基于频谱分析的匀速运动模糊图像模糊方向识别

点扩展函数的设置是图像复原中的关键问题,对于匀速直线运动模糊图像,运动方向和模糊长度决定了点扩展函数。根据运动模糊图像和原始图像在频谱上存在的对应关系,即运动模糊图像频谱存在着对应于传递函数零点的暗条纹,提出对运动模糊图像,通过二维傅里叶变换、二值化以及Radon变换检测运动模糊图像频谱图上暗条纹的方向和位置,来实现运动方向测量的方法。用该方法对模糊图像进行检测,模糊方向的识别精度小于1°。实验证明该方法可以实现平面内任意方向运动的测量。     

Cross -sections of star bodies and dual mixed volumes

In this paper, we establish an extension of Funk's section theorem. Our result has the following corollary: If is a star body in whose central -slices have the same volume (with appropriate dimension) as the central -slices of a centered body , then the dual quermassintegrals satisfy , for any , with equality if and only if . The case that is a centered body implies Funk's section theorem.

     

estimates for overdetermined Radon transforms

We prove several variations on the results of F. Ricci and G. Travaglini (2001), concerning bounds for convolution with all rotations of arc length measure on a fixed convex curve in . Estimates are obtained for averages over higher-dimensional convex (nonsmooth) hypersurfaces, smooth -dimensional surfaces, and nontranslation-invariant families of surfaces. We compare Ricci and Travaglini's approach, based on average decay of the Fourier transform, with an approach based on boundedness of Fourier integral operators, and show that essentially the same geometric condition arises in proofs using the two techniques.

     

Potential Analysis on Carnot Groups，Part II：Relationship between Hausdorff Measures and Capacities

Abstract In this paper, we establish the relationship between Hausdorff measures and Bessel capacities on any nilpotent stratified Lie group (i. e., Carnot group). In particular, as a special corollary of our much more general results, we have the following theorem (see Theorems A and E in Section 1): Let Q be the homogeneous dimension of . Given any set E ⊂ , B _α,p (E) = 0 implies ℋ ^{Q−αp+ ε}(E) = 0 for all ε > 0. On the other hand, ℋ ^Q−αp (E) < ∞ implies B _α,p (E) = 0. Consequently, given any set E ⊂ of Hausdorff dimension Q − d, where 0 < d < Q, B _α,p (E) = 0 holds if and only if αp ≤ d. A version of O. Frostman’s theorem concerning Hausdorff measures on any homogeneous space is also established using the dyadic decomposition on such a space (see Theorem 4.4 in Section 4). Research supported partly by the U. S. National Science Foundation Grant No. DMS99–70352     

Convex curves, Radon transforms and convolution operators defined by singular measures

Let be a convex curve in the plane and let be the arc-length measure of Let us rotate by an angle and let be the corresponding measure. Let . Then This is optimal for an arbitrary . Depending on the curvature of , this estimate can be improved by introducing mixed-norm estimates of the form where and are conjugate exponents.     

Coincidence of the upper Kuratowski topology with the co-compact topology on compact sets, and the Prohorov property

For a Hausdorff space X, let F be the hyperspace of all closed subsets of X and H a sublattice of F. Following Nogura and Shakhmatov, X is said to be H-trivial if the upper Kuratowski topology and the co-compact topology coincide on H. F-trivial spaces are the consonant spaces first introduced and studied by Dolecki, Greco and Lechicki. In this paper, we deal with K-trivial spaces and Fin-trivial space, where K and Fin are respectively the lattices of compact and of finite subsets of X. It is proved that if C_k(X) is a Baire space or more generally if X has ‘the moving off property’ of Gruenhage and Ma, then X is K-trivial. If X is countable, then C_p(X) is Baire if and only if X is Fin-trivial and all compact subsets of X are finite. As for consonant spaces, it turns out that every regular K-trivial space is a Prohorov space. This result remains true for any regular Fin-trivial space in which all compact subsets are scattered. It follows that every regular first countable space without isolated points, all compact subsets of which are countable, is Fin-nontrivial. Examples of K-trivial non-consonant spaces, of Fin-trivial K-nontrivial spaces and of countably compact Prohorov Fin-nontrivial spaces, are given. In particular, we show that all (generalized) Fréchet–Urysohn fans are K-trivial, answering a question by Nogura and Shakhmatov. Finally, we describe an example of a continuous open compact-covering mapping f :X→Y, where X is Prohorov and Y is not Prohorov, answering a long-standing question by Topsøe.     

Radon变换和衰减Radon变换的分析研究

衰减Radon变换出现在单光子放射型计算机层析成像中。本文首先回顾和研究了Radon变换和衰减Radon变换及其反演的有关结论，进而提出了Tretiak-Metz结果的一种新证明方法，对于一般对象，本文用变换方法非滤子背投影法导出了衰减Radon变换的反演公式。     

Variation of radon concentrations in soil and groundwater and its correlation with radon exhalation rate from soil in Budhakedar, Garhwal Himalaya

Radon was measured in soil-gas and groundwater in the Budhakedar area of Tehri Garhwal, India in summer and winter to obtain the seasonal variation and its correlation with radon exhalation rate. The environmental surface gamma dose rate was also measured in the same area. The radon exhalation rate in the soil sample collected from different geological unit of Budhakedar area was measured using plastic track detector (LR-115 type II) technique. The variation in the radon concentration in soil-gas was found to vary from 1098 to 31,776 Bq.m⁻³ with an average of 7456 Bq.m⁻³ in summer season and 3501 to 42883 Bq.m⁻³ with an average of 17148 Bq.m⁻³ in winter season. In groundwater, it was found to vary from 8 to 3047 Bq.l⁻¹ with an average value 510 Bq.l⁻¹ in summer and 26 to 2311 Bq.l⁻¹ with an average value 433 Bq.L⁻¹ in winter. Surface gamma dose rate in the study area varied from 32.4 to 83.6 μR.h⁻¹ with an overall mean of 58.7 μ-R.h⁻¹ in summer and 34.6 to 79.3 μR.h⁻¹ with an average value 58.2 μR.h⁻¹ in winter. Radon exhalation rate from collected soil samples was found to vary from 0.1 × 10⁻⁵ to 5.7 × 10⁻⁵ Bq.kg⁻¹.h⁻¹ with an average of 1.5 × 10⁻⁵ Bq.kg⁻¹.h⁻¹ in summer season and 1.7 × 10⁻⁵ to 9.6 × 10⁻⁵ Bq.kg⁻¹.h⁻¹ with an average of 5.5 × 10⁻⁵ Bq.kg⁻¹.h⁻¹. A weak negative correlation was observed between radon exhalation rate from soil and radon concentration in the soil. Radon exhalation rate from the soil was also not found to be correlated with the gamma dose rate, while it shows a positive correlation with radon concentration in water in summer season. Inter-correlations among various parameters are discussed in detail.