Superoptimal Preconditioned Conjugate Gradient Iteration for Image Deblurring

We study the superoptimal Frobenius operators in the two-level circulant algebra. We consider two specific viewpoints: ( 1) the regularizing properties in imaging and ( 2) the computational effort in connection with the preconditioned conjugate gradient method. Some numerical experiments illustrating the effectiveness of the proposed technique are given and discussed

On the Trade-Off Between Enhancement of the Spatial Resolution and Noise Amplification in Conical-Scanning Microwave Radiometers

The ability to enhance the spatial resolution of measurements collected by a conical-scanning microwave radiometer (MWR) is discussed in terms of noise amplification and improvement of the spatial resolution. Simulated (and actual) brightness temperature profiles are analyzed at variance of different intrinsic spatial resolutions and adjacent beams overlapping modeling a simplified 1-D measurement configuration (MC). The actual measurements refer to Special Sensor Microwave Imager (SSM/I) data collected using the 19.35 and the 37.00 GHz channels that match the simulated configurations. The reconstruction of the brightness profile at enhanced spatial resolution is performed using an iterative gradient method which allows a fine tuning of the level of regularization. Objective metrics are introduced to quantify the enhancement of the spatial resolution and noise amplification. Numerical experiments, performed using the simplified 1-D MC, show that the regularized deconvolution results in negligible advantages when dealing with low-overlapping/fine-spatial-resolution configurations. Regularization is a mandatory step when addressing the high-overlapping/low-spatial-resolution case and the spatial resolution can be enhanced up to 2.34 with a noise amplification equal to 1.56. A more stringent requirement on the noise amplification (up to 0.6) results in an improvement of the spatial resolution up to 1.64

Mapping the dielectric properties of unknown targets by using a network of microwave sensors: A proof-of-concept

The subject of this paper is the possible use of a network of microwave sensors to achieve a map of the electromagnetic properties of unknown targets. The basic idea is to use a set of microwave sensors to illuminate a region of interest and to measure the resulting axial component of the electric field. Measurements are then processed by means of a technique based on inverse-scattering, which provides an estimate map of the dielectric values of the area under examination, allowing to discriminate among possible targets. In order to initially evaluate the feasibility of the proposed approach, numerical results in a simulated environment are preliminarily considered and discussed. Furthermore, an initial test on experimental data in a simplified configuration is also presented

Alternating Direction Implicit (ADI) schemes for a PDE-based image osmosis model

We consider \emph{Alternating Direction Implicit} (ADI) splitting schemes to compute efficiently the numerical solution of the PDE osmosis model considered by Weickert et al. for several imaging applications. The discretised scheme is shown to preserve analogous properties to the continuous model. The dimensional splitting strategy traduces numerically into the solution of simple tridiagonal systems for which standard matrix factorisation techniques can be used to improve upon the performance of classical implicit methods, even for large time steps. Applications to the shadow removal problem are presented

phaseless tomographic inverse scattering in banach spaces

In conventional microwave imaging, a hidden dielectric object under test is illuminated by microwave incident waves and the field it scatters is measured in magnitude and phase in order to retrieve the dielectric properties by solving the related non-homogenous Helmholtz equation or its Lippmann-Schwinger integral formulation. Since the measurement of the phase of electromagnetic waves can be still considered expensive in real applications, in this paper only the magnitude of the scattering wave fields is measured in order to allow a reduction of the cost of the measurement apparatus. In this respect, we firstly analyse the properties of the phaseless scattering nonlinear forward modelling operator in its integral form and we provide an analytical expression for computing its Frechet derivative. Then, we propose an inexact Newton method to solve the associated nonlinear inverse problems, where any linearized step is solved by a Lp Banach space iterative regularization method which acts on the dual space Lp* . Indeed, it is well known that regularization in special Banach spaces, such us Lp with 1 < p < 2, allows to promote sparsity and to reduce Gibbs phenomena and over-smoothness. Preliminary results concerning numerically computed field data are shown

A class of filtering superoptimal preconditioners for highly ill-conditioned linear systems

Popular preconditioners for conjugate gradient methods often reveal poor regularization properties that make them useless for very ill-conditioned linear systems arising in inverse problems. Recent results have awakened the interest towards the Tyrtyshnikov superoptimal preconditioners since it has been demonstrated that they exhibit good filtering capabilities. Here, in order to improve the regularizing behaviour, we generalize the definition of superoptimal preconditioner. Later on, by means of this more general definition, we develop a particular family of preconditioners for Toeplitz highly ill-conditioned linear systems