Superresolution: an ill-posed problem in Fourier optics

info:eu-repo/semantics/published

Ill-posed Inverse Problems and Logarithmic Continuity in Electromagnetics

info:eu-repo/semantics/published

Ill-Posedness, Regularization and Number of Degrees of Freedom

info:eu-repo/semantics/published

Guidelines on artificial nutrition versus hydration in terminal cancer patients

Whether a terminally ill cancer patient should be actively fed or simply hydrated through subcutaneous or intravenous infusion of isotonic fluids is a matter of ongoing controversy among clinicians involved in the care of these patients. Under the auspices of the European Association for Palliative Care, a committee of experts developed guidelines to help clinicians make a reasonable decision on what type of nutritional support should be provided on a case-by-case basis. It was acknowledged that part of the controversy related to the definition of the terminal cancer patient, since this is a heterogeneous group of patients with different needs, expectations, and potential for a medical intervention. A major difficulty is the prediction of life expectancy and the patient's likely response to vigorous nutritional support. In an attempt to reach a decision on the type of treatment support (artificial nutrition vs. hydration) which would best meet the needs and expectations of the patient, we propose a three-step process: Step I: define the eight key elements necessary to reach a decision: Step II: make the decision; and Step III: reevaluate the patient and the proposed treatment at specified intervals. Step I involves assessing the patient concerning the following: 1) oncological/clinical condition; 2) symptoms; 3) expected length of survival; 4) hydration and nutritional status; 5) spontaneous or voluntary nutrient intake; 6) psychological profile; 7) gut function and potential route of administration; and 8) need for special services based on type of nutritional support prescribed. Step II involves the overall assessment of pros and cons, based on information determined in Step I, in order to reach an appropriate decision based on a well-defined end point (i.e. improvement of quality of life; maintaining patient survival; attaining rehydration). Step III involves the periodic reevaluation of the decision made in Step II based on the proposed goal and the attained result.

A regularized iterative algorithm for limited-angle inverse Radon transform

The tomography problem is investigated when the available projections are restricted to a limited angular domain. It is shown that a previous algorithm proposed for extrapolating the data to the missing cone in Fourier space is unstable in the presence of noise because of the ill-posedness of the problem. A regularized algorithm is proposed, which converges to stable solutions. The efficiency of both algorithms is tested by means of numerical simulations. © 1983 Taylor and Francis Group, LLC.

Regularized iterative and noniterative procedures for object restoration in the presence of noise :an error analysis

An analysis is carried out, using the prolate spheroidal wave functions, of certain regularized iterative and noniterative methods previously proposed for the achievement of object restoration (or, equivalently, spectral extrapolation) from noisy image data. The ill-posedness inherent in the problem is treated by means of a regularization parameter, and the analysis shows explicitly how the deleterious effects of the noise are then contained. The error in the object estimate is also assessed, and it is shown that the optimal choice for the regularization parameter depends on the signal-to-noise ratio. Numerical examples are used to demonstrate the performance of both unregularized and regularized procedures and also to show how, in the unregularized case, artefacts can be generated from pure noise. Finally, the relative error in the estimate is calculated as a function of the degree of superresolution demanded for reconstruction problems characterized by low space–bandwidth products.

Be rich or don’t be sick: Estimating Vietnamese patients’ risk of falling into destitution

This paper represents the first research attempt to estimate the probabilities for Vietnamese patients to fall into destitution facing financial burdens occurring during their curative stay in hospital. The study models the risk against such factors as level of insurance coverage, location of patient, costliness of treatment, among others. The results show that very high probabilities of destitution, approximately 70%, apply to a large group of patients, who are nonresident, poor and ineligible for significant insurance coverage. There is also a probability of 58% that low-income patients who are seriously ill and face higher health care costs would quit their treatment. These facts will put Vietnamese government’s ambitious plan of increasing both universal coverage (UC) to 100% of expenditure and rate of UC beneficiaries to 100% at a serious test. The study also raises issues of asymmetric information and alternative financing options for the poor, who are most exposed to risk of destitution, following market-based health care reforms.

Positive regularised solutions in electromagnetic inverse scattering

Fredholm integral equations of the first kind are the mathematical model common to several electromagnetic, optical and acoustical inverse scattering problems. In most of these problems the solution must be positive in order to satisfy physical plausibility. We consider ill-posed deconvolution problems and investigate several linear regularization algorithms which provide positive approximate solutions at least in the absence of errors on the data.

Stability Problems in Inverse Diffraction

Inverse diffraction consists in determining the field distribution on a boundary surface from the knowledge of the distribution on a surface situated within the domain where the wave propagates. This problem is a good example for illustrating the use of least-squares methods (also called regularization methods) for solving linear ill-posed inverse problem. We focus on obtaining error bounds For regularized solutions and show that the stability of the restored field far from the boundary surface is quite satisfactory: the error is proportional to ∊(ðŗ‚ ≃ 1) ,ðŗœ being the error in the data (Hölder continuity). However, the error in the restored field on the boundary surface is only proportional to an inverse power of │In∊│ (logarithmic continuity). Such a poor continuity implies some limitations on the resolution which is achievable in practice. In this case, the resolution limit is seen to be about half of the wavelength. Copyright © 1981 by The Institute of Electrical and Electronics Engineers, Inc.