Synthetic aperture imaging radiometers (SAIRs) are powerful passive microwave systems for high-resolution by use of synthetic technique. However, the ill-posed inverse problem SAIRs makes it difficult to reconstruct high-precision brightness temperature map. The traditional regularization methods add a unique penalty all frequency bands solution, which may cause reconstructed result be too smoo...

given a mapping $f:xto x$ we naturally associate to it a monotonic map $gg_f:exp xto exp x$ from the power set of $x$ into itself, thus inducing a generalized topology on $x$. in this paper we investigate some properties of generalized topologies which are defined by such a procedure.

PURPOSE To develop a saturation recovery myocardial T1 mapping method for the simultaneous multislice acquisition of three slices. METHODS Saturation pulse-prepared heart rate independent inversion recovery (SAPPHIRE) T1 mapping was implemented with simultaneous multislice imaging using FLASH readouts for faster coverage of the myocardium. Controlled aliasing in parallel imaging (CAIPI) was u...

Parameter identification problems for partial differential equations usually lead to nonlinear inverse problems. A typical property of such problems is their instability, which requires regularization techniques, like, e.g., Tikhonov regularization. The main focus of this paper will be on efficient methods for determining a suitable regularization parameter by using adaptive finite element disc...

We present an efficient method for the reduction of model equations in the linearized diffuse optical tomography (DOT) problem. We first implement the maximum a posteriori (MAP) estimator and Tikhonov regularization, which are based on applying preconditioners to linear perturbation equations. For model reduction, the precondition is split into two parts: the principal components are consid...

In article the incorrect task for abstract polycaloric equation is studied and a stability assessment according to Tikhonov given.