Several mathematical methods are discussed in this paper, which are applied in image compression and restoration. Singular value decomposition (SVD) is used in compressing image. Conjugate gradients (CG) method and truncated Singular value decomposition (TSVD) regularization method are applied in image restoration. From the experience results we can see that those methods are effective in image...

Cortical dipole imaging has been developed to visualize brain electrical activity in high spatial resolution. It is necessary to solve an inverse problem to estimate the cortical dipole distribution from the scalp potentials. In the present study, the accuracy of cortical dipole imaging was improved by focusing on filtering property of the spatial inverse filter. We proposed an inverse filter t...

The desingularized meshless method (DMM) has been successfully used to solve boundary-value problems with specified boundary conditions (a direct problem) numerically. In this paper, the DMM is applied to deal with the problems with over-specified boundary conditions. The accompanied ill-posed problem in the inverse problem is remedied by using the Tikhonov regularization method and the truncat...

The generalized singular value decomposition (GSVD) often is used to solve Tikhonov regularization problems with a regularization matrix without exploitable structure. This paper describes how the standard methods for the computation of the GSVD of a matrix pair can be simplified in the context of Tikhonov regularization. Also, other regularization methods, including truncated GSVD, are conside...

In this paper, we propose different algorithms for the solution of a tensor linear discrete ill-posed problem arising in application meshless method solving PDEs three-dimensional space using multiquadric radial basis functions. It is well known that truncated singular value decomposition (TSVD) most common effective solver ill-conditioned systems, but unfortunately operation count system with ...

Linear discrete ill-posed problems of small to medium size are commonly solved by first computing the singular value decomposition of the matrix and then determining an approximate solution by one of several available numerical methods, such as the truncated singular value decomposition or Tikhonov regularization. The determination of an approximate solution is relatively inexpensive once the s...

In this work we analyze ill{posed problems modelled by rst kind Fred-holm integral equations with non degenerate kernel. We survey the main properties of the least{squares solutions and derive the regularized solutions in the cases of Truncated Singular Value Decomposition, Tikhonov method and Conjugate Gradient regularization method. Numerical results are reported in the case of medical imagin...

Radio Tomographic Imaging (RTI) is an emerging technology that uses received signal strength measurements to image the attenuation of objects within a wireless network area. RTI is by nature an ill-posed inverse problem, therefore, regularization techniques must be utilized to obtain accurate images. This paper discusses some common regularization techniques, including Tikhonov, truncated singu...

This paper presents for the first time the hardware design of low complexity detection algorithms for the recovery of Spectrally Efficient Frequency Division Multiplexing (SEFDM) signals. The work shows that a practical design is feasible using Field Programmable Gate Arrays (FPGAs). Two detection techniques can be implemented using the proposed system architecture, namely Zero Forcing (ZF) and...

A helicopter deck is the main load-bearing component under emergency landing conditions for helicopters. However, it generally difficult to directly obtain load from measurements due high randomness of position. As design deck, very important its structural design. large value leads an overly conservative and affects control ship’s weight center gravity, while a small may lead lack security aff...