It is well-known that standard migration is not a true inverse operation and is based on the adjoint of the forward modeling operator. Due to this approximation the resulting migrated image can often suffer from various artifacts and uneven illumination issues, especially in regions of complex geology. Least-squares depth migration approximates the inverse of the forward modeling and can be use...

Important problems in many scientific computational areas are least squares problems. The problem of constraint least squares with full column weight matrix is a class of these problems. In this presentation, we are concerned with the connection between the condition numbers and the rounding error in the solution of the problem of constrained and weighted linear least squares. The fact that thi...

In this paper an inverse QR decomposition based recursive least-squares algorithm for linearly constrained minimum variance filtering is proposed. The proposed algorithm is numerically stable in finite precision environments and is suitable for implementation in systolic arrays or DSP vector architectures. Its performance is illustrated by simulations of a blind receiver for a multicarrier CDMA...

By using the complex representation of quaternion matrices, the Moore–Penrose generalized inverse and the Kronecker product of matrices, the expressions of the least squares η-Hermitian solution with the least norm and the expressions of the least squares η-anti-Hermitian solution with the least norm are derived for the matrix equation AXB+CXD = E over quaternions.

A recent study on the condition numbers of mixed least squares-total squares (MTLS) problem is due to Zheng and Yang (Numer Linear Algebra Appl. 2019;26(4):e2239). However, associated expressions are not compact Kronecker-product operations make computation costly. In this paper, we first present new alternative closed formula for order perturbation estimate MTLS solution. Then reveal relations...

Obtaining migrated images with meaningful amplitudes is a challenging problem when the migration operator is not unitary. One possible solution to this problem is iterative inversion. However, inversion is an expensive process that can be rather difficult to apply, especially with 3D data. In this paper, I propose estimating migrated images similar to the least-squares inverse images by approxi...