In this paper Legendre wavelet bases have been used for finding approximate solutions to singular boundary value problems arising in physiology. When the number of basis functions are increased the algebraic system of equations would be ill-conditioned (because of the singularity), to overcome this for large $M$, we use some kind of Tikhonov regularization. Examples from applied sciences are pr...

We present an image reconstruction method for diffuse optical tomography (DOT) by using the sparsity regularization and expectation-maximization (EM) algorithm. Typical image reconstruction approaches in DOT employ Tikhonov-type regularization, which imposes restrictions on the L(2) norm of the optical properties (absorption/scattering coefficients). It tends to cause a blurring effect in the r...

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 witho...

The rational function model (RFM) utilized for high resolution satellite imagery (HRSI) provides a transformation from image to object space coordinates in a geographic reference system. Compared with the rigorous model based on the collinearity condition equation or the affine model, the RFM with 80 coefficients would be over parameterized. That would result in an ill-conditioned normal equati...

This paper presents a novel physics-driven spatiotemporal regularization (STRE) method for high-dimensional predictive modeling in complex healthcare systems. This model not only captures the physics-based interrelationship between time-varying explanatory and response variables that are distributed in the space, but also addresses the spatial and temporal regularizations to improve the predict...

This paper develops a Tikhonov regularization theory for nonlinear ill-posed operator equations in Banach spaces. As the main challenge, we consider so-called oversmoothing state sense that penalization is not able to capture true solution regularity and leads infinite penalty value solution. We establish vast extension of Hilbertian convergence through use invertible sectorial operators from h...