On the regularization of linear inverse problems in Fourier optics

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Ill-posed Inverse Problems and Logarithmic Continuity in Electromagnetics

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The Stability of Inverse Problems

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Applied Inverse Problems in Optics

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Linear inverse problems with discrete data: II. Stability and regularization

For pt.I. see ibid. vol.1, p.301 (1985). In the first part of this work a general definition of an inverse problem with discrete data has been given and an analysis in terms of singular systems has been performed. The problem of the numerical stability of the solution, which in that paper was only briefly discussed, is the main topic of this second part. When the condition number of the problem is too large, a small error on the data can produce an extremely large error on the generalised solution, which therefore has no physical meaning. The authors review most of the methods which have been developed for overcoming this difficulty, including numerical filtering, Tikhonov regularisation, iterative methods, the Backus-Gilbert method and so on. Regularisation methods for the stable approximation of generalised solutions obtained through minimisation of suitable seminorms (C-generalised solutions), such as the method of Phillips (1962), are also considered.

SVD for linear inverse problems

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A new inversion procedure for confocal scanning microscopy and other bandlimited signal processing problems

We find a simple analytic expression for the inverse of an infinite matrix related to the problem of data reduction in confocal scanning microscopy and other band-limited signal processing problems. Potential applications of this result to practical problems are outlined. The matrix arises from a sampling expansion approach to the integral equation.

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.

Superresolution in linear inverse problems

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Estudio de la diferenciación y madurez sexual en la langosta de agua dulce, Cherax quadricarinatus (Decapoda, Astacidea, Parastacidae) y su aplicación en acuicultura

Cherax quadricarinatus, es una especie de langosta de agua dulce nativa de Australia y Papua Nueva Guinea que se cultiva en varios países incluyendo Argentina, por lo que las investigaciones acerca de su biología reproductiva están orientadas a conocer las condiciones óptimas de cultivo, y desarrollar técnicas para su reproducción y crecimiento. El objetivo general fue determinar el momento del desarrollo en que ocurre la diferenciación sexual y el posible rol regulador de la temperatura, caracterizar el proceso de diferenciación gonadal y madurez sexual, y los cambios morfométricos asociados. Los resultados indicaron que la diferenciación sexual secundaria ocurre a partir de los 0,23 g aproximadamente, correspondiente al estadio juvenil VI ó VII. La temperatura no ejerció un claro efecto sobre la diferenciación sexual. Las hembras, desde la diferenciación gonadal hasta su maduración, presentaron tres morfotipos ováricos. En función de la coloración ovárica, la estructura histológica y la proporción de los distintos tipos celulares se distinguieron cuatro estadios de desarrollo ovárico: I (blanco-transparente), II (crema pálido-naranja pálido), III (naranja con oocitos verdes) y IV (verde oliva). En los machos se identificaron tres estadios de desarrollo y dos tipos de appendices masculinae ó papilas fálicas. Se reconocieron diferentes patrones de intersexualidad y cuatro posibles combinaciones de aberturas genitales que permitieron definir cuatro tipos de intersexo: intersexo hembra (I), intersexo macho (II), y dos tipos de intersexo macho-hembra (III y IV). Los resultados del análisis morfométrico mostraron que los intersexos hembras representan un tipo sexual morfométricamente diferenciado de las hembras y los machos, aunque desde el punto de vista funcional son hembras. Los cambios en las relaciones morfométricas de las dimensiones de los quelípedos se vincularon con el inicio de la la madurez sexual desde el punto de vista histológico en los machos e intersexos hembra.

Aptitud reproductiva en toros : etología sexual y fertilidad

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Graphical representation and generalization in sequences problems

In this paper we present different ways used by Secondary students to generalize when they try to solve problems involving sequences. 359 Spanish students solved generalization problems in a written test. These problems were posed through particular terms expressed in different representations. We present examples that illustrate different ways of achieving various types of generalization and how students express generalization. We identify graphical representation of generalization as a useful tool of getting other ways of expressing generalization, and we analyze its connection with other ways of expressing it.

Shop scheduling problems under precedence constraints

The paper considers a scheduling model that generalizes the well-known open shop, flow shop, and job shop models. For that model, called the super shop, we study the complexity of finding a time-optimal schedule in both preemptive and non-preemptive cases assuming that precedence constraints are imposed over the set of jobs. Two types of precedence rela-tions are considered. Most of the arising problems are proved to be NP-hard, while for some of them polynomial-time algorithms are presented.

An application of quasi-Newton methods for the numerical solution of interface problems

Quasi-Newton methods are applied to solve interface problems which arise from domain decomposition methods. These interface problems are usually sparse systems of linear or nonlinear equations. We are interested in applying these methods to systems of linear equations where we are not able or willing to calculate the Jacobian matrices as well as to systems of nonlinear equations resulting from nonlinear elliptic problems in the context of domain decomposition. Suitability for parallel implementation of these algorithms on coarse-grained parallel computers is discussed.

Heuristics for short route job shop scheduling problems

We consider two “minimum”NP-hard job shop scheduling problems to minimize the makespan. In one of the problems every job has to be processed on at most two out of three available machines. In the other problem there are two machines, and a job may visit one of the machines twice. For each problem, we define a class of heuristic schedules in which certain subsets of operations are kept as blocks on the corresponding machines. We show that for each problem the value of the makespan of the best schedule in that class cannot be less than 3/2 times the optimal value, and present algorithms that guarantee a worst-case ratio of 3/2.