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 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：贝叶斯图像分析在过去40多年中在解决图像降噪、去模糊、特征增强和目标检测等问题中发挥了重要作用。然而，由于空间位置间建模的相互依赖性，这些问题可能变得复杂并导致计算困难。本文提出的傅里叶空间贝叶斯图像分析（BIFS）方法，将传统贝叶斯图像分析范式重新表述为傅里叶空间上一组独立（但异质）的过程。原始图像空间中的高维估计问题由此分解为傅里叶空间中（易于并行化的）独立一维问题。BIFS方法能够实现快速直接计算的简化模型设定，支持多种先验特征，便于在先验中建模各向同性特性，并使得模型对图像分辨率变化具有有效的不变性。