Image restoration is fundamental to visual information processing systems. In many real world scenarios, noise and blur are the two main unavoidable sources of degra- dation in images. The problem is deemed as an ill-posed inverse by nature due to the simultaneous occurrences of noise and blur in the image. Blurring function categorizes the degradation as space variant (SVD) if di erent spatial locations of the recorded scene are convolved by varying point spread function. In contrast, the degradation is categorized as spatially invariant (SID) if a unique point spread function blurs the whole image. This dissertation focuses on spatial degradations, initiating from space invariant towards space variant. Existing methods for restoration of SVD images, for example, neural networks and numerical optimization bear the limitations of high cost, lower restoration, less gen- eralization, discontinuity and instability for di erent spatial locations. It is learnt that three factors are vital to develop an e ective framework for restoration, which are: 1. The optimization of the ill-posed inverse restoration problem by minimizing constrained error function 2. A smoothness constraint 3. A regularization scheme The main objective of this dissertation is to improve the restoration results, by possible applications of new intelligent methods. This dissertation provides com- prehensive solutions to both spatial degradation problems, by considering above three factors. Firstly, SID images are restored, by a steepest descent based restora- tion approach. In this approach, an e cient smoothness constraint is proposed, to model the error function. In the next step, the steepest descent based approach is improved and a novel fuzzy regularization scheme is also proposed to better model the error function. It performed better than the existing methods on a speci c blur function and low power additive noise. However, local search properties of gradient based approaches and eventually lower restoration for SVD images, due to their high sensitivity for varying textures, noise powers and blurs allowed for the possible application of computational intelligence models. Finally, in this dissertation, a new optimization framework is proposed for image restoration of SVD images. In the proposed framework, particle swarm optimiza- tion based evolution is retained to minimize the Modi ed Error Estimate (MEE), for better restoration. The framework added hyper-heuristic layer to combine local and global search properties. Therefore, randomness in the evolution, augmented with apriori knowledge from problem domain, assisted in achieving the objective of better restoration. It introduced new swarm initialization and mutation of global best particle of the swarm. In addition, an adaptive weighted regularization scheme is introduced in MEE to cater with the uncertainty due to ill-posed nature of the in- verse problem. Furthermore, a new fuzzy logic and mathematical morphology based regularization scheme is also proposed in the framework, to improve the restoration stability and generalization, for SVD images. Di erent experiments are performed to observe the performance of proposed solu- tions. Visual and quantitative results are obtained and provided for each experiment. Signal-to-noise ratio (SNR) and mean-squared-error (MSE) are computed for com- parative analysis, which endorsed better restoration quantitatively, over well-known restoration methods. However, the stability in restoration performance of proposed framework is observed in visual results, for SVD images. Detailed experimental and comparative analysis shown better restoration, stabilization and generalization of the proposed framework for varied textures in standard and simulated images, and noises over well-known restoration approaches.
مولانا ابوبکر اصلاحی افسوس ہے کہ ۲؍ مئی کو جماعت اسلامی کے ایک ذمہ دار بزرگ اور اعظم گڑھ کے اطراف کے مشہور عالم مولانا ابوبکر اصلاحی صاحب نے داعی اجل کو لبیک کہا، مدرسۃ الاصلاح سے فراغت کے بعد انہوں نے ضلع بستی میں دینی تعلیم کی اشاعت اور درس و تدریس کی خدمت انجام دی، ۴۶ء میں مدرسۃ الاصلاح آئے۔ راقم نے صرف و نحو اور فقہ کی بعض کتابیں ان سے پڑھیں، وہ جماعت کے بڑے سرگرم رکن تھے، اس لیے مدرسہ سے سبکدوش ہوکر اس کے تنظیمی کاموں میں لگ گئے، ان کی اچھی کارگزاری کی بنا پر جب جامعۃ الفلاح قائم ہوا تو اس کی ترقی و استحکام کا کام انہیں سپرد کیا گیا اور وہ عرصہ تک اس کے نیک نام ناظم و صدر مدرس رہے۔ اب علالت و معذوری کی وجہ سے سرائمیر میں اپنے گھر ہی رہتے تھے۔ دارالمصنفین بھی تشریف لاتے تھے، مولانا شاہ معین الدین احمد ندوی سے تعلق خاطر تھا۔ مولانا ابوبکر صاحب کی وفات سے جماعت اسلامی اپنے ایک اچھے اور مخلص کارکن سے محروم ہوگئی، اﷲ تعالیٰ مغفرت فرمائے اور پس ماندگان کو صبر جمیل عطا کرے۔ آمین! (ضیاء الدین اصلاحی، مئی ۱۹۹۸ء)
According to Hadith literature, the Quran is revealed in seven Ahruf, the plural of harf. Ahruf are distinct from Qira'at. This is a very momentous and lengthy topic, indeed, one of the most complicated discussions on the sciences of the Qur’an. It is very difficult to discuss it in full details in this work but the important things about it are being presented in this article. The first problem we face with this Hadith is what is meant by the Revelation of Qur’an on Seven “Ahruf”? We find a great deal of difference of opinion on this subject. Up to thirty five different views have been quoted by Ibn al-‘Arabi and others. Some of the popular views are quoted in this article. The context of these narrations indicates clearly that the word ‘seven’ does not denote an unspecified large number but it denotes the specific numerical value ‘seven’. Hence, in the light of these narrations this view (that seven means more than that) does not hold good and the majority of scholars reject it. In the vast collections of Hadiths, we do not find any mention of difference in the Qur’an other than that accounted for in “ahruf”. How then may we explain differences in reading and “ahruf”? I have not been able to find a satisfactory answer to this confusion with the advocates of this theory.
The use of mathematical programming for short term (10-day) operation of Indus River System under uncertainty was investigated. A two stage mix optimization procedure was proposed for the stochastic optimization of the Indus River System. The first stage of the proposed procedure cycles through three main programs, a transition probability matrix (tmp) computation algorithm, a DDP-SDP (Deterministic-Stochastic Dynamic Programming) model and a simulation program. In DDP-SDP program, four model types and three objective types were investigated for multiresevoir system. These non-linear objectives were calibrated for the large scale complex system to minimize the irrigation shortfalls, to maximize the hydropower generation and to optimize the flood storage benefits. Simulation program was used for the validation of each policy derived through this cycle. The accumulation of these programs is called 10 day reservoir operation model of the multireservoir Indus River System. Various model types in SDP/DDP formulation may produce different results in different reservoir conditions and different hydrologic regimes. The model types are therefore system specific. For the Indus Reservoir System best fit SDP model type was identified, alternate multi objective functions were proposed and analysed. Taking one or two objectives and ignoring other or considering all the objectives to optimize, produced different results in different model types. Especially the results were significantly different in terms of storage contents of the reservoir during simulation. The proposed procedure identifies the best stochastic operational policies for the system under uncertainty. The second stage of proposed procedure uses advantages of the stochastic optimal policies derived in the first stage of the optimization with a Network Flow programming (NFP) model developed for the Indus River System for 10 day operation. The whole system was represented by a capacitated network in which nodes are reservoirs, system inflow locations or canal diversion locations. The nodes are connected with the arcs which represent rivers, canal reaches or syphons in the system. The maximum and minimum flow conditions were defined from the physical data. The NFP model was solved with the help of two main programs, the out of kilter algorithm and on line reservoir operation model with stochastic operating policies. The accumulation of these programs is called 10 day stochastic network flow programming (SNFP) model of the multireservoir Indus River System. The proposed SNFP model provides two main benefits. First, the incorporation of the stochastic operating policies at reservoir nodes controls the uncertainty and improves the system operation performance. The stochastic behaviour of the inputs and non-linear objectives in the linear programming model is incorporated in this way. Second, the complete system is under control and presents acomplete physical picture of the system. The results obtained from the above two stage procedure were verified with help of simulating the system with forecasted inflows and comparing these results with actual historic data record. For this purpose, 10 day forecasting models were investigated, calibrated and verified. The results also proved the methodology effective for the test case. The reservoir operation model is characterized as generalised and flexible model, and can be used for any other reservoir. The SNFP model is system (the Indus River System) specific to and needs minor modifications to be used for other water resource systems.ii The proposed optimization procedure presents the optimum operation of reservoirs for irrigation water supplies, hydropower production and flood protection, optimal allocation of water resources in the canal network of Indus River System and identifies the resource limitations at various locations in the system. While comparing with the historic data records, the model performance was found to be better than the historic data at all locations in the system during simulation. The complete model may be used as a guiding tool for the optimum 10 day operation of the Indus River System. A two stage frame work consisting of a steady state SDP 10 day reservoir operation model followed by a Network Flow model appears to be promising for the optimization of Indus River System. The model has also been used for future planning of water resources in Pakistan. The methodology developed provides a viable way of applying stochastic optimization into deterministic optimization procedure under multireservoir, multiobjective water resource system with 10 day operation under uncertainty.