16339

14575

كارشناسي ارشد

آناليز عددي

اصفهان : دانشگاه صنعتي اصفهان

1399

سيزده، 71 ص. : مصور، جدول، نمودار

رضا مختاري

حميدرضا مرزبان، محمود منجگاني

1399/12/12

كتابنامه

رياضي كاربردي

رياضي

1399/12/16

2679580

Investigating some half quadratic algorithms for restoration and reconstruction Hajar Shooshtari h shooshtari@math iut ac ir 21 10 2020 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Reza Mokhtari mokhtari@cc iut ac ir 2010 MSC 68U 10 65K10 Keywords lp regularization Half quadratic algorithm Majorize minimize algorithm Impulse noise Compressive sensing Magnetic resonance imaging AbstractIn this thesis we study the lp lq minimization problem with q 2 p 0 has which receivedsigni cant attention in image restoration and compressive sensing The half quadratic reg ularization method is usually a technique to solve this problem The class of L1 regularizedoptimization problems has received much attention recently because of the introduction ofcompressed sensing which allows images and signals to be reconstructed from small amountsof data Despite this recent attention many L1 regularized problems remain di cult tosolve or require very problem speci c techniques To improve this technique s performance instead of the conjugate gradient CG method used an alternating direction method of mul tipliers ADM M as the inner iterations to solve the corresponding linear equations Theconjugate gradient method is an algorithm for the numerical solution of particular linearequations systems namely those whose matrix is positive de nite The conjugate gradientmethod is often implemented as an iterative algorithm applicable to sparse systems thatare too large to be handled by a direct implementation or other direct methods such as theCholesky decomposition The ADM M is an improved variant of the classical augmentedLagrangian method for solving linearly constrained convex programming problems to im age restoration The augmented Lagrangian method has been successfully applied to imagerestoration The convergence of the resulting algorithm is discussed Moreover based onthis we also study a half quadratic algorithm to solve the lp lq problem This algorithmis indeed a majorize minimize algorithm Some convergence results can be obtained immedi ately For example the objective function value is monotonically decreasing and convergent This iterative method is called the M M algorithm One of the virtues of this acronym isthat it does double duty In minimization problems the rst M of M M stands for majorizeand the second M for minimizing We apply this algorithm to T V l1 image restorationand compressive sensing in magnetic resonance M R imaging applications The numericalresults show that this algorithm is fast and e cient in restoring blurred images that arecorrupted by impulse noise and also in reconstructing M R images from very few k spacedata

رضا مختاري

حميدرضا مرزبان، محمود منجگاني