On the regularizing behavior of the SDA and SDC gradient methods in the solution of linear ill-posed problems

We analyze the regularization properties of two recently proposed gradient methods, SDA and SDC, applied to discrete linear inverse problems. By studying their filter factors, we show that the tendency of these methods to eliminate first the eigencomponents of the gradient corresponding to large singular values allows to reconstruct the most significant part of the solution, thus yielding a useful filtering effect. This behavior is confirmed by numerical experiments performed on some image restoration problems. Furthermore, the experiments show that, for severely ill-conditioned problems and high noise levels, the SDA and SDC methods can be competitive with the Conjugate Gradient (CG) method, since they are slightly slower than CG, but exhibit a better semiconvergence behavior

An efficient gradient method using the Yuan steplength

We propose a new gradient method for quadratic programming, named SDC, which alternates some steepest descent (SD) iterates with some gradient iterates that use a constant steplength computed through the Yuan formula. The SDC method exploits the asymptotic spectral behaviour of the Yuan steplength to foster a selective elimination of the components of the gradient along the eigenvectors of the Hessian matrix, i.e., to push the search in subspaces of smaller and smaller dimensions. The new method has global and R-linear convergence. Furthermore, numerical experiments show that it tends to outperform the Dai–Yuan method, which is one of the fastest methods among the gradient ones. In particular, SDC appears superior as the Hessian condition number and the accuracy requirement increase. Finally, if the number of consecutive SD iterates is not too small, the SDC method shows a monotonic behaviour

Supervised classification methods for mining cell differences as depicted by Raman spectroscopy

Discrimination of different cell types is very important in many medical and biological applications. Existing methodologies are based on cost inefficient technologies or tedious one-by-one empirical examination of the cells. Recently, Raman spectroscopy, a inexpensive and efficient method, has been employed for cell discrimination. Nevertheless, the traditional protocols for analyzing Raman spectra require preprocessing and peak fitting analysis which does not allow simultaneous examination of many spectra. In this paper we examine the applicability of supervised learning algorithms in the cell differentiation problem. Five different methods are presented and tested on two different datasets. Computational results show that machine learning algorithms can be employed in order to automate cell discrimination tasks. © 2011 Springer-Verlag Berlin Heidelberg