Bayesian image reconstruction with space-variant noise suppression

In this paper we present a Bayesian image reconstruction algorithm with entropy prior (FMAPE) that uses a space-variant hyperparameter. The spatial variation of the hyperparameter allows different degrees of resolution in areas of different statistical characteristics, thus avoiding the large residuals resulting from algorithms that use a constant hyperparameter. In the first implementation of the algorithm, we begin by segmenting a Maximum Likelihood Estimator (MLE) reconstruction. The segmentation method is based on using a wavelet decomposition and a self-organizing neural network. The result is a predetermined number of extended regions plus a small region for each star or bright object. To assign a different value of the hyperparameter to each extended region and star, we use either feasibility tests or cross-validation methods. Once the set of hyperparameters is obtained, we carried out the final Bayesian reconstruction, leading to a reconstruction with decreased bias and excellent visual characteristics. The method has been applied to data from the non-refurbished Hubble Space Telescope. The method can be also applied to ground-based images.

Potencialidad de la modelización state-space y el filtro de Kalman para el anàlisis regional : una aplicación para el índice de actividad industrial

El déficit existente a nuestro país con respecto a la disponibilidad de indicadores cuantitativos con los que llevar a término un análisis coyuntural de la actividad industrial regional ha abierto un debate centrado en el estudio de cuál es la metodología más adecuada para elaborar indicadores de estas características. Dentro de este marco, en este trabajo se presentan las principales conclusiones obtenidas en anteriores estudios (Clar, et. al., 1997a, 1997b y 1998) sobre la idoneidad de extender las metodologías que actualmente se están aplicando a las regiones españolas para elaborar indicadores de la actividad industrial mediante métodos indirectos. Estas conclusiones llevan a plantear una estrategia distinta a las que actualmente se vienen aplicando. En concreto, se propone (siguiendo a Israilevich y Kuttner, 1993) un modelo de variables latentes para estimar el indicador de la producción industrial regional. Este tipo de modelo puede especificarse en términos de un modelo statespace y estimarse mediante el filtro de Kalman. Para validar la metodología propuesta se estiman unos indicadores de acuerdo con ella para tres de las cuatro regiones españolas que disponen d¿un Índice de Producción Industrial (IPI) elaborado mediante el método directo (Andalucía, Asturias y el País Vasco) y se comparan con los IPIs publicados (oficiales). Los resultados obtenidos muestran el buen comportamiento de l¿estrategia propuesta, abriendo así una línea de trabajo con la que subsanar el déficit al que se hacía referencia anteriormente

Potencialidad de la modelización state-space y el filtro de Kalman para el anàlisis regional : una aplicación para el índice de actividad industrial

El déficit existente a nuestro país con respecto a la disponibilidad de indicadores cuantitativos con los que llevar a término un análisis coyuntural de la actividad industrial regional ha abierto un debate centrado en el estudio de cuál es la metodología más adecuada para elaborar indicadores de estas características. Dentro de este marco, en este trabajo se presentan las principales conclusiones obtenidas en anteriores estudios (Clar, et. al., 1997a, 1997b y 1998) sobre la idoneidad de extender las metodologías que actualmente se están aplicando a las regiones españolas para elaborar indicadores de la actividad industrial mediante métodos indirectos. Estas conclusiones llevan a plantear una estrategia distinta a las que actualmente se vienen aplicando. En concreto, se propone (siguiendo a Israilevich y Kuttner, 1993) un modelo de variables latentes para estimar el indicador de la producción industrial regional. Este tipo de modelo puede especificarse en términos de un modelo statespace y estimarse mediante el filtro de Kalman. Para validar la metodología propuesta se estiman unos indicadores de acuerdo con ella para tres de las cuatro regiones españolas que disponen d¿un Índice de Producción Industrial (IPI) elaborado mediante el método directo (Andalucía, Asturias y el País Vasco) y se comparan con los IPIs publicados (oficiales). Los resultados obtenidos muestran el buen comportamiento de l¿estrategia propuesta, abriendo así una línea de trabajo con la que subsanar el déficit al que se hacía referencia anteriormente

Variational analysis of the Gross-Neveu model in an S^1 space

The Gross-Neveu model in an S^1 space is analyzed by means of a variational technique: the Gaussian effective potential. By making the proper connection with previous exact results at finite temperature, we show that this technique is able to describe the phase transition occurring in this model. We also make some remarks about the appropriate treatment of Grassmann variables in variational approaches.

Pairing in a two-component ultracold Fermi gas: Phases with broken-space symmetries

We explore the phase diagram of a two-component ultracold atomic Fermi gas interacting with zero-range forces in the limit of weak coupling. We focus on the dependence of the pairing gap and the free energy on the variations in the number densities of the two species while the total density of the system is held fixed. As the density asymmetry is increased, the system exhibits a transition from a homogenous Bardeen-Cooper-Schrieffer (BCS) phase to phases with spontaneously broken global space symmetries. One such realization is the deformed Fermi surface superfluidity (DFS) which exploits the possibility of deforming the Fermi surfaces of the species into ellipsoidal form at zero total momentum of Cooper pairs. The critical asymmetries at which the transition from DFS to the unpaired state occurs are larger than those for the BCS phase. In this precritical region the DFS phase lowers the pairing energy of the asymmetric BCS state. We compare quantitatively the DFS phase to another realization of superconducting phases with broken translational symmetry: the single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell phase, which is characterized by a nonvanishing center-of-mass momentum of the Cooper pairs. The possibility of the detection of the DFS phase in the time-of-flight experiments is discussed and quantified for the case of 6Li atoms trapped in two different hyperfine states.

Poincaré is a subgroup of Galilei in one space dimension more

Through an imaginary change of coordinates, the ordinary Poincar algebra is shown to be a subalgebra of the Galilei one in four space dimensions. Through a subsequent contraction the remaining Lie generators are eliminated in a natural way. An application of these results to connect Galilean and relativistic field equations is discussed.

Nonlinear filtering in object and Fourier space in a joint transform optical correlator: comparison and experimental realization

The use of different kinds of nonlinear filtering in a joint transform correlator are studied and compared. The study is divided into two parts, one corresponding to object space and the second to the Fourier domain of the joint power spectrum. In the first part, phase and inverse filters are computed; their inverse Fourier transforms are also computed, thereby becoming the reference in the object space. In the Fourier space, the binarization of the power spectrum is realized and compared with a new procedure for removing the spatial envelope. All cases are simulated and experimentally implemented by a compact joint transform correlator.

Massless minimally coupled fields in de Sitter space: O(4)-symmetric states versus de Sitter invariant vacuum

The issue of de Sitter invariance for a massless minimally coupled scalar field is examined. Formally, it is possible to construct a de Sitterinvariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observers spacetime path grows linearly with the observers proper time for a quantum state that does not break de Sitter invariance. Also, we use the Hadamard formalism to compute the renormalized expectation value of the energy-momentum tensor, both in the O(4)-invariant states introduced by Allen and Follaci, and in the de Sitterinvariant vacuum. We find that the vacuum energy density in the O(4)-invariant case is larger than in the de Sitterinvariant case.