One of the most important social problem after world warII in developing country is rapid urbanization. In most of the developing country yearly growth urban population is among 5 untill 8 percent. This urban explosive grow and the slums are effect of the inside immigration from village to urban, that call in various place and various form like marginal, squatter, Illegal, Irregular, spontaneous, unauthorized, informal settlement.Our country (IRAN) like other developing country encounter with this problem. At present in most urban and industrial city like Arak city there are slums.These thesis investigate structural and cultural feature of slums (Bagh Khalaj district) that doing with document and surveying at first abstract of science literature (definitions, scores and feature) of slums in other country and Iran and then survey physical and humanly structure of Arak city.After that survey slums and especially Bagh Khalaj district (case study) in Arak city. At the end of thesis on the base of results and to point out strategy, limitations, facilities and problems and then present solutions.

Ill-conditioned linear systems may frequently arise in discretization of integral equations and many other real world applications. Solving such systems by classical methods might fail or result to solutions that are meaningless from practical point view. Moreover a slight perturbation in the right hand side vector might also lead to an enormous change of the solution vector due to ill-conditioned ness. To find meaningful solutions of such systems, the Tikhonov regularization is an effective technique that has been widely used. In this paper we use it to solve ill-conditioned linear systems and also to find closest feasible linear systems to nearly feasible linear systems by smallest changes in problem data. Throughout the paper numerical results are reported to demonstrate the practical efficiency of the presented algorithms.

summary Downward continuation of potential field data plays an important role in interpretation of gravity and magnetic data. For its inherent instability, many methods have been presented to downward continue stably and precisely. The Tikhonov regularization approach is one of the most robust. It is based on a lowpass filter derivation in the Fourier spectral domain, by means of a minimization problem solution. In this manuscript, we propose an improved regularization operator for downward continuation of potential field data. First, we simply define a special wavenumber named the cutoff wavenumber to divide the potential field spectrum into the signal part and the noise part based on the radially averaged power spectrum of potential field data. Next, we use the conventional downward continuation operator to downward continue the signal and the Tikhonov regularization operator to suppress the noise. Moreover, the parameters of the improved operator are defined by the cutoff wavenumber which has an obvious physical significance. For computing the α parameter, it is necessary that the C-norm of the potential field must be calculated. The improved operator can not only eliminate the influence of the high-wavenumber noise but also avoid the attenuation of the signal. Experiments through synthetic gravity and real gravity data from Kohe Namak region, Ghom province, Iran show that the downward continuation precision of the proposed operator is higher than the Tikhonov regularization operator...

The methods applied to regularization of the ill-posed problems can be classified under “direct” and “indirect” methods. Practice has shown that the effects of different regularization techniques on an ill-posed problem are not the same, and as such each ill-posed problem requires its own investigation in order to identify its most suitable regularization method. In the geoid computations without applying Stokes formula, the downward continuation based on Abel-Poisson integral is an inverse problem, which requires regularization. Since so far the regularization of this ill-posed problem has been thoroughly studied, in this paper the regularization of the downward continuation problem based on Abel-Poisson integral, is investigated and various techniques falling into the aforementioned classes of regularizations are applied and their efficiency is compared. From the first class Truncated Singular Value Decomposition (TSVD) and Truncated Generalized Singular Value Decomposition (TGSVD) methods and from the second class Generalized Tikhonov (GT) with the norms and semi-norms in Sobolev subspaces W12(a,b), W22(a,b) are applied and their capabilities for the regularization of the problem is compared. Our numerical results derived from simulated studies reveal that the GT method with discretized norm of Sobolev subspace W22(a,b) gives the best results among the studied methods for the regularization of the downward continuation problem based on the Abel-Poisson integral. On the contrary, the TGSVD method with the discretized second order derivatives has less consistency with the ill-posed problem and yields less accuracy. Finally, the GT method with discretized norm of Sobolev subspace W22(a,b) is applied to the downward continuation of real gravity data of the type modulus of gravity acceleration within the geographical region of Iran to derive a geoid model for this region.

In this study, a numerical approach of the spectral collocation method coupled with a regularization technique is applied for solving an inverse parabolic problem of the heat equation in a quarter plane. The problem includes the estimation of an unknown boundary condition from an overspecified condition. The stable solution of the problem exists and is proved by Tikhonov regularization technique. The algorithm works without any mesh points or elements, and accurate results can be obtained efficiently. By employing the numerical algorithm on the problem, the resultant matrix equation is ill-condition. To regularize this matrix equation, we apply regularization technique, with the L-curve and general cross-validation criteria for choosing the regularization parameter. For demonstrating the performance and ability of the proposed algorithm, a test example is presented. The numerical results showed that the solution obtained with the algorithm designed in this paper is stable with the noisy data and the unknown boundary condition was recovered very well.

Super-resolution (SR) aims to overcome the ill-posed conditions of image acquisition. SR facilitates scene recognition from low-resolution image(s). Various approaches have tried to aggregate the informative details of multiple low-resolution images into a high-resolution one. In this paper, we present a new robust fuzzy super resolution approach. Our approach, firstly registers two input image using SIFT-BP-RANSAC registration. Secondly, due to the importance of information gain ratio in the SR outcomes, the fuzzy regularization scheme uses the prior knowledge about the low-resolution image to add the amount of lost details of the input images to the registered one using the common linear observation model. Due to this fact, our approach iteratively tries to make a prediction of the high-resolution image based on the predefined regularization rules. Afterwards the low-resolution image have made out of the new high-resolution image. Minimizing the difference between the resulted low-resolution image and the input low-resolution image will justify our regularization rules. Flexible characteristics of fuzzy regularization adaptively behave on edges, detailed segments, and flat regions of local segments within the image. General information gain ratio also should grow during the regularization. Our fuzzy regularization indicates independence from the acquisition model. Consequently, robustness of our method on different ill-posed capturing conditions and against registration error noise compensates the shortcomings of same regularization approaches in the literature. Our final results show reduced aliasing achievements in comparison with similar recent state of the art works.