Efficient methodologies for real-time image restoration

In this thesis we investigate the problem of image restoration. The main focus of our research is to come up with novel algorithms and enhance existing techniques in order to deliver efficient and effective methodologies, applicable in real-time image restoration scenarios. Our research starts with a literature review, which identifies the gaps in existing techniques and helps us to come up with a novel classification on image restoration, which integrates and discusses more recent developments in the area of image restoration. With this novel classification, we identified three major areas which need our attention. The first developments relate to non-blind image restoration. The two mostly used techniques, namely deterministic linear algorithms and stochastic nonlinear algorithms are compared and contrasted. Under deterministic linear algorithms, we develop a class of more effective novel quadratic linear regularization models, which outperform the existing linear regularization models. In addition, by looking in a new perspective, we evaluate and compare the performance of deterministic and stochastic restoration algorithms and explore the validity of the performance claims made so far on those algorithms. Further, we critically challenge the ne- cessity of some complex mechanisms in Maximum A Posteriori (MAP) technique under stochastic image deconvolution algorithms. The next developments are focussed in blind image restoration, which is claimed to be more challenging. Constant Modulus Algorithm (CMA) is one of the most popular, computationally simple, tested and best performing blind equalization algorithms in the signal processing domain. In our research, we extend the use of CMA in image restoration and develop a broad class of blind image deconvolution algorithms, in particular algorithms for blurring kernels with a separable property. These algorithms show significantly faster convergence than conventional algorithms. Although CMA method has a proven record in signal processing applications related to data communications systems, no research has been carried out to the investigation of the applicability of CMA for image restoration in practice. In filling this gap and taking into account the differences of signal processing in im- age processing and data communications contexts, we extend our research on the applicability of CMA deconvolution under the assumptions on the ground truth image properties. Through analyzing the main assumptions of ground truth image properties being zero-mean, independent and uniformly distributed, which char- acterize the convergence of CMA deconvolution, we develop a novel technique to overcome the effects of image source correlation based on segmentation and higher order moments of the source. Multichannel image restoration techniques recently gained much attention over the single channel image restoration due to the benefits of diversity and redundancy of the information between the channels. Exploiting these benefits in real time applications is often restricted due to the unavailability of multiple copies of the same image. In order to overcome this limitation, as the last area of our research, we develop a novel multichannel blind restoration model with a single image, which eliminates the constraint of the necessity of multiple copies of the blurred image. We consider this as a major contribution which could be extended to wider areas of research integrated with multiple disciplines such as demosaicing

Statistical Methods for Polarimetric Imagery

Estimation theory is applied to a physical model of incoherent polarized light to address problems in polarimetric image registration, restoration, and analysis for electro-optical imaging systems. In the image registration case, the Cramer-Rao lower bound on unbiased joint estimates of the registration parameters and the underlying scene is derived, simplified using matrix methods, and used to explain the behavior of multi-channel linear polarimetric imagers. In the image restoration case, a polarimetric maximum likelihood blind deconvolution algorithm is derived and tested using laboratory and simulated imagery. Finally, a principal components analysis is derived for polarization imaging systems. This analysis expands upon existing research by including an allowance for partially polarized and unpolarized light

Blind Two-Dimensional Super-Resolution and Its Performance Guarantee

In this work, we study the problem of identifying the parameters of a linear system from its response to multiple unknown input waveforms. We assume that the system response, which is the only given information, is a scaled superposition of time-delayed and frequency-shifted versions of the unknown waveforms. Such kind of problem is severely ill-posed and does not yield a unique solution without introducing further constraints. To fully characterize the linear system, we assume that the unknown waveforms lie in a common known low-dimensional subspace that satisfies certain randomness and concentration properties. Then, we develop a blind two-dimensional (2D) super-resolution framework that applies to a large number of applications such as radar imaging, image restoration, and indoor source localization. In this framework, we show that under a minimum separation condition between the time-frequency shifts, all the unknowns that characterize the linear system can be recovered precisely and with very high probability provided that a lower bound on the total number of the observed samples is satisfied. The proposed framework is based on 2D atomic norm minimization problem which is shown to be reformulated and solved efficiently via semidefinite programming. Simulation results that confirm the theoretical findings of the paper are provided