Deconvolution of Images Taken with the Suzaku X-ray Imaging Spectrometer

We present a non-iterative method to deconvolve the spatial response function or the point spread function (PSF) from images taken with the Suzaku X-ray Imaging Spectrometer (XIS). The method is optimized for analyses of extended sources with high photon statistics. Suzaku has four XIS detectors each with its own X-ray CCD and X-Ray Telescope (XRT) and has been providing unique opportunities in spatially-resolved spectroscopic analyses of extended objects. The detectors, however, suffer from broad and position-dependent PSFs with their typical half-power density (HPD) of about 110''. In the authors' view, this shortcoming has been preventing the high collecting area and high spectral resolution of Suzaku to be fully exploited. The present method is intended to recover spatial resolution to ~15'' over a dynamic range around 1:100 in the brightness without assuming any source model. Our deconvolution proceeds in two steps: An XIS image is multiplied with the inverse response matrix calculated from its PSF after rebinning CCD pixels to larger-size tiles (typically 6''x 6''); The inverted image is then adaptively smoothed to obtain the final deconvolved image. The PSF is modeled on a ray-tracing program and an observed point-source image. The deconvolution method has been applied to images of Centaurus A, PSR B1509-58 and RCW 89 taken by one XIS (XIS-1). The results have been compared with images obtained with Chandra to conclude that the spatial resolution has been recovered to ~20'' down to regions where surface brightness is about 1:50 of the brightest tile in the image. We believe the spatial resolution and the dynamic range can be improved in the future with higher fidelity PSF modeling and higher precision pointing information.Comment: 21 pages, accepted for publication in PASJ. A PS file with original-quality figures is available at http://www.slac.stanford.edu/~sugizaki/preprint/pasj3256/sugizaki_No3256.p

Abelian maximal pattern complexity of words

In this paper we study the maximal pattern complexity of infinite words up to Abelian equivalence. We compute a lower bound for the Abelian maximal pattern complexity of infinite words which are both recurrent and aperiodic by projection. We show that in the case of binary words, the bound is actually achieved and gives a characterization of recurrent aperiodic words

Behavior of various complexity functions

AbstractFor a nonempty closed set Ω⊂AN with 2≤#A<∞, we consider 3 complexity functions of k=0,1,2,…: (1)(block complexity) pΩBL(k):=#Ω|{0,1,…,k−1},(2)(maximal pattern complexity) pΩ∗(k):=supS⊂N,#S=k#Ω|S,(3)(minimal pattern complexity) p∗Ω(k):=infS⊂N,#S=k#Ω|S, where # denotes the number of elements in a set, and Ω|S is the restriction of Ω to S⊂N. If pΩ∗(k)=p∗Ω(k)(k=0,1,2,…) holds, then the above 3 complexities coincide and are called uniform complexity, denoted by pΩ(k).Behaviors of these 4 complexity functions are discussed