of bases. We show that `generically' a standard Gumbel law results as it is known from the case of orthonormal wavelet bases. However, for specific highly redundant frames other limiting laws may occur. We indeed verify that the translation invariant wavelet transform shows a different asymptotic behaviour.Comment: [Content: 39 pages, 4 figures] Note that in this version 4 we have slightely changed the title of the paper and we have rewritten parts of the introduction. Except for corrected typos the other parts of the paper are the same as the original versions

Multiresolution analysis using wavelet, ridgelet, and curvelet transforms for medical image segmentation

Copyright @ 2011 Shadi AlZubi et al. This article has been made available through the Brunel Open Access Publishing Fund.The experimental study presented in this paper is aimed at the development of an automatic image segmentation system for classifying region of interest (ROI) in medical images which are obtained from different medical scanners such as PET, CT, or MRI. Multiresolution analysis (MRA) using wavelet, ridgelet, and curvelet transforms has been used in the proposed segmentation system. It is particularly a challenging task to classify cancers in human organs in scanners output using shape or gray-level information; organs shape changes throw different slices in medical stack and the gray-level intensity overlap in soft tissues. Curvelet transform is a new extension of wavelet and ridgelet transforms which aims to deal with interesting phenomena occurring along curves. Curvelet transforms has been tested on medical data sets, and results are compared with those obtained from the other transforms. Tests indicate that using curvelet significantly improves the classification of abnormal tissues in the scans and reduce the surrounding noise

A nonlinear Stein based estimator for multichannel image denoising

The use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions. However, the observed images are often corrupted by an additive Gaussian noise. In this paper, we are interested in multichannel image denoising based on a multiscale representation of the images. A multivariate statistical approach is adopted to take into account both the spatial and the inter-component correlations existing between the different wavelet subbands. More precisely, we propose a new parametric nonlinear estimator which generalizes many reported denoising methods. The derivation of the optimal parameters is achieved by applying Stein's principle in the multivariate case. Experiments performed on multispectral remote sensing images clearly indicate that our method outperforms conventional wavelet denoising technique

Joint Bilateral Filter for Signal Recovery from Phase Preserved Curvelet Coefficients for Image Denoising

Thresholding of Curvelet Coefficients, for image denoising, drains out subtle signal component in noise subspace. This produces ringing artifacts near edges and granular effect in the denoised image. We found the noise sensitivity of Curvelet phases (in contrast to their magnitude) reduces with higher noise level. Thus, we preserved the phase of the coefficients below threshold at coarser scale and estimated their magnitude by Joint Bilateral Filtering (JBF) technique from the thresholded and noisy coefficients. In the finest scale, we apply Bilateral Filter (BF) to keep edge information. Further, the Guided Image Filter (GIF) is applied on the reconstructed image to localize the edges and to preserve the small image details and textures. The lower noise sensitivity of Curvelet phase at higher noise strength accelerate the performance of proposed method over several state-of-theart techniques and provides comparable outcome at lower noise levels.Comment: 10 pages, 8 figures. 3 tables, journa

Directional edge and texture representations for image processing

An efficient representation for natural images is of fundamental importance in image processing and analysis. The commonly used separable transforms such as wavelets axe not best suited for images due to their inability to exploit directional regularities such as edges and oriented textural patterns; while most of the recently proposed directional schemes cannot represent these two types of features in a unified transform. This thesis focuses on the development of directional representations for images which can capture both edges and textures in a multiresolution manner. The thesis first considers the problem of extracting linear features with the multiresolution Fourier transform (MFT). Based on a previous MFT-based linear feature model, the work extends the extraction method into the situation when the image is corrupted by noise. The problem is tackled by the combination of a "Signal+Noise" frequency model, a refinement stage and a robust classification scheme. As a result, the MFT is able to perform linear feature analysis on noisy images on which previous methods failed. A new set of transforms called the multiscale polar cosine transforms (MPCT) are also proposed in order to represent textures. The MPCT can be regarded as real-valued MFT with similar basis functions of oriented sinusoids. It is shown that the transform can represent textural patches more efficiently than the conventional Fourier basis. With a directional best cosine basis, the MPCT packet (MPCPT) is shown to be an efficient representation for edges and textures, despite its high computational burden. The problem of representing edges and textures in a fixed transform with less complexity is then considered. This is achieved by applying a Gaussian frequency filter, which matches the disperson of the magnitude spectrum, on the local MFT coefficients. This is particularly effective in denoising natural images, due to its ability to preserve both types of feature. Further improvements can be made by employing the information given by the linear feature extraction process in the filter's configuration. The denoising results compare favourably against other state-of-the-art directional representations

水中イメージングシステムのための画質改善に関する研究

Underwater survey systems have numerous scientific or industrial applications in the fields of geology, biology, mining, and archeology. These application fields involve various tasks such as ecological studies, environmental damage assessment, and ancient prospection. During two decades, underwater imaging systems are mainly equipped by Underwater Vehicles (UV) for surveying in water or ocean. Challenges associated with obtaining visibility of objects have been difficult to overcome due to the physical properties of the medium. In the last two decades, sonar is usually used for the detection and recognition of targets in the ocean or underwater environment. However, because of the low quality of images by sonar imaging, optical vision sensors are then used instead of it for short range identification. Optical imaging provides short-range, high-resolution visual information of the ocean floor. However, due to the light transmission’s physical properties in the water medium, the optical imaged underwater images are usually performance as poor visibility. Light is highly attenuated when it travels in the ocean. Consequence, the imaged scenes result as poorly contrasted and hazy-like obstructions. The underwater imaging processing techniques are important to improve the quality of underwater images. As mentioned before, underwater images have poor visibility because of the medium scattering and light distortion. In contrast to common photographs, underwater optical images suffer from poor visibility owing to the medium, which causes scattering, color distortion, and absorption. Large suspended particles cause scattering similar to the scattering of light in fog or turbid water that contain many suspended particles. Color distortion occurs because different wavelengths are attenuated to different degrees in water; consequently, images of ambient in the underwater environments are dominated by a bluish tone, because higher wavelengths are attenuated more quickly. Absorption of light in water substantially reduces its intensity. The random attenuation of light causes a hazy appearance as the light backscattered by water along the line of sight considerably degrades image contrast. Especially, objects at a distance of more than 10 meters from the observation point are almost unreadable because colors are faded as characteristic wavelengths, which are filtered according to the distance traveled by light in water. So, traditional image processing methods are not suitable for processing them well. This thesis proposes strategies and solutions to tackle the above mentioned problems of underwater survey systems. In this thesis, we contribute image pre-processing, denoising, dehazing, inhomogeneities correction, color correction and fusion technologies for underwater image quality improvement. The main content of this thesis is as follows. First, comprehensive reviews of the current and most prominent underwater imaging systems are provided in Chapter 1. A main features and performance based classification criterion for the existing systems is presented. After that, by analyzing the challenges of the underwater imaging systems, a hardware based approach and non-hardware based approach is introduced. In this thesis, we are concerned about the image processing based technologies, which are one of the non-hardware approaches, and take most recent methods to process the low quality underwater images. As the different sonar imaging systems applied in much equipment, such as side-scan sonar, multi-beam sonar. The different sonar acquires different images with different characteristics. Side-scan sonar acquires high quality imagery of the seafloor with very high spatial resolution but poor locational accuracy. On the contrast, multi-beam sonar obtains high precision position and underwater depth in seafloor points. In order to fully utilize all information of these two types of sonars, it is necessary to fuse the two kinds of sonar data in Chapter 2. Considering the sonar image forming principle, for the low frequency curvelet coefficients, we use the maximum local energy method to calculate the energy of two sonar images. For the high frequency curvelet coefficients, we take absolute maximum method as a measurement. The main attributes are: firstly, the multi-resolution analysis method is well adapted the cured-singularities and point-singularities. It is useful for sonar intensity image enhancement. Secondly, maximum local energy is well performing the intensity sonar images, which can achieve perfect fusion result [42]. In Chapter 3, as analyzed the underwater laser imaging system, a Bayesian Contourlet Estimator of Bessel K Form (BCE-BKF) based denoising algorithm is proposed. We take the BCE-BKF probability density function (PDF) to model neighborhood of contourlet coefficients. After that, according to the proposed PDF model, we design a maximum a posteriori (MAP) estimator, which relies on a Bayesian statistics representation of the contourlet coefficients of noisy images. The denoised laser images have better contrast than the others. There are three obvious virtues of the proposed method. Firstly, contourlet transform decomposition prior to curvelet transform and wavelet transform by using ellipse sampling grid. Secondly, BCE-BKF model is more effective in presentation of the noisy image contourlet coefficients. Thirdly, the BCE-BKF model takes full account of the correlation between coefficients [107]. In Chapter 4, we describe a novel method to enhance underwater images by dehazing. In underwater optical imaging, absorption, scattering, and color distortion are three major issues in underwater optical imaging. Light rays traveling through water are scattered and absorbed according to their wavelength. Scattering is caused by large suspended particles that degrade optical images captured underwater. Color distortion occurs because different wavelengths are attenuated to different degrees in water; consequently, images of ambient underwater environments are dominated by a bluish tone. Our key contribution is to propose a fast image and video dehazing algorithm, to compensate the attenuation discrepancy along the propagation path, and to take the influence of the possible presence of an artificial lighting source into consideration [108]. In Chapter 5, we describe a novel method of enhancing underwater optical images or videos using guided multilayer filter and wavelength compensation. In certain circumstances, we need to immediately monitor the underwater environment by disaster recovery support robots or other underwater survey systems. However, due to the inherent optical properties and underwater complex environment, the captured images or videos are distorted seriously. Our key contributions proposed include a novel depth and wavelength based underwater imaging model to compensate for the attenuation discrepancy along the propagation path and a fast guided multilayer filtering enhancing algorithm. The enhanced images are characterized by a reduced noised level, better exposure of the dark regions, and improved global contrast where the finest details and edges are enhanced significantly [109]. The performance of the proposed approaches and the benefits are concluded in Chapter 6. Comprehensive experiments and extensive comparison with the existing related techniques demonstrate the accuracy and effect of our proposed methods.九州工業大学博士学位論文 学位記番号:工博甲第367号　学位授与年月日:平成26年3月25日CHAPTER 1 INTRODUCTION|CHAPTER 2 MULTI-SOURCE IMAGES FUSION|CHAPTER 3 LASER IMAGES DENOISING|CHAPTER 4 OPTICAL IMAGE DEHAZING|CHAPTER 5 SHALLOW WATER DE-SCATTERING|CHAPTER 6 CONCLUSIONS九州工業大学平成25年