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An efficient algorithm for adaptive kernel smoothing (AKS) of two-dimensional imaging data has been developed and implemented using the Interactive Data Language (IDL). The functional form of the kernel can be varied (top-hat, Gaussian etc.) to allow different weighting of the event counts registered within the smoothing region. For each individual pixel the algorithm increases the smoothing scale until the signal-to-noise ratio (s.n.r.) within the kernel reaches a preset value. Thus, noise is suppressed very efficiently, while at the same time real structure, i.e. signal that is locally significant at the selected s.n.r. level, is preserved on all scales. In particular, extended features in noise-dominated regions are visually enhanced. The ASMOOTH algorithm differs from other AKS routines in that it allows a quantitative assessment of the goodness of the local signal estimation by producing adaptively smoothed images in which all pixel values share the same signal-to-noise ratio above the background. We apply ASMOOTH to both real observational data (an X-ray image of clusters of galaxies obtained with the Chandra X-ray Observatory) and to a simulated data set. We find the ASMOOTHed images to be fair representations of the input data in the sense that the residuals are consistent with pure noise, i.e. they possess Poissonian variance and a near-Gaussian distribution around a mean of zero, and are spatially uncorrelated.
Data cube materialization is a classical database operator introduced in Gray et al.~(Data Mining and Knowledge Discovery, Vol.~1), which is critical for many analysis tasks. Nandi et al.~(Transactions on Knowledge and Data Engineering, Vol.~6) first
We determine the expected error by smoothing the data locally. Then we optimize the shape of the kernel smoother to minimize the error. Because the optimal estimator depends on the unknown function, our scheme automatically adjusts to the unknown fun
Understanding dissipation in 2D quantum many-body systems is a remarkably difficult open challenge. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady-states of 2D quan
Recently, records on stereo matching benchmarks are constantly broken by end-to-end disparity networks. However, the domain adaptation ability of these deep models is quite poor. Addressing such problem, we present a novel domain-adaptive pipeline ca
We propose the adversarially robust kernel smoothing (ARKS) algorithm, combining kernel smoothing, robust optimization, and adversarial training for robust learning. Our methods are motivated by the convex analysis perspective of distributionally rob