1,720,995 research outputs found
Regularization processes for real functions and ill-posed Toeplitz problems
No full textMost preconditioners for Toeplitz systems A(n)(f) arising in the discretization of ill-posed problems give rise to instability and noise amplification. Indeed, since these preconditioners are constructed from linear approximation processes of the generating function f, they inherit the ill-posedness of the problem.Here we first identify a novel set of approximation processes which regularizes the inversion of real functions. Then, such processes are used as a basic tool for the computation of preconditioners endowed with regularizing properties. We show that these preconditioners provide fast convergence and noise control of iterative methods for discrete ill-posed Toeplitz systems
Superoptimal approximation for unbounded symbols
No full textThe superoptimal Frobenius approximation of Toeplitz matrices is considered in connection with the case of unbounded symbols. In particular, we use the superoptimal approximation as preconditioner for the CG method when a Fisher-Hartwig singularity is present in the symbol, with special regard to systems coming from times series and financial applications. A theoretical discussion concerning classical circulant preconditioners and a numerical comparison with the Strang and with the optimal approximations are presented particularly with reference to the presence of noise
Structure preserving preconditioners for image deblurring
No full textRegularizing preconditioners for accelerating the convergence of iterative regularization methods without spoiling the quality of the approximated solution have been extensively investigated in the last twenty years. Several strategies have been proposed for defining proper preconditioners. Usually, in methods for image restoration, the structure of the preconditioner is chosen Block Circulant with Circulant Blocks (BCCB) because it can be efficiently exploited by Fast Fourier Transform (FFT). Nevertheless, for ill-conditioned problems, it is well-known that BCCB preconditioners cannot provide a strong clustering of the eigenvalues. Moreover, in order to get an effective preconditioner, it is crucial to preserve the structure of the coefficient matrix. The structure of such a matrix, in case of image deblurring problem, depends on the boundary conditions imposed on the imaging model. Therefore, we propose a technique to construct a preconditioner which has the same structure of the blurring matrix related to the restoration problem at hand. The construction of our preconditioner requires two FFTs like the BCCB preconditioner. The presented preconditioning strategy represents a generalization and an improvement with respect to both circulant and structured preconditioning available in the literature. The technique is further extended to provide a non-stationary preconditioning in the same spirit of a recent proposal for BCCB matrices. Some numerical results show the importance of preserving the matrix structure from the point of view of both restoration quality and robustness of the regularization parameter
Microwave Characterization of Brain Stroke Through a Mild Data-Driven Inversion Strategy
No full textStroke Detection and Monitoring by Means of a Multifrequency Microwave Inversion Approach
No full textIn the area of biomedical diagnostics, microwave imaging techniques have been recently proposed for performing brain stroke detection and monitoring. Indeed, theoretically, these techniques make it possible to meet the timeliness requirements of such a diagnosis with portable systems. Moreover, relying on the use of microwaves, they are noninvasive and allow continuous monitoring of critical patients. In this paper, the microwave imaging problem is solved by exploiting multifrequency data by an inexact-Newton method formulated in the framework of non-constant exponent Lebesgue spaces. First, the method is numerically validated with three-dimensional head models affected by anatomically-realistic strokes. Then, a further assessment through experimental data obtained with a cylindrical phantom is conducted. A quite accurate reconstruction of the variations of dielectric properties inside the patient’s head due to the insurgence of stroke is obtained in both numerical and experimental cases, showing the potentiality of the proposed approach
A novel method to improve the spatial resolution of microwave radiometer measurements using variable exponent Lebesgue space
No full textSpatial resolution enhancement of microwave radiometer measurements is addressed using a new method that is based on an Lp penalisation approach with a variable p exponent. The key idea is letting p to vary in the range 1.2 - 2 to take benefit of both Hilbert (i.e. p=2) and Banach (i.e. p=1.2) advantages. Results, obtained processing both simulated and actual Special Sensor Microwave Imager (SSM/I) measurements, demonstrate the benefits of the proposed approach in reconstructing abrupt discontinuities and smooth gradients with respect to approaches in Hilbert and Banach spaces
A resolution-enhanced product for the SMAP L-band radiometer
No full textThis study addresses the spatial resolution enhancement of synthetic microwave radiometer observations obtained by the Soil Moisture Active Passive (SMAP) L-Band Radiometer. An antenna pattern deconvolution method is used together with an iterative regularization scheme to reconstruct the brightness field at enhanced spatial resolution. Results obtained processing both synthetic and actual SMAP measurements show that sharper edges and coastlines can be reconstructed in a very effective way
A NEW ANTENNA PATTERN DECONVOLUTION METHOD TO ENHANCE THE SPATIAL RESOLUTION OF MULTI-CHANNEL MICROWAVE RADIOMETER MEASUREMENTS
No full textIn this study, a new antenna pattern deconvolution method to enhance the spatial resolution of multi-channel microwave radiometer (MWR) measurements is developed. This technique, based on a conventional gradient-like iterative method, utilizes the information contained in a high-frequency channel to enhance the spatial resolution of the lower-frequency channel in a data-fusion fashion. The physical idea consists of initializing the gradient-like inversion scheme using higher frequency details that are filtered out by the system measurement function. Experiments, performed on a dataset that includes both simulated and actual radiometer measurements, show that the proposed technique allows outperforming the conventional gradient method, while being very robust with respect to artifacts that could be induced by the higher frequency channel
Microwave imaging by means of Lebesgue-space inversion: An overview
No full textAn overview of the recent advancements in the development of microwave imaging procedures based on the exploitation of the regularization theory in Lebesgue spaces is reported in this paper. Such inversion schemes have been found to provide accurate results in several microwave imaging scenarios, thanks to the different geometrical properties that Lebesgue spaces can exhibit with respect to the more classical Hilbert ones. Moreover, the recent extension to the more general case of variable-exponent Lebesgue spaces is also addressed. Experimental results involving reference data are shown for supporting the theoretical description of the approaches
On the Use of Preconditioners to Improve the Accuracy and Effectiveness of Iterative Methods to Enhance the Spatial Resolution of Radiometer Measurements
No full textIn this letter, a new approach is proposed to ameliorate the performance of iterative gradient-like regularization schemes aimed at enhancing the spatial resolution of microwave radiometer measurements in the Hilbert space. The approach consists of preconditioning the ill-conditioned discrete problem to let the iterative gradient-based inversion technique be more computer-time effective. Experiments undertaken on the simulated radiometer brightness profiles demonstrate the soundness of the proposed rationale that outperforms conventional gradient-like methods in terms of both computer-time effectiveness and accuracy in reconstructing spot-like discontinuities while resulting in larger fluctuations over the background
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