Contourlet Domain Image Modeling and its Applications in Watermarking and Denoising

Statistical image modeling in sparse domain has recently attracted a great deal of research interest. Contourlet transform as a two-dimensional transform with multiscale and multi-directional properties is known to effectively capture the smooth contours and geometrical structures in images. The objective of this thesis is to study the statistical properties of the contourlet coefficients of images and develop statistically-based image denoising and watermarking schemes. Through an experimental investigation, it is first established that the distributions of the contourlet subband coefficients of natural images are significantly non-Gaussian with heavy-tails and they can be best described by the heavy-tailed statistical distributions, such as the alpha-stable family of distributions. It is shown that the univariate members of this family are capable of accurately fitting the marginal distributions of the empirical data and that the bivariate members can accurately characterize the inter-scale dependencies of the contourlet coefficients of an image. Based on the modeling results, a new method in image denoising in the contourlet domain is proposed. The Bayesian maximum a posteriori and minimum mean absolute error estimators are developed to determine the noise-free contourlet coefficients of grayscale and color images. Extensive experiments are conducted using a wide variety of images from a number of databases to evaluate the performance of the proposed image denoising scheme and to compare it with that of other existing schemes. It is shown that the proposed denoising scheme based on the alpha-stable distributions outperforms these other methods in terms of the peak signal-to-noise ratio and mean structural similarity index, as well as in terms of visual quality of the denoised images. The alpha-stable model is also used in developing new multiplicative watermark schemes for grayscale and color images. Closed-form expressions are derived for the log-likelihood-based multiplicative watermark detection algorithm for grayscale images using the univariate and bivariate Cauchy members of the alpha-stable family. A multiplicative multichannel watermark detector is also designed for color images using the multivariate Cauchy distribution. Simulation results demonstrate not only the effectiveness of the proposed image watermarking schemes in terms of the invisibility of the watermark, but also the superiority of the watermark detectors in providing detection rates higher than that of the state-of-the-art schemes even for the watermarked images undergone various kinds of attacks

Effective SAR image despeckling based on bandlet and SRAD

Despeckling of a SAR image without losing features of the image is a daring task as it is intrinsically affected by multiplicative noise called speckle. This thesis proposes a novel technique to efficiently despeckle SAR images. Using an SRAD filter, a Bandlet transform based filter and a Guided filter, the speckle noise in SAR images is removed without losing the features in it. Here a SAR image input is given parallel to both SRAD and Bandlet transform based filters. The SRAD filter despeckles the SAR image and the despeckled output image is used as a reference image for the guided filter. In the Bandlet transform based despeckling scheme, the input SAR image is first decomposed using the bandlet transform. Then the coefficients obtained are thresholded using a soft thresholding rule. All coefficients other than the low-frequency ones are so adjusted. The generalized cross-validation (GCV) technique is employed here to find the most favorable threshold for each subband. The bandlet transform is able to extract edges and fine features in the image because it finds the direction where the function gives maximum value and in the same direction it builds extended orthogonal vectors. Simple soft thresholding using an optimum threshold despeckles the input SAR image. The guided filter with the help of a reference image removes the remaining speckle from the bandlet transform output. In terms of numerical and visual quality, the proposed filtering scheme surpasses the available despeckling schemes

Wavelet Domain Watermark Detection and Extraction using the Vector-based Hidden Markov Model

Multimedia data piracy is a growing problem in view of the ease and simplicity provided by the internet in transmitting and receiving such data. A possible solution to preclude unauthorized duplication or distribution of digital data is watermarking. Watermarking is an identifiable piece of information that provides security against multimedia piracy. This thesis is concerned with the investigation of various image watermarking schemes in the wavelet domain using the statistical properties of the wavelet coefficients. The wavelet subband coefficients of natural images have significantly non-Gaussian and heavy-tailed features that are best described by heavy-tailed distributions. Moreover the wavelet coefficients of images have strong inter-scale and inter-orientation dependencies. In view of this, the vector-based hidden Markov model is found to be best suited to characterize the wavelet coefficients. In this thesis, this model is used to develop new digital image watermarking schemes. Additive and multiplicative watermarking schemes in the wavelet domain are developed in order to provide improved detection and extraction of the watermark. Blind watermark detectors using log-likelihood ratio test, and watermark decoders using the maximum likelihood criterion to blindly extract the embedded watermark bits from the observation data are designed. Extensive experiments are conducted throughout this thesis using a number of databases selected from a wide variety of natural images. Simulation results are presented to demonstrate the effectiveness of the proposed image watermarking scheme and their superiority over some of the state-of-the-art techniques. It is shown that in view of the use of the hidden Markov model characterize the distributions of the wavelet coefficients of images, the proposed watermarking algorithms result in higher detection and decoding rates both before and after subjecting the watermarked image to various kinds of attacks

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

Advancements and Breakthroughs in Ultrasound Imaging

Ultrasonic imaging is a powerful diagnostic tool available to medical practitioners, engineers and researchers today. Due to the relative safety, and the non-invasive nature, ultrasonic imaging has become one of the most rapidly advancing technologies. These rapid advances are directly related to the parallel advancements in electronics, computing, and transducer technology together with sophisticated signal processing techniques. This book focuses on state of the art developments in ultrasonic imaging applications and underlying technologies presented by leading practitioners and researchers from many parts of the world

Convergence Rates of Stochastic Gradient Descent under Infinite Noise Variance

Recent studies have provided both empirical and theoretical evidence illustrating that heavy tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy tails potentially result in iterates with diverging variance, which hinders the use of conventional convergence analysis techniques that rely on the existence of the second-order moments. In this paper, we provide convergence guarantees for SGD under a state-dependent and heavy-tailed noise with a potentially infinite variance, for a class of strongly convex objectives. In the case where the $p$-th moment of the noise exists for some $p\in [1,2)$, we first identify a condition on the Hessian, coined '$p$-positive (semi-)definiteness', that leads to an interesting interpolation between positive semi-definite matrices ($p=2$) and diagonally dominant matrices with non-negative diagonal entries ($p=1$). Under this condition, we then provide a convergence rate for the distance to the global optimum in $L^p$. Furthermore, we provide a generalized central limit theorem, which shows that the properly scaled Polyak-Ruppert averaging converges weakly to a multivariate $\alpha$-stable random vector. Our results indicate that even under heavy-tailed noise with infinite variance, SGD can converge to the global optimum without necessitating any modification neither to the loss function or to the algorithm itself, as typically required in robust statistics. We demonstrate the implications of our results to applications such as linear regression and generalized linear models subject to heavy-tailed data

Remote Sensing of the Oceans

This book covers different topics in the framework of remote sensing of the oceans. Latest research advancements and brand-new studies are presented that address the exploitation of remote sensing instruments and simulation tools to improve the understanding of ocean processes and enable cutting-edge applications with the aim of preserving the ocean environment and supporting the blue economy. Hence, this book provides a reference framework for state-of-the-art remote sensing methods that deal with the generation of added-value products and the geophysical information retrieval in related fields, including: Oil spill detection and discrimination; Analysis of tropical cyclones and sea echoes; Shoreline and aquaculture area extraction; Monitoring coastal marine litter and moving vessels; Processing of SAR, HF radar and UAV measurements