各向异性高斯场的Radon变换估计
Estimation of anisotropic Gaussian fields through Radon transform
摘要：
我们估计了各向异性分数布朗场的各向异性指数。对于所有方向，我们给出了一个收敛估计的各向异性指数在这个方向上，广义二次变分的基础上。我们还证明了一个中心极限定理。首先，我们提出了一个结果的识别依赖于一个过程的谱密度的渐近行为。然后，我们定义了各向异性分数布朗场的Radon变换，并证明了这些过程允许满足上述假设的谱密度。最后，我们使用模拟领域来测试所提出的估计在不同的各向异性和各向同性的情况下。结果表明，估计的行为相似，在所有情况下，是能够检测各向异性相当准确。
英文摘要：
We estimate the anisotropic index of an anisotropic fractional Brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional Brownian field and prove that these processes admit a spectral density satisfying the previous assumptions. Finally we use simulated fields to test the proposed estimator in different anisotropic and isotropic cases. Results show that the estimator behaves similarly in all cases and is able to detect anisotropy quite accurately.
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