Parameter Identification of Image Models by the Recursive Maximum Likelihood Method

This paper considers the problem of identifying the blur parameters of the observed image. It is assumed that the original image is a sample from the homogeneous random field described by a two-dimensional (2-D) semicausal model, and that the point spread function (PSF) characterizing the image blur is symmetric. It is also assumed that the observation noise is negligibly small. By applying the discrete sine transform, we derive a set of nearly uncorrelated ARMA models, which are of non-minimum phase, for the blurred image. Although all-pass components of the MA part of the models can not be estimated, we show that the parameters of the non-minimum phase MA part can be restored by exploiting the fact that the PSF is symmetric. We develop a new algorithm for identifying the blur parameters of the image model from the MA parameters estimated by the recursive maximum likelihood (RML) method. Simulation studies are also included to show the feasibility of the algorithm

Blur Identification Based on Higher Order Spectral Nulls

The identification of the point spread function (PSF) from the degraded image data constitutes an important first step in image restoration that is known as blur identification. Though a number of blur identification algorithms have been developed in recent years, two of the earlier methods based on the power spectrum and power cepstrum remain popular, because they are easy to implement and have proved to be effective in practical situations. Both methods are limited to PSF\u27s which exhibit spectral nulls, such as due to defocused lens and linear motion blur. Another limitation of these methods is the degradation of their performance in the presence of observation noise. The central slice of the power bispectrum has been employed as an alternative to the power spectrum which can suppress the effects of additive Gaussian noise. In this paper, we utilize the bicepstrum for the identification of linear motion and defocus blurs. We present simulation results where the performance of the blur identification methods based on the spectrum, the cepstrum, the bispectrum and the bicepstrum is compared for different blur sizes and signal-to-noise ratio levels

Restoration of Atmospheric Turbulence Degraded Video using Kurtosis Minimization and Motion Compensation

In this thesis work, the background of atmospheric turbulence degradation in imaging was reviewed and two aspects are highlighted: blurring and geometric distortion. The turbulence burring parameter is determined by the atmospheric turbulence condition that is often unknown; therefore, a blur identification technique was developed that is based on a higher order statistics (HOS). It was observed that the kurtosis generally increases as an image becomes blurred (smoothed). Such an observation was interpreted in the frequency domain in terms of phase correlation. Kurtosis minimization based blur identification is built upon this observation. It was shown that kurtosis minimization is effective in identifying the blurring parameter directly from the degraded image. Kurtosis minimization is a general method for blur identification. It has been tested on a variety of blurs such as Gaussian blur, out of focus blur as well as motion blur. To compensate for the geometric distortion, earlier work on the turbulent motion compensation was extended to deal with situations in which there is camera/object motion. Trajectory smoothing is used to suppress the turbulent motion while preserving the real motion. Though the scintillation effect of atmospheric turbulence is not considered separately, it can be handled the same way as multiple frame denoising while motion trajectories are built.Ph.D.Committee Chair: Mersereau, Russell; Committee Co-Chair: Smith, Mark; Committee Member: Lanterman, Aaron; Committee Member: Wang, May; Committee Member: Tannenbaum, Allen; Committee Member: Williams, Dougla

Parameters Estimation For Image Restoration

Image degradation generally occurs due to transmission channel error, camera mis-focus, atmospheric turbulence, relative object-camera motion, etc. Such degradations are unavoidable while a scene is captured through a camera. As degraded images are having less scientific values, restoration of such images is extremely essential in many practical applications. In this thesis, attempts have been made to recover images from their degraded observations. Various degradations including, out-of-focus blur, motion blur, atmospheric turbulence blur along with Gaussian noise are considered. Basically image restoration schemes are based on classical, regularisation parameter estimation and PSF estimation. In this thesis, five different contributions have been made based on various aspects of restoration. Four of them deal with spatial invariant degradation and in one of the approach we attempt for removal of spatial variant degradation. Two different schemes are proposed to estimate the motion blur parameters. Two dimensional Gabor filter has been used to calculate the direction of the blur. Radial basis function neural network (RBFNN) has been utilised to find the length of the blur. Subsequently, Wiener filter has been used to restore the images. Noise robustness of the proposed scheme is tested with different noise strengths. The blur parameter estimation problem is modelled as a pattern classification problem and is solved using support vector machine (SVM). The length parameter of motion blur and sigma (σ) parameter of Gaussian blur are identified through multi-class SVM. Support vector regression (SVR) has been utilised to obtain a true mapping of the images from the observed noisy blurred image. The parameters in SVR play a key role in SVR performance and these are optimised through particle swarm optimisation (PSO) technique. The optimised SVR model is used to restore the noisy blurred images. Blur in the presence of noise makes the restoration problem ill-conditioned. The regularisation parameter required for restoration of noisy blurred image is discussed and for the purpose, a global optimisation scheme namely PSO is utilisedto minimise the cost function of generalised cross validation (GCV) measure, which is dependent on regularisation parameter. This eliminates the problem of falling into a local minima. The scheme adapts to degradations due to motion and out-of-focus blur, associated with noise of varying strengths. In another contribution, an attempt has been made to restore images degraded due to rotational motion. Such situation is considered as spatial variant blur and handled by considering this as a combination of a number of spatial invariant blurs. The proposed scheme divides the blurred image into a number of images using elliptical path modelling. Each image is deblurred separately using Wiener filter and finally integrated to construct the whole image. Each model is studied separately, and experiments are conducted to evaluate their performances. The visual as well as the peak signal to noise ratio (PSNR in dB) of restored images are compared with competent recent schemes

Blind image deconvolution: nonstationary Bayesian approaches to restoring blurred photos

High quality digital images have become pervasive in modern scientific and everyday life — in areas from photography to astronomy, CCTV, microscopy, and medical imaging. However there are always limits to the quality of these images due to uncertainty and imprecision in the measurement systems. Modern signal processing methods offer the promise of overcoming some of these problems by postprocessing these blurred and noisy images. In this thesis, novel methods using nonstationary statistical models are developed for the removal of blurs from out of focus and other types of degraded photographic images. The work tackles the fundamental problem blind image deconvolution (BID); its goal is to restore a sharp image from a blurred observation when the blur itself is completely unknown. This is a “doubly illposed” problem — extreme lack of information must be countered by strong prior constraints about sensible types of solution. In this work, the hierarchical Bayesian methodology is used as a robust and versatile framework to impart the required prior knowledge. The thesis is arranged in two parts. In the first part, the BID problem is reviewed, along with techniques and models for its solution. Observation models are developed, with an emphasis on photographic restoration, concluding with a discussion of how these are reduced to the common linear spatially-invariant (LSI) convolutional model. Classical methods for the solution of illposed problems are summarised to provide a foundation for the main theoretical ideas that will be used under the Bayesian framework. This is followed by an indepth review and discussion of the various prior image and blur models appearing in the literature, and then their applications to solving the problem with both Bayesian and nonBayesian techniques. The second part covers novel restoration methods, making use of the theory presented in Part I. Firstly, two new nonstationary image models are presented. The first models local variance in the image, and the second extends this with locally adaptive noncausal autoregressive (AR) texture estimation and local mean components. These models allow for recovery of image details including edges and texture, whilst preserving smooth regions. Most existing methods do not model the boundary conditions correctly for deblurring of natural photographs, and a Chapter is devoted to exploring Bayesian solutions to this topic. Due to the complexity of the models used and the problem itself, there are many challenges which must be overcome for tractable inference. Using the new models, three different inference strategies are investigated: firstly using the Bayesian maximum marginalised a posteriori (MMAP) method with deterministic optimisation; proceeding with the stochastic methods of variational Bayesian (VB) distribution approximation, and simulation of the posterior distribution using the Gibbs sampler. Of these, we find the Gibbs sampler to be the most effective way to deal with a variety of different types of unknown blurs. Along the way, details are given of the numerical strategies developed to give accurate results and to accelerate performance. Finally, the thesis demonstrates state of the art results in blind restoration of synthetic and real degraded images, such as recovering details in out of focus photographs

Self-correcting multi-channel Bussgang blind deconvolution using expectation maximization (EM) algorithm and feedback

A Bussgang based blind deconvolution algorithm called self-correcting multi-channel Bussgang (SCMB) blind deconvolution algorithm was proposed. Unlike the original Bussgang blind deconvolution algorithm where the probability density function (pdf) of the signal being recovered is assumed to be completely known, the proposed SCMB blind deconvolution algorithm relaxes this restriction by parameterized the pdf with a Gaussian mixture model and expectation maximization (EM) algorithm, an iterative maximum likelihood approach, is employed to estimate the parameter side by side with the estimation of the equalization filters of the original Bussgang blind deconvolution algorithm. A feedback loop is also designed to compensate the effect of the parameter estimation error on the estimation of the equalization filters. Application of the SCMB blind deconvolution framework for binary image restoration, multi-pass synthetic aperture radar (SAR) autofocus and inverse synthetic aperture radar (ISAR) autofocus are exploited with great results.Ph.D.Committee Chair: Dr. Russell Mersereau; Committee Member: Dr. Doug Willams; Committee Member: Dr. Mark Richards; Committee Member: Dr. Xiaoming Huo; Committee Member: Dr. Ye (Geoffrey) L

Image Restoration

This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with

Motion deblurring for optical character recognition

Master'sMASTER OF SCIENC