In various capacities of statistical signal processing two-dimensional (2-D) chirp models have been considered significantly, particularly in image processing—to model gray-scale and texture images, magnetic resonance imaging, optical imaging etc. In this paper we address the problem of estimation of the unknown parameters of a 2-D chirp model under the assumption that the errors are independently and identically distributed ( i.i.d. ). The key attribute of the proposed estimation procedure is that it is computationally more efficient than the least squares estimation method. Moreover, the proposed estimators are observed to have the same asymptotic properties as the least squares estimators, thus providing computational effectiveness without any compromise on the efficiency of the estimators. We extend the propounded estimation method to provide a sequential procedure to estimate the unknown parameters of a 2-D chirp model with multiple components and under the assumption of i.i.d. errors we study the large sample properties of these sequential estimators. Simulation studies and two synthetic data analyses have been performed to show the effectiveness of the proposed estimators.

中文翻译：

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一种估计二维线性调频信号模型参数的有效方法

在统计信号处理的各种能力中，二维 (2-D) 啁啾模型已被广泛考虑，特别是在图像处理中——对灰度和纹理图像、磁共振成像、光学成像等进行建模。在本文中，我们解决了在假设误差独立且同分布 (iid) 的情况下，估计 2-D chirp 模型的未知参数的问题。所提出的估计程序的关键属性是它在计算上比最小二乘估计方法更有效。此外，所提出的估计量被观察到具有与最小二乘估计量相同的渐近特性，因此在不影响估计量效率的情况下提供计算效率。我们扩展了提出的估计方法，以提供一个序列程序来估计具有多个分量的 2-D chirp 模型的未知参数，并且在假设 iid 错误的情况下，我们研究了这些序列估计器的大样本特性。已经进行了模拟研究和两个合成数据分析，以显示所提出的估计器的有效性。