Bayesian image analysis has played a large role over the last 40+ years in solving problems in image noise-reduction, de-blurring, feature enhancement, and object detection. However, these problems can be complex and lead to computational difficulties, due to the modeled interdependence between spatial locations. The Bayesian image analysis in Fourier space (BIFS) approach proposed here reformulates the conventional Bayesian image analysis paradigm for continuous valued images as a large set of independent (but heterogeneous) processes over Fourier space. The original high-dimensional estimation problem in image space is thereby broken down into (trivially parallelizable) independent one-dimensional problems in Fourier space. The BIFS approach leads to easy model specification with fast and direct computation, a wide range of possible prior characteristics, easy modeling of isotropy into the prior, and models that are effectively invariant to changes in image resolution.

翻译：过去40余年间，贝叶斯图像分析在图像降噪、去模糊、特征增强及目标检测等问题的求解中发挥着重要作用。然而，由于空间位置建模的相互依赖性，这类问题可能具有复杂性并导致计算困难。本文提出的傅立叶空间贝叶斯图像分析（BIFS）方法，将连续值图像的传统贝叶斯图像分析范式重构为傅立叶空间中大量独立（但非同质）过程的集合。由此，原始图像空间中的高维估计问题被分解为傅立叶空间中可轻松并行处理的独立一维问题。BIFS方法具有以下特性：模型设定简便且计算快速直接、可灵活选择多种先验特征、易于在先验中融入各向同性特征，且模型对图像分辨率的变化具有有效性不变性。