Dissertations / Theses on the topic 'Non-separable'

We consider two one-dimensional harmonic chains coupled along their length via linear springs. Casting the elastic wave equation for this system in a Dirac-like form reveals a directional representation. The elastic band structure, in a spectral representation, is constituted of two branches corresponding to symmetric and antisymmetric modes. In the directional representation, the antisymmetric states of the elastic waves possess a plane wave orbital part and a 4x1 spinor part. Two of the components of the spinor part of the wave function relate to the amplitude of the forward component of waves propagating in both chains. The other two components relate to the amplitude of the backward component of waves. The 4x1 spinorial state of the two coupled chains is supported by the tensor product Hilbert space of two identical subsystems composed of a non-interacting chain with linear springs coupled to a rigid substrate. The 4x1 spinor of the coupled system is shown to be in general not separable into the tensor product of the two 2x1 spinors of the uncoupled subsystems in the directional representation. (C) 2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

The location of groups of similar observations (clusters) in data is a well-studied problem, and has many practical applications. There are a wide range of approaches to clustering, which rely on different definitions of similarity, and are appropriate for datasets with different characteristics. Despite a rich literature, there exist a number of open problems in clustering, and limitations to existing algorithms. This thesis develops methodology for clustering high-dimensional, mixed datasets with complex clustering structures, using low-density cluster separators that bi-partition datasets using cluster boundaries that pass through regions of minimal density, separating regions of high probability density, associated with clusters. The bi-partitions arising from a succession of minimum density cluster separators are combined using divisive hierarchical and partitional algorithms, to locate a complete clustering, while estimating the number of clusters. The proposed algorithms locate cluster separators using one-dimensional arbitrarily oriented subspaces, circumventing the challenges associated with clustering in high-dimensional spaces. This requires continuous observations; thus, to extend the applicability of the proposed algorithms to mixed datasets, methods for producing an appropriate continuous representation of datasets containing non-continuous features are investigated. The exact evaluation of the density intersected by a cluster boundary is restricted to linear separators. This limitation is lifted by a non-linear mapping of the original observations into a feature space, in which a linear separator permits the correct identification of non-linearly separable clusters in the original dataset. In large, high-dimensional datasets, searching for one-dimensional subspaces, which result in a minimum density separator is computationally expensive. Therefore, a computationally efficient approach to low-density cluster separation using approximately optimal projection directions is proposed, which searches over a collection of one-dimensional random projections for an appropriate subspace for cluster identification. The proposed approaches produce high-quality partitions, that are competitive with well-established and state-of-the-art algorithms.

The quadratic class of time-frequency distributions (TFDs) forms a set of tools which allow to effectively extract important information from a nonstationary signal. To determine which TFD best represents the given signal, it is a common practice to visually compare different TFDs' time-frequency plots, and select as best the TFD with the most appealing plot. This visual comparison is not only subjective, but also difficult and unreliable especially when signal components are closely-spaced in the time-frequency plane. To objectively compare TFDs, a quantitative performance measure should be used. Several measures of concentration/complexity have been proposed in the literature. However, those measures by being derived with certain theoretical assumptions about TFDs are generally not suitable for the TFD selection problem encountered in practical applications. The non-existence of practically-valuable measures for TFDs' resolution comparison, and hence the non-existence of methodologies for the signal optimal TFD selection, has significantly limited the use of time-frequency tools in practice. In this thesis, by extending and complementing the concept of spectral resolution to the case of nonstationary signals, and by redefining the set of TFDs' properties desirable for practical applications, we define an objective measure to quantify the quality of TFDs. This local measure of TFDs' resolution performance combines all important signal time-varying parameters, along with TFDs' characteristics that influence their resolution. Methodologies for automatically selecting a TFD which best suits a given signal, including real-life signals, are also developed. The optimisation of the resolution performances of TFDs, by modifying their kernel filter parameters to enhance the TFDs' resolution capabilities, is an important prerequisite in satisfying any additional application-specific requirements by the TFDs. The resolution performance measure and the accompanying TFDs' comparison criteria allow to improve procedures for designing high-resolution quadratic TFDs for practical time-frequency analysis. The separable kernel TFDs, designed in this way, are shown to best resolve closely-spaced components for various classes of synthetic and real-life signals that we have analysed.

The quadratic class of time-frequency distributions (TFDs) forms a set of tools which allow to effectively extract important information from a nonstationary signal. To determine which TFD best represents the given signal, it is a common practice to visually compare different TFDs' time-frequency plots, and select as best the TFD with the most appealing plot. This visual comparison is not only subjective, but also difficult and unreliable especially when signal components are closely-spaced in the time-frequency plane. To objectively compare TFDs, a quantitative performance measure should be used. Several measures of concentration/complexity have been proposed in the literature. However, those measures by being derived with certain theoretical assumptions about TFDs are generally not suitable for the TFD selection problem encountered in practical applications. The non-existence of practically-valuable measures for TFDs' resolution comparison, and hence the non-existence of methodologies for the signal optimal TFD selection, has significantly limited the use of time-frequency tools in practice. In this thesis, by extending and complementing the concept of spectral resolution to the case of nonstationary signals, and by redefining the set of TFDs' properties desirable for practical applications, we define an objective measure to quantify the quality of TFDs. This local measure of TFDs' resolution performance combines all important signal time-varying parameters, along with TFDs' characteristics that influence their resolution. Methodologies for automatically selecting a TFD which best suits a given signal, including real-life signals, are also developed. The optimisation of the resolution performances of TFDs, by modifying their kernel filter parameters to enhance the TFDs' resolution capabilities, is an important prerequisite in satisfying any additional application-specific requirements by the TFDs. The resolution performance measure and the accompanying TFDs' comparison criteria allow to improve procedures for designing high-resolution quadratic TFDs for practical time-frequency analysis. The separable kernel TFDs, designed in this way, are shown to best resolve closely-spaced components for various classes of synthetic and real-life signals that we have analysed.

Dans le but de faire face aux défis interdépendants en termes d’épuisement des ressources énergétiques, de dégradation environnementale et des préoccupations de santé publique dans le contexte chinois en réponse au développement durable, nous nous concentrons sur l'étude des politiques en matière d’énergie, d’environnement et de santé en Chine. Dans le chapitre 1, nous donnons un aperçu des politiques chinoises en matière d’énergie, d’environnement et de santé au cours des 20 dernières années afin de connaître les orientations politiques futures auxquelles le gouvernement n'a pas donné une attention suffisante. Dans les trois chapitres suivants, nous proposons une série d'études empiriques afin de tirer quelques implications politiques utiles. Dans le chapitre 2, nous étudions l'impact de l'urbanisation, de l'adaptation de la structure industrielle, du prix de l'énergie et de l'exportation sur les intensités énergétiques agrégés et désagrégés des provinces. Dans le chapitre 3, nous étudions les facteurs qui expliquent la transition énergétique vers des combustibles propres des ménages ruraux. Dans le chapitre 4, nous examinons les effets conjoints des risques environnementaux, du revenu individuel, des politiques de santé sur l'état de santé des adultes chinois. En particulier, nos résultats empiriques suggèrent d’intégrer le développement urbain dans la stratégie d'économies d'énergie; de considérer des substitutions/complémentarités complexes parmi les sources d'énergie et entre l'énergie et l’alimentation pour les ménages ruraux; d’aligner les politiques environnementales, énergétiques et alimentaires avec les politiques de santé<br>With the purpose of coping with the intertwined challenges of energy depletion, environmental degradation and public health concerns in the Chinese-specific context in response to sustainable development, we focus on investigating China’s energy, environment and health policies. In chapter 1, we provide an overview of China’s energy, environment and health policies over the past 20 years in order to know about the future policy directions to which the government has not given a sufficient attention. In the following three chapters, we provide a series of empirical studies so as to derive some useful policy implications. In chapter 2, we investigate the impact of urbanization, industrial structure adjustment, energy price and export on provincial aggregate and disaggregate energy intensities. In chapter 3, we study the factors explaining the switches from dirty to clean fuel sources in rural households. In chapter 4, we examine the joint effects of environmental hazards, individual income and health policies on the health status of Chinese adults. Our empirical findings particularly suggest integrating urban development into the strategy of energy saving; considering the complex substitutions/complementarities among energy sources and between energy and food for rural households; aligning the environment, energy and food policies with health policies

De nos jours, les matériaux composites sont très largement utilisés dans l’industrie aéronautique et aérospatiale car ils ont de très bonnes tenues mécaniques, mais ces matériaux comportent de fortes hétérogénéités dues aux fibres et aux liants qui les constituent. Ainsi, depuis de nombreuses années, l’équipe TIFC «Thermal Imaging Fields and Characterization » du département TREFLE de l’institut I2M développe des méthodes de mesure des propriétés thermophysiques de matériaux hétérogènes dans le plan ou dans l’épaisseur. Ces méthodes sont très variées du point de vue des méthodes inverses (transformée intégrale, double décomposition en valeurs singulières, …) ou expérimentale (Flash, diode laser, …). Le faible coût des diodes lasers et des systèmes de déplacement de miroirs galvanométriques ont permis de développer un système complet de scanner optique laser, monté sur un banc de mesure. Il permet de revisiter les différents types de sollicitations thermiques et de réaliser une infinité de combinaisons spatiotemporelles d’excitations thermiques par méthode laser. Ceci est une des principales originalités de ce travail. De nouvelles méthodes inverses basées sur la réponse thermique au point source impulsionnel et sur la séparabilité des champs de température ont été proposées. Ces méthodes ont permis d’estimer le tenseur de diffusivité thermique selon les axes principaux d’anisotropie, mais aussi hors des axes du repère de l’image, où il est possible de déterminer l’orientation des axes d’anisotropie, lorsque le transfert de chaleur s’effectue hors des axes du repère de l’image. Ces méthodes ont permis d’obtenir des résultats intéressants comptetenu de leur simplicité. De plus, elles ont permis d’obtenir des cartographies de diffusivités thermiques dans le plan car, comparées aux autres méthodes, elles permettent d’obtenir des estimations du tenseur de diffusivité thermique localement grâce à l’obtention d’une cartographie de flux thermique surfacique via le scanner optique laser<br>Nowadays, composite materials are widely used in the aeronautic and aerospace industries because of their high mechanical resistance. However, they have a large heterogeneity due to the fiber and matrix they are made of. In this way, for many years, the TIC team «Thermal Imaging Fields and Characterization » from TREFLE department of I2M laboratory develops methods to measure thermal in-plane properties of heterogeneous materials such as inverses (integral transforms, double singular value decomposition…) or experimental (Flash, laser diode…) methods. The recent progress made in optical control, lasers and infrared (IR) cameras enables the development of a new scanning system (based on galvanometer-mirror) which allows the easy control of a laser hot spot spatial and temporal displacements over a plane surface. The low cost of laser diodes and optical control (galvanometric mirror) systems allows to develop a laser scanning system fixed on a test bench. We can revisit the different types of thermal excitation and realize infinite spatio-temporal combinations of thermal excitations by laser method. This is one of this thesis aims. New inverse methods based on the thermal response to an instantaneous point source heating, and temperature fields separability, have been proposed. These methods allow to estimate the thermal diffusivity tensor along the main axes of anisotropy, but also out of those axes, where it is possible to estimate the anisotropy axes orientation when the heat transfer takes place out of the image axes. These methods have produced interesting results in view of their simplicity. Moreover, they made it possible to obtain in-plane thermal diffusivities maps because, compared to the other methods, they allow to obtain, locally, thermal diffusivity tensor estimations by getting a surface heat flux map using the laser optical scanner

La thermographie infrarouge est une méthode largement employée pour la caractérisation des propriétés thermophysiques des matériaux. L’avènement des diodes laser pratiques, peu onéreuses et aux multiples caractéristiques, étendent les possibilités métrologiques des caméras infrarouges et mettent à disposition un ensemble de nouveaux outils puissants pour la caractérisation thermique et le contrôle non desturctif. Cependant, un lot de nouvelles difficultés doit être surmonté, comme le traitement d’une grande quantité de données bruitées et la faible sensibilité de ces données aux paramètres recherchés. Cela oblige de revisiter les méthodes de traitement du signal existantes, d’adopter de nouveaux outils mathématiques sophistiqués pour la compression de données et le traitement d’informations pertinentes. Les nouvelles stratégies consistent à utiliser des transformations orthogonales du signal comme outils de compression préalable de données, de réduction et maîtrise du bruit de mesure. L’analyse de sensibilité, basée sur l’étude locale des corrélations entre les dérivées partielles du signal expérimental, complète ces nouvelles approches. L'analogie avec la théorie dans l'espace de Fourier a permis d'apporter de nouveaux éléments de réponse pour mieux cerner la «physique» des approches modales.La réponse au point source impulsionnel a été revisitée de manière numérique et expérimentale. En utilisant la séparabilité des champs de température nous avons proposé une nouvelle méthode d'inversion basée sur une double décomposition en valeurs singulières du signal expérimental. Cette méthode par rapport aux précédentes, permet de tenir compte de la diffusion bi ou tridimensionnelle et offre ainsi une meilleure exploitation du contenu spatial des images infrarouges. Des exemples numériques et expérimentaux nous ont permis de valider dans une première approche cette nouvelle méthode d'estimation pour la caractérisation de diffusivités thermiques longitudinales. Des applications dans le domaine du contrôle non destructif des matériaux sont également proposées. Une ancienne problématique qui consiste à retrouver les champs de température initiaux à partir de données bruitées a été abordée sous un nouveau jour. La nécessité de connaitre les diffusivités thermiques du matériau orthotrope et la prise en compte des transferts souvent tridimensionnels sont complexes à gérer. L'application de la double décomposition en valeurs singulières a permis d'obtenir des résultats intéressants compte tenu de la simplicité de la méthode. En effet, les méthodes modales sont basées sur des approches statistiques de traitement d'une grande quantité de données, censément plus robustes quant au bruit de mesure, comme cela a pu être observé<br>Infrared thermography is a widely used method for characterization of thermophysical properties of materials. The advent of the laser diodes, which are handy, inexpensive, with a broad spectrum of characteristics, extend metrological possibilities of infrared cameras and provide a combination of new powerful tools for thermal characterization and non destructive evaluation. However, this new dynamic has also brought numerous difficulties that must be overcome, such as high volume noisy data processing and low sensitivity to estimated parameters of such data. This requires revisiting the existing methods of signal processing, adopting new sophisticated mathematical tools for data compression and processing of relevant information.New strategies consist in using orthogonal transforms of the signal as a prior data compression tools, which allow noise reduction and control over it. Correlation analysis, based on the local cerrelation study between partial derivatives of the experimental signal, completes these new strategies. A theoretical analogy in Fourier space has been performed in order to better understand the «physical» meaning of modal approaches.The response to the instantaneous point source of heat, has been revisited both numerically and experimentally. By using separable temperature fields, a new inversion technique based on a double singular value decomposition of experimental signal has been introduced. In comparison with previous methods, it takes into account two or three-dimensional heat diffusion and therefore offers a better exploitation of the spatial content of infrared images. Numerical and experimental examples have allowed us to validate in the first approach our new estimation method of longitudinal thermal diffusivities. Non destructive testing applications based on the new technique have also been introduced.An old issue, which consists in determining the initial temperature field from noisy data, has been approached in a new light. The necessity to know the thermal diffusivities of an orthotropic medium and the need to take into account often three-dimensional heat transfer, are complicated issues. The implementation of the double singular value decomposition allowed us to achieve interesting results according to its ease of use. Indeed, modal approaches are statistical methods based on high volume data processing, supposedly robust as to the measurement noise

Neural networks are models which have been developed to simulate the anatomy of the nervous system. The connection between the elements of these networks, the so called artificial neurons, is similar to the connection between the biological neurons. In developing neural networks people are trying to create systems which have the same computational and communication properties as the brain. On the basis of the things we know from neurophysiology the first models for the neural networks are developed. One of these networks was the perceptron, which is one of the most used neural networks. In this thesis we'll study this special neural network. When the input vectors of the perceptron can be linearly separated into two categories, this network can be trained to correctly classify these input vectors. However in most practical cases the linearly separability assumption isn't satisfied. That's why the main part of this study is devoted to the case where the input vectors aren't linearly separable.<br>Graduation date: 1995

Research Doctorate - Doctor of Philosophy (PhD)<br>Fourier Analysis is a primary technique in the analysis of images, yet it has several limitations when it comes to the higher dimensional case of colour images. This thesis seeks to address some of these limitations through two main areas. First, we consider the recently developed Clifford-Fourier Transform of Brackx et al, which has the advantage over the classical Fourier Transform of combining the different channels of a colour image. We characterise the Hardy Spaces of this transform and show that functions in these Hardy spaces have monogenic extensions with bounded integral averages. We also characterise the Paley-Wiener spaces and show that functions in a Paley-Wiener space with radius R have monogenic extensions with integral averages that grow according to the radius R. Second, we consider the case of two dimensional compactly supported wavelets with orthonormal shifts and develop projection algorithms to find compactly supported, continuous wavelets with orthonormal shifts and dilations and 2 vanishing moments which are not tensor products of one dimensional wavelets. We also apply these techniques in one dimension and discover an example of an anti-symmetric, compactly supported, continuous wavelet with orthonormal shifts and dilations and 2 vanishing moments.

碩士<br>義守大學<br>電子工程學系<br>89<br>In this paper, a pipeline-parallel VLSI architecture based on the AOCA algorithm is developed for the 2D discrete periodized wavelet transform (DPWT). Due to adapting the 2D filter coefficient and using the mirror effect between the OCA operators, the new architecture needs less multipliers and bus width than the traditional architectures. The main advantages of this VLSI architecture is by using parallel data processing, so it has 100% hardware utilization and short latency. Moreover we use special homeomorphic filter, so it simplizes the boundary data processing and makes image perfect reconstruction realize.The new VLSI architecture also can be suitable for real-time applications.

In Euro area countries fiscal policy plays a central role in the stabilization of business cycles mainly because monetary policy is defined for the whole area. A small open economy model is employed to assess the consequences of government expenditure shocks. The main novelty of this thesis is the inclusion of non-separable preferences between private consumption and government expenditure. Numerical simulation suggests that fiscal policy is more e↵ective in a fixed exchange regime. In this regime, fiscal multipliers reach 1.6% on impact and 1% in the long-run.<br>Nos países da zona Euro a política orçamental tem um papel chave na estabilização dos ciclos económicos principalmente porque a política monetária é definida para o conjunto das economias. Um modelo de pequenas economias abertas é utilizado para avaliar as consequências de um choque nos gastos do governo. O contributo principal desta tese é a introdução de preferências não separáveis entre o consumo privado e os gastos do Estado. Uma simulação numérica sugere que a política orçamental é mais eficaz num regime de câmbios fixos. Neste regime, os multiplicadores orçamentais atingem 1.6% no impacto e 1% no longo prazo

碩士<br>國立屏東大學<br>應用數學系碩士班<br>107<br>By building on the pre-existing results of the pseudo equal allocation of non-separable costs (PEANSC) and the weight function simultaneously, we introduce a different solution in the framework of transferable-utility (TU) games. Inspired by the notions of Hart, et al. [12], Moulin [23], Lin, et al. [20] and Luo, et al. [21], a specific reduction and related consistency are adopted to characterize this weighted solution.

碩士<br>國立高雄大學<br>亞太工商管理學系碩士班<br>100<br>The electrical energy is the basic motive power of the development of a country. Recently, the related data of electricity generation within the Taiwan Power Company (Taipower) shows that the national economic development is on the occasion of a surging need of electricity. From 2009 to 2010, the electricity sales increased from 179.159 billion to 193.313 billion kWh, at a growth rate of 7.9%. However, due to the rise of domestic environmental awareness as well as the nuclear dispute, the current electricity generation planning of Taipower is greatly influenced. Therefore, the purpose of this study aimed to provide Taipower with the substantial suggestions through conducting the operational performance analysis of its thermal power plants in hope of subserving Taipower’s future energy development plan and tried to answer the different points of Taipower’s improvement on the thermal power achievement. Also, it tried to see if there’s anything left to be desire and if it can achieve both environmental protection and power generation problems. As for the research methods, this study used DEA non-separable mode, adding the consideration of the defective products, to measure the input and output data of Taipower’s thermal power department from 2006 to 2010. It assessed the operational efficiency of the thermal power plants in the thermal power department, and used the overall efficiency analysis to partly give the suggestions to every thermal power plant for its overall operational improvement. Through using balance analysis and sensitivity analysis, it provided the objective and substantial suggestions to every thermal power plant on improving the resource allocation and key efficiency input and output factors. In this study, I used the non-separable mode in the DEA non-desirable output mode. In each of the thermal power sector in the thermal power department of Taipower, the overall efficiency of relatively better performance is Xingda steam power unit, LinKou power plants and Taichung thermal power plants, and the Datam power plant, whose number is 0.423, is the worst. Within the analysis of efficiency related referential set, the reference number of Linkou is 22 times, and it is the maximum. In the analysis of balance variable, the Xingda steam power unit, LinKou power plants and Taichung thermal power plants perform well, and there’s no waste or idling in the equipment utilization and resources allocation. The Datam power plant acts the worst, with the average management efficiency of 0.425. As for the sensitivity analysis, the output of the net power generation capacity is the high sensitivity item among the majority of the power generation units, followed by the factors of operational costs and equipment capacity. The substantial contribution of this study is to conduct the data analysis based on more objective information through adding the consideration of defective products factors, and make the thermal power department of Taipower conduct a more appropriate operational planning and resources allocation in face of the harsh environment. It can provide the country with the needed resources under her development in the transitional period of new energy development; also, it makes the country to keep obtaining better electricity quality under the steadily growing use of electricity nowadays, and stabilizes the country’s future economic development.

This dissertation studies a class of path-dependent stochastic control problems with applications to Finance. In particular, we solve the open problem of the continuous time expected utility maximization with addictive consumption habit formation in incomplete markets under two independent scenarios. In the first project, we study the continuous time utility optimization problem with consumption habit formation in general incomplete semimartingale financial markets. Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into an abstract time-separable utility maximization problem with a shadow random endowment on the product space. We establish existence and uniqueness of the optimal solution using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living. We also provide market independent sufficient conditions both on the stochastic discounting processes of the habit formation process and on the utility function for the well-posedness of our original optimization problem. Under the same assumptions, we can carefully modify the classical proofs in the approach of convex duality analysis when the auxiliary dual process is not necessarily integrable. In the second project, we examine an example of the optimal investment and consumption problem with both habit-formation and partial observations in incomplete markets driven by It\^{o} processes. The individual investor develops addictive consumption habits gradually while only observing the market stock prices but not the instantaneous rates of return, which follow an Ornstein-Uhlenbeck process. Applying the Kalman-Bucy filtering theorem and Dynamic Programming arguments, we solve the associated Hamilton-Jacobi-Bellman(HJB) equation fully explicitly for this path dependent stochastic control problem in the case of power utility preferences. We provide the optimal investment and consumption policy in explicit feedback form using rigorous verification arguments.<br>text

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.