A robust orthogonal adaptive approach to SISO deconvolution

This paper formulates in a common framework some results from the fields of robust filtering, function approximation with orthogonal basis, and adaptive filtering, and applies them for the design of a general deconvolution processor for SISO systems. The processor is designed to be robust to small parametric uncertainties in the system model, with a partially adaptive orthogonal structure. A simple gradient type of adaptive algorithm is applied to update the coefficients that linearly combine the fixed robust basis functions used to represent the deconvolver. The advantages of the design are inherited from the mentioned fields: low sensitivity to parameter uncertainty in the system model, good numerical and structural behaviour, and the capability of tracking changes in the systems dynamics. The linear equalization of a simple ADSL channel model is presented as an example including comparisons between the optimal nominal, adaptive FIR, and the proposed design.Facultad de IngenieríaComisión de Investigaciones Científicas de la provincia de Buenos Aire

A robust orthogonal adaptive approach to SISO deconvolution

This paper formulates in a common framework some results from the fields of robust filtering, function approximation with orthogonal basis, and adaptive filtering, and applies them for the design of a general deconvolution processor for SISO systems. The processor is designed to be robust to small parametric uncertainties in the system model, with a partially adaptive orthogonal structure. A simple gradient type of adaptive algorithm is applied to update the coefficients that linearly combine the fixed robust basis functions used to represent the deconvolver. The advantages of the design are inherited from the mentioned fields: low sensitivity to parameter uncertainty in the system model, good numerical and structural behaviour, and the capability of tracking changes in the systems dynamics. The linear equalization of a simple ADSL channel model is presented as an example including comparisons between the optimal nominal, adaptive FIR, and the proposed design.Facultad de IngenieríaComisión de Investigaciones Científicas de la provincia de Buenos Aire

Phase and TV Based Convex Sets for Blind Deconvolution of Microscopic Images

In this article, two closed and convex sets for blind deconvolution problem are proposed. Most blurring functions in microscopy are symmetric with respect to the origin. Therefore, they do not modify the phase of the Fourier transform (FT) of the original image. As a result blurred image and the original image have the same FT phase. Therefore, the set of images with a prescribed FT phase can be used as a constraint set in blind deconvolution problems. Another convex set that can be used during the image reconstruction process is the epigraph set of Total Variation (TV) function. This set does not need a prescribed upper bound on the total variation of the image. The upper bound is automatically adjusted according to the current image of the restoration process. Both of these two closed and convex sets can be used as a part of any blind deconvolution algorithm. Simulation examples are presented.Comment: Submitted to IEEE Selected Topics in Signal Processin

Parametric high resolution techniques for radio astronomical imaging

The increased sensitivity of future radio telescopes will result in requirements for higher dynamic range within the image as well as better resolution and immunity to interference. In this paper we propose a new matrix formulation of the imaging equation in the cases of non co-planar arrays and polarimetric measurements. Then we improve our parametric imaging techniques in terms of resolution and estimation accuracy. This is done by enhancing both the MVDR parametric imaging, introducing alternative dirty images and by introducing better power estimates based on least squares, with positive semi-definite constraints. We also discuss the use of robust Capon beamforming and semi-definite programming for solving the self-calibration problem. Additionally we provide statistical analysis of the bias of the MVDR beamformer for the case of moving array, which serves as a first step in analyzing iterative approaches such as CLEAN and the techniques proposed in this paper. Finally we demonstrate a full deconvolution process based on the parametric imaging techniques and show its improved resolution and sensitivity compared to the CLEAN method.Comment: To appear in IEEE Journal of Selected Topics in Signal Processing, Special issue on Signal Processing for Astronomy and space research. 30 page

Linear chemically sensitive electron tomography using DualEELS and dictionary-based compressed sensing

We have investigated the use of DualEELS in elementally sensitive tilt series tomography in the scanning transmission electron microscope. A procedure is implemented using deconvolution to remove the effects of multiple scattering, followed by normalisation by the zero loss peak intensity. This is performed to produce a signal that is linearly dependent on the projected density of the element in each pixel. This method is compared with one that does not include deconvolution (although normalisation by the zero loss peak intensity is still performed). Additionaly, we compare the 3D reconstruction using a new compressed sensing algorithm, DLET, with the well-established SIRT algorithm. VC precipitates, which are extracted from a steel on a carbon replica, are used in this study. It is found that the use of this linear signal results in a very even density throughout the precipitates. However, when deconvolution is omitted, a slight density reduction is observed in the cores of the precipitates (a so-called cupping artefact). Additionally, it is clearly demonstrated that the 3D morphology is much better reproduced using the DLET algorithm, with very little elongation in the missing wedge direction. It is therefore concluded that reliable elementally sensitive tilt tomography using EELS requires the appropriate use of DualEELS together with a suitable reconstruction algorithm, such as the compressed sensing based reconstruction algorithm used here, to make the best use of the limited data volume and signal to noise inherent in core-loss EELS