‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...

Regularization approaches based on spectral filtering can be highly effective in solving ill-posed inverse problems. These methods, however, require computing the singular value decomposition (SVD) and choosing appropriate regularization parameters. These tasks can be prohibitively expensive for large-scale problems. In this paper, we present a framework that uses operator approximations to eff...

We present a second-order expansion for singular subspace decomposition in the context of real matrices. Furthermore, we show that, when some particular assumptions are considered, the obtained results reduce to existing ones, namely those by Vaccaro [SIAM J. on Matrix Anal. and Appl., 15(1994), pp. 661-671], or those by Zhengyuan [IEEE Trans. Signal Proc., 50(2002), pp. 2820-2830]. We make use...

Ionospheric tomography is a method to investigate the ionospheric electron density in two or three dimensions. In this study, the function-based tomographic technique has been used for regional reconstruction of a 3D tomographic model of the ionospheric electron density using the GPS measurements of the Iranian Permanent GPS Network. Two-dimensional Haar wavelets and empirical orthogonal functi...

Spectral computed tomography (CT) has become increasingly of interest with the development of photon counting X-ray detector technology. The energy selective measurement capabilities of these devices open the doors to many exciting directions in CT research across a number of fields including security applications. Over the past year our work under ALERT support has been directed at the continu...

the problem of downward continuation of the gravity field from the earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying stokes formula is sought in terms of the disturbing potential on the ellipsoid but the disturbing gravity observations are only available on the earth’s surface. downward contin...