232 research outputs found
Skellam shrinkage: Wavelet-based intensity estimation for inhomogeneous Poisson data
The ubiquity of integrating detectors in imaging and other applications
implies that a variety of real-world data are well modeled as Poisson random
variables whose means are in turn proportional to an underlying vector-valued
signal of interest. In this article, we first show how the so-called Skellam
distribution arises from the fact that Haar wavelet and filterbank transform
coefficients corresponding to measurements of this type are distributed as sums
and differences of Poisson counts. We then provide two main theorems on Skellam
shrinkage, one showing the near-optimality of shrinkage in the Bayesian setting
and the other providing for unbiased risk estimation in a frequentist context.
These results serve to yield new estimators in the Haar transform domain,
including an unbiased risk estimate for shrinkage of Haar-Fisz
variance-stabilized data, along with accompanying low-complexity algorithms for
inference. We conclude with a simulation study demonstrating the efficacy of
our Skellam shrinkage estimators both for the standard univariate wavelet test
functions as well as a variety of test images taken from the image processing
literature, confirming that they offer substantial performance improvements
over existing alternatives.Comment: 27 pages, 8 figures, slight formatting changes; submitted for
publicatio
Bayesian Image Analysis in Fourier Space
Bayesian image analysis has played a large role over the last 40+ years in
solving problems in image noise-reduction, de-blurring, feature enhancement,
and object detection. However, these problems can be complex and lead to
computational difficulties, due to the modeled interdependence between spatial
locations. The Bayesian image analysis in Fourier space (BIFS) approach
proposed here reformulates the conventional Bayesian image analysis paradigm
for continuous valued images as a large set of independent (but heterogeneous)
processes over Fourier space. The original high-dimensional estimation problem
in image space is thereby broken down into (trivially parallelizable)
independent one-dimensional problems in Fourier space. The BIFS approach leads
to easy model specification with fast and direct computation, a wide range of
possible prior characteristics, easy modeling of isotropy into the prior, and
models that are effectively invariant to changes in image resolution.Comment: 26 pages, 9 figure
A Tutorial on Speckle Reduction in Synthetic Aperture Radar Images
Speckle is a granular disturbance, usually modeled as a multiplicative noise, that affects synthetic aperture radar (SAR) images, as well as all coherent images. Over the last three decades, several methods have been proposed for the reduction of speckle, or despeckling, in SAR images. Goal of this paper is making a comprehensive review of despeckling methods since their birth, over thirty years ago, highlighting trends and changing approaches over years. The concept of fully developed speckle is explained. Drawbacks of homomorphic filtering are pointed out. Assets of multiresolution despeckling, as opposite to spatial-domain despeckling, are highlighted. Also advantages of undecimated, or stationary, wavelet transforms over decimated ones are discussed. Bayesian estimators and probability density function (pdf) models in both spatial and multiresolution domains are reviewed. Scale-space varying pdf models, as opposite to scale varying models, are promoted. Promising methods following non-Bayesian approaches, like nonlocal (NL) filtering and total variation (TV) regularization, are reviewed and compared to spatial- and wavelet-domain Bayesian filters. Both established and new trends for assessment of despeckling are presented. A few experiments on simulated data and real COSMO-SkyMed SAR images highlight, on one side the costperformance tradeoff of the different methods, on the other side the effectiveness of solutions purposely designed for SAR heterogeneity and not fully developed speckle. Eventually, upcoming methods based on new concepts of signal processing, like compressive sensing, are foreseen as a new generation of despeckling, after spatial-domain and multiresolution-domain method
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Variational Bayesian image restoration with group-sparse modeling of wavelet coefficients
In this work, we present a recent wavelet-based image restoration framework based on a group-sparse Gaussian scale mixture model. A hierarchical Bayesian estimation is derived using a combination of variational Bayesian inference and a subband-adaptive majorization–minimization method that simplifies computation of the posterior distribution. We show that both of these iterative methods can converge together without needing nested loops, and thus good solutions can be found rapidly in the non-convex search space. We also integrate our method, variational Bayesian with majorization minimization (VBMM), with tree-structured modeling of the wavelet coefficients. This extension achieves significant gains in performance over the coefficient-sparse version of the algorithm. The experimental results demonstrate that the proposed method and its tree-structured extensions are effective for various imaging applications such as image deconvolution, image superresolution and compressive sensing magnetic resonance imaging (MRI) reconstruction, and that they outperform more conventional sparsity-inducing methods based on the _l1-norm.This is the author accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S1051200415001438
Bayesian Estimation for Continuous-Time Sparse Stochastic Processes
We consider continuous-time sparse stochastic processes from which we have
only a finite number of noisy/noiseless samples. Our goal is to estimate the
noiseless samples (denoising) and the signal in-between (interpolation
problem).
By relying on tools from the theory of splines, we derive the joint a priori
distribution of the samples and show how this probability density function can
be factorized. The factorization enables us to tractably implement the maximum
a posteriori and minimum mean-square error (MMSE) criteria as two statistical
approaches for estimating the unknowns. We compare the derived statistical
methods with well-known techniques for the recovery of sparse signals, such as
the norm and Log (- relaxation) regularization
methods. The simulation results show that, under certain conditions, the
performance of the regularization techniques can be very close to that of the
MMSE estimator.Comment: To appear in IEEE TS
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
A CURE for noisy magnetic resonance images: Chi-square unbiased risk estimation
In this article we derive an unbiased expression for the expected
mean-squared error associated with continuously differentiable estimators of
the noncentrality parameter of a chi-square random variable. We then consider
the task of denoising squared-magnitude magnetic resonance image data, which
are well modeled as independent noncentral chi-square random variables on two
degrees of freedom. We consider two broad classes of linearly parameterized
shrinkage estimators that can be optimized using our risk estimate, one in the
general context of undecimated filterbank transforms, and another in the
specific case of the unnormalized Haar wavelet transform. The resultant
algorithms are computationally tractable and improve upon state-of-the-art
methods for both simulated and actual magnetic resonance image data.Comment: 30 double-spaced pages, 11 figures; submitted for publicatio
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