Usually, image compression techniques that use only one transform exhibit some poor properties. For instance, the Discrete Cosine Transform (DCT) cannot efficiently represent high frequency components, resulting in blurred images. The Multiple Bases Representation (MBR) compression technique, which uses two or more transforms, is found to be superior to the single transform techniques in terms of representation efficiency. However, some bits in the MBR representation are needed to track the basis information. The MBR image quality is deteriorated by discontinuities at block boundaries, as is the standard DCT transform. In this thesis, test images are distorted by MBR compression using a Recursive Residual Projection algorithm. This algorithm is a sub-optimal method to find the best basis vector subset for representing images based on multiple orthogonal bases. The MBR distorted images are reconstructed by the iterative method of Projection onto Convex Sets (POCS). Many constraints that form convex sets are reviewed and examined. Due to the high distortion at the block boundaries, some constraints are introduced particularly to reduce artifacts at the boundaries. Some constraints add energy to the reconstructed images while others remove energy. Thus, the initial vectors play a key role in the performance of the POCS method for better MBR reconstruction. This thesis also determines the most appropriate initial vector for each constraint. Finally, the composite projections associated with the sign, minimum decreasing and norm-of-slope constraints are used to improve the reconstruction of the MBR distorted images and the effect of ordering of the projections is investigated. / Master of Science

Due to the vast success of bioengineering techniques, a series of large-scale analysis tools has been developed to discover the functional organization of cells. Among them, cDNA microarray has emerged as a powerful technology that enables biologists to cDNA microarray technology has enabled biologists to study thousands of genes simultaneously within an entire organism, and thus obtain a better understanding of the gene interaction and regulation mechanisms involved. Although microarray technology has been developed so as to offer high tolerances, there exists high signal irregularity through the surface of the microarray image. The imperfection in the microarray image generation process causes noises of many types, which contaminate the resulting image. These errors and noises will propagate down through, and can significantly affect, all subsequent processing and analysis. Therefore, to realize the potential of such technology it is crucial to obtain high quality image data that would indeed reflect the underlying biology in the samples. One of the key steps in extracting information from a microarray image is segmentation: identifying which pixels within an image represent which gene. This area of spotted microarray image analysis has received relatively little attention relative to the advances in proceeding analysis stages. But, the lack of advanced image analysis, including the segmentation, results in sub-optimal data being used in all downstream analysis methods. Although there is recently much research on microarray image analysis with many methods have been proposed, some methods produce better results than others. In general, the most effective approaches require considerable run time (processing) power to process an entire image. Furthermore, there has been little progress on developing sufficiently fast yet efficient and effective algorithms the segmentation of the microarray image by using a highly sophisticated framework such as Cellular Neural Networks (CNNs). It is, therefore, the aim of this thesis to investigate and develop novel methods processing microarray images. The goal is to produce results that outperform the currently available approaches in terms of PSNR, k-means and ICC measurements.

published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

Magnetic resonance imaging (MRI) is a highly exible and non-invasive medical imaging modality based on the concept of nuclear magnetic resonance (NMR). Compared to other imaging techniques, major limitation of MRI is the relatively long acquisition time. The slowness of acquisition makes MRI difficult to apply to time-sensitive clinical applications. Acquisition of MRA images with a spatial resolution close to conventional digital subtraction angiography is feasible, but at the expense of reduction in temporal resolution. Parallel MRI employs multiple receiver coils to speed up the MRI acquisition by reducing the number of data points collected. Although, the reconstructed images from undersampled data sets often suffer from different different types of degradation and artifacts. In contrast-enhanced magnetic resonance imaging, information is effectively measured in 3D k-space one line at a time therefore the 3D data acquisition extends over several minutes even using parallel receiver coils. This limits the assessment of high ow lesions and some vascular tumors in patients. To improve spatio-temporal resolution in contrast enhanced magnetic resonance angiography (CE-MRA), the use of incorporating prior knowledge in the image recovery process is considered in this thesis. There are five contributions in this thesis. The first contribution is the modification of generalized unaliasing using support and sensitivity encoding (GUISE). GUISE was introduced by this group to explore incorporating prior knowledge of the image to be reconstructed in parallel MRI. In order to provide improved time-resolved MRA image sequences of the blood vessels, the GUISE method requires an accurate segmentation of the relatively noisy 3D data set into vessel and background. The method that was originally used for definition of the effective region of support was primitive and produced a segmented image with much false detection because of the effect of overlying structures and the relatively noisy background in images. We proposed to use the statistical principle as employed for the modified maximum intensity projection (MIP) to achieve better 3D segmentation and optimal visualization of blood vessels. In comparison with the previous region of support (ROS), the new one enables higher accelerations MRA reconstructions due to the decreased volume of the ROS and leads to less computationally expensive reconstruction. In the second contribution we demonstrated the impact of imposing the Karhunen-Loeve transform (KLT) basis for the temporal changes, based on prior expectation of the changes in contrast concentration with time. In contrast with other transformation, KLT of the temporal variation showed a better contrast to noise ratio (CNR) can be achieved. By incorporating a data ordering step with compressed sensing (CS), an improvement in image quality for reconstructing parallel MR images was exhibited in prior estimate based compressed sensing (PECS). However, this method required a prior estimate of the image to be available. A singular value decomposition (SVD) modification of PECS algorithm (SPECS) to explore ways of utilising the data ordering step without requiring a prior estimate was extended as the third contribution. By employing singular value decomposition as the sparsifying transform in the CS algorithm, the recovered image was used to derive the data ordering in PECS. The preliminary results outperformed the PECS results. The fourth contribution is a novel approach for training a dictionary for sparse recovery in CE-MRA. The experimental results demonstrate improved reconstructions on clinical undersampled dynamic images. A new method recently has been developed to exploit the structure of the signal in sparse representation. Group sparse compressed sensing (GSCS) allows the efficient reconstruction of signals whose support is contained in the union of a small number of groups (sets) from a collection of pre-defined disjoint groups. Exploiting CS applications in dynamic MR imaging, a group sparse method was introduced for our contrast-enhanced data set. Instead of incorporating data ordering resulted from prior information, pre-defined sparsity patterns were used in the PECS recovery algorithm, resulting to a suppression of noise in the reconstruction.

Cao Liangliang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 64-69). / Abstracts in English and Chinese. / Chapter 1 --- Introduction and Related Work --- p.1 / Chapter 1.1 --- Reconstruction from Single Line Drawings and the Applications --- p.1 / Chapter 1.2 --- Optimization-based Reconstruction --- p.2 / Chapter 1.3 --- Other Reconstruction Methods --- p.2 / Chapter 1.3.1 --- Line Labeling and Algebraic Methods --- p.2 / Chapter 1.3.2 --- CAD Reconstruction --- p.3 / Chapter 1.3.3 --- Modelling from Images --- p.3 / Chapter 1.4 --- Finding Faces of Line Drawings --- p.4 / Chapter 1.5 --- Generalized Cylinder --- p.4 / Chapter 1.6 --- Research Problems and Our Contribution --- p.5 / Chapter 1.6.1 --- A New Criteria --- p.5 / Chapter 1.6.2 --- Recover Objects from Line Drawings without Hidden Lines --- p.6 / Chapter 1.6.3 --- Reconstruction of Curved Objects --- p.6 / Chapter 1.6.4 --- Planar Limbs Assumption and the Derived Models --- p.6 / Chapter 2 --- A New Criteria for Reconstruction --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- Human Visual Perception and the Symmetry Measure --- p.10 / Chapter 2.3 --- Reconstruction Based on Symmetry and Planarity --- p.11 / Chapter 2.3.1 --- Finding Faces --- p.11 / Chapter 2.3.2 --- Constraint of Planarity --- p.11 / Chapter 2.3.3 --- Objective Function --- p.12 / Chapter 2.3.4 --- Reconstruction Algorithm --- p.13 / Chapter 2.4 --- Experimental Results --- p.13 / Chapter 2.5 --- Summary --- p.18 / Chapter 3 --- Line Drawings without Hidden Lines: Inference and Reconstruction --- p.19 / Chapter 3.1 --- Introduction --- p.19 / Chapter 3.2 --- Terminology --- p.20 / Chapter 3.3 --- Theoretical Inference of the Hidden Topological Structure --- p.21 / Chapter 3.3.1 --- Assumptions --- p.21 / Chapter 3.3.2 --- Finding the Degrees and Ranks --- p.22 / Chapter 3.3.3 --- Constraints for the Inference --- p.23 / Chapter 3.4 --- An Algorithm to Recover the Hidden Topological Structure --- p.25 / Chapter 3.4.1 --- Outline of the Algorithm --- p.26 / Chapter 3.4.2 --- Constructing the Initial Hidden Structure --- p.26 / Chapter 3.4.3 --- Reducing Initial Hidden Structure --- p.27 / Chapter 3.4.4 --- Selecting the Most Plausible Structure --- p.28 / Chapter 3.5 --- Reconstruction of 3D Objects --- p.29 / Chapter 3.6 --- Experimental Results --- p.32 / Chapter 3.7 --- Summary --- p.32 / Chapter 4 --- Curved Objects Reconstruction from 2D Line Drawings --- p.35 / Chapter 4.1 --- Introduction --- p.35 / Chapter 4.2 --- Related Work --- p.36 / Chapter 4.2.1 --- Face Identification --- p.36 / Chapter 4.2.2 --- 3D Reconstruction of planar objects --- p.37 / Chapter 4.3 --- Reconstruction of Curved Objects --- p.37 / Chapter 4.3.1 --- Transformation of Line Drawings --- p.37 / Chapter 4.3.2 --- Finding 3D Bezier Curves --- p.39 / Chapter 4.3.3 --- Bezier Surface Patches and Boundaries --- p.40 / Chapter 4.3.4 --- Generating Bezier Surface Patches --- p.41 / Chapter 4.4 --- Results --- p.43 / Chapter 4.5 --- Summary --- p.45 / Chapter 5 --- Planar Limbs and Degen Generalized Cylinders --- p.47 / Chapter 5.1 --- Introduction --- p.47 / Chapter 5.2 --- Planar Limbs and View Directions --- p.49 / Chapter 5.3 --- DGCs in Homogeneous Coordinates --- p.53 / Chapter 5.3.1 --- Homogeneous Coordinates --- p.53 / Chapter 5.3.2 --- Degen Surfaces --- p.54 / Chapter 5.3.3 --- DGCs --- p.54 / Chapter 5.4 --- Properties of DGCs --- p.56 / Chapter 5.5 --- Potential Applications --- p.59 / Chapter 5.5.1 --- Recovery of DGC Descriptions --- p.59 / Chapter 5.5.2 --- Deformable DGCs --- p.60 / Chapter 5.6 --- Summary --- p.61 / Chapter 6 --- Conclusion and Future Work --- p.62 / Bibliography --- p.64

In Part I of the thesis, we focus on the fast and efficient algorithms for the TV-L1 minimization problem which can be applied to recover the blurred images corrupted by impulse noise. We construct the half-quadratic algorithm (HQA) for TV-L1 image restoration based on the half-quadratic technique. By introducing the proximal point algorithm into the HQA, we then obtain a modified HQA. We call it the proximal point half-quadratice algorithm (PHA). We introduce the PHA aiming to decrease the condition number of the coefficient matrix as updating the iterator in HQA. Until recently, there have been many efficient methods to solve the TV-L1 minimization problem. Examples are the primal-dual method, the fast total variational deconvolution method (FTVDM), and the augmented Lagrangian method (ALM). By numerical results of the FTVDM and ALM, we see that the images restored by these methods may sometimes appear to be blocky. Come back to our methods. The HQA and the PHA are both fast and efficient algorithms to solve the TV-L1 minimization problem. We prove that our algorithms are both majorize-minimize algorithms for solving a regularized TV-L1 problem. Given the assumption ker(∇)∩ker(BT B) = {0}, the convergence and linear convergence of the HQA is then easily obtained. Without such an assumption, a convergence result of PHA is also obtained. We apply our algorithms to deblur images corrupted with impulse noise. The results show that the HQA is faster and more accurate than the ALM and FTVDM for salt-and-pepper noise and comparable to the two methods for random-valued impulse noise. The PHA is comparable to the HQA in both recovered effect and computing consuming. Comparing with ALM and FTVDM, the PHA is faster and more accurate than ALM and FTVDM for salt-and-pepper noise and comparable to the two methods for random-valued impulse noise. Furthermore, the recovered images by the HQA and the PHA are less blocky. / In this thesis, we study two aspects in image processing. Part I is on the fast and efficient algorithms for the TV-L1 image restoration. Part II is on the fast and efficient algorithms for the positively constraint maximum penalized TV image restoration. / Part II of the thesis focuses on the positively constraint maximum penalized total variation image restoration. We develop and implement a multiplicative iteration approach for the positively constrained total variation image restoration. We call our algorithm MITV. The MITV algorithm is based on the multiplicative iterative algorithm originally developed for tomographic image reconstruction. The advantages of the MITV are that it is very easy to derive and implement under different image noise models and it respects the positivity constraint. Our method can be applied to kinds of noise models, the Gaussian noise model, Poisson noise model and the impulse noise model. In numerical test, we apply our algorithm to deblur images corrupted with Gaussian noise. The results show that our method give better restored images than the forward-backward splitting algorithm. / Liang, Haixia. / Adviser: Hon Fu Raymond Chan. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 87-92). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Shan, Qi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 124-132). / Abstracts in English and Chinese. / Chapter 1 --- Overview --- p.1 / Chapter 1.1 --- Image Blur Overview --- p.1 / Chapter 1.2 --- Blur Identification in a Transparency's Perspective --- p.3 / Chapter 1.3 --- From Transparencies to Natural Image Priors --- p.7 / Chapter 1.4 --- Discussion of the Linear Motion Model --- p.9 / Chapter 1.5 --- Binary Texture Restoration and High-Order MRF Optimization --- p.9 / Chapter 2 --- A Review on Previous Work --- p.13 / Chapter 2.1 --- Spatially-Invariant Blur Recovery --- p.13 / Chapter 2.2 --- Spatially-Variant Blur Recovery --- p.16 / Chapter 2.3 --- Markov Random Field Inference --- p.18 / Chapter 3 --- Motion Blur in a Transparency's Perspective --- p.20 / Chapter 3.1 --- Analysis of Object Motion Blur --- p.20 / Chapter 3.1.1 --- 1D Object Motion Blur --- p.20 / Chapter 3.1.2 --- 2D Object Motion Blur --- p.23 / Chapter 3.2 --- Modeling 2D Object Motion Blur --- p.26 / Chapter 3.3 --- Optimization Procedure --- p.27 / Chapter 3.3.1 --- Blur Kernel Estimation --- p.29 / Chapter 3.3.2 --- Latent Binary Matte Estimation --- p.30 / Chapter 3.4 --- Generalized Transparency in Motion Blur --- p.33 / Chapter 3.4.1 --- Camera Motion Blur Estimation --- p.35 / Chapter 3.4.2 --- Implementation --- p.37 / Chapter 3.5 --- Analysis and Results --- p.38 / Chapter 3.5.1 --- Evaluation of the Kernel Initialization --- p.40 / Chapter 3.5.2 --- Evaluation of Binary Alpha Initialization --- p.40 / Chapter 3.5.3 --- Robustness to Noise --- p.41 / Chapter 3.5.4 --- Natural Image Deblurring Results --- p.41 / Chapter 3.6 --- Proofs --- p.50 / Chapter 4 --- Rotational Motion Deblurring --- p.55 / Chapter 4.1 --- Motion blur descriptor --- p.55 / Chapter 4.1.1 --- Descriptor analysis --- p.56 / Chapter 4.2 --- Optimization --- p.59 / Chapter 4.2.1 --- Parameter initialization --- p.59 / Chapter 4.2.2 --- Iterative optimization --- p.62 / Chapter 4.2.3 --- Recover the color image --- p.65 / Chapter 4.3 --- Result and analysis --- p.65 / Chapter 5 --- Image Deblurring using Natural Image Priors --- p.70 / Chapter 5.1 --- Problem Definition --- p.70 / Chapter 5.2 --- Analysis of Ringing Artifacts --- p.71 / Chapter 5.3 --- Our model --- p.74 / Chapter 5.3.1 --- Definition of the probability terms --- p.75 / Chapter 5.4 --- Optimization --- p.81 / Chapter 5.4.1 --- Optimizing L --- p.83 / Chapter 5.4.2 --- Optimizing f --- p.86 / Chapter 5.4.3 --- Optimization Details and Parameters --- p.87 / Chapter 5.5 --- Experimental Results --- p.90 / Chapter 6 --- High Order MRF and its Optimization --- p.94 / Chapter 6.1 --- The Approach --- p.95 / Chapter 6.1.1 --- Polynomial Standardization --- p.95 / Chapter 6.1.2 --- Polynomial Graph Construction --- p.97 / Chapter 6.1.3 --- Polynomial Graph Partition --- p.103 / Chapter 6.1.4 --- Multi-Label Expansion --- p.105 / Chapter 6.1.5 --- Analysis --- p.106 / Chapter 6.2 --- Experimental Results --- p.108 / Chapter 6.3 --- Summary --- p.112 / Chapter 6.4 --- Proofs --- p.112 / Chapter 7 --- Conclusion --- p.117 / Chapter 7.1 --- Solving Linear Motion Blur in a Transparency's Perspective --- p.117 / Chapter 7.2 --- Rotational Motion Deblurring --- p.119 / Chapter 7.3 --- Image Deblurring using Natural Image Priors --- p.119 / Chapter 7.4 --- Contribution --- p.121 / Chapter 7.5 --- Discussion and Open Questions --- p.121 / Bibliography --- p.124

Huang, Ting. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 37-41). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Related Area --- p.2 / Chapter 1.2 --- Previous Work --- p.4 / Chapter 1.3 --- Proposed Framework --- p.7 / Chapter 1.4 --- Overview --- p.8 / Chapter 2 --- Markov Random Fields and Optimization Schemes --- p.9 / Chapter 2.1 --- MRF Model --- p.10 / Chapter 2.1.1 --- MAP Understanding --- p.11 / Chapter 2.2 --- Belief Propagation Optimization Scheme --- p.14 / Chapter 2.2.1 --- Max-Product BP on MRFs --- p.14 / Chapter 2.2.2 --- Sum-Product BP on MRFs --- p.15 / Chapter 3 --- Our Formulation --- p.17 / Chapter 3.1 --- An MRF Model --- p.18 / Chapter 3.2 --- Coarse-to-Fine Optimization by BP --- p.21 / Chapter 3.2.1 --- Coarse-Level Belief Propagation --- p.23 / Chapter 3.2.2 --- Fine-Level Belief Propagation --- p.24 / Chapter 3.2.3 --- Performance Enhancement --- p.25 / Chapter 4 --- Experiments --- p.27 / Chapter 4.1 --- Comparison --- p.27 / Chapter 4.2 --- Failure Case --- p.32 / Chapter 5 --- Conclusion --- p.35 / Bibliography --- p.37