Reverse-time de-migration (RTDM) is formulated as the adjoint operator of reverse-time migration (RTM). In acoustic medium, RTM provides a good approximation to the inverse of RTDM, and can be used to iteratively invert for the reflectivity image in least-squares RTM (LSRTM). In viscoelastic medium, however, the adjoint of the RTDM operator is far from its inverse because of amplitude attenuati...

In this paper, a two-stage iterative algorithm is proposed to improve the convergence of Krylov based iterative methods, typically those of GMRES variants. The principle of the proposed approach is to build an external iteration over the Krylov method, and to frequently store its current residual (at each GMRES restart for instance). After a given number of outer iterations, a least-squares min...

We develop a general convergence theory for the generalized minimal residual method for least squares problems preconditioned with inner iterations. The inner iterations are performed by stationary iterative methods. We also present theoretical justifications for using specific inner iterations such as the Jacobi and SOR-type methods. The theory is improved particularly in the rankdeficient cas...

localizing the optic disc (od) in retinal fundus images is of critical importance, since it is very similar to hard exudates (found in pathology) in color and brightness. because of the importance of od localization in clinical applications, many techniques have been developed. in this paper, we present the results obtained from two methods, correlation and least square, to approximate the opti...

iv erative methods to solve least squares problems more efficiently. We especially focused on one kind of preconditioners, in which preconditioners are the approximate generalized inverses of the coefficient matrices of the least squares problems. We proposed two different approaches for how to construct the approximate generalized inverses of the coefficient matrices: one is based on the Minim...

We consider the behavior of the GMRES method for solving a linear system Ax = b when A is singular or nearly so, i.e., ill conditioned. The (near) singularity of A may or may not affect the performance of GMRES, depending on the nature of the system and the initial approximate solution. For singular A, we give conditions under which the GMRES iterates converge safely to a least-squares solution...

For the solution of large, sparse, non-Hermitian linear systems, Lanczos-type product methods that are based on the Lanczos three-term recurrence are derived in a systematic way. These methods either square the Lanczos process or combine it with a local minimization of the residual. For them a quasi-minimal residual (QMR) smoothing is proposed that can also be implemented by short-term recurren...

background: the wilms tumor 1 (wt1) gene is originally defined as a tumor suppressor gene and a transcription factor that overexpressed in leukemic cells. it is highly expressed in more than 80% of acute myeloid leukemia (aml) patients, both in bone marrow (bm) and in peripheral blood (pb), and it is used as a powerful and independent marker of minimal residual disease (mrd);we have determined ...