研究图像配准中模糊与量化误差的逻辑关系，揭示干扰现象并提出恢复方法。
On the Logic Elements Associated with Round-Off Errors and Gaussian Blur in Image Registration: A Simple Case of Commingling
- 将模糊、采样和量化视为类程序运算，用逻辑框架分析信号恢复。
- 当间断点间距为采样间隔1.5至2倍时，出现最简干扰模式'混杂'。
- 可准确恢复信号幅值，适合低模糊场景下的图像重建研究者。
离散图像配准可用于从受模糊和噪声污染的样本中重建信号。本文研究一维空间受限的分段常数函数在高斯或高斯混合模糊及舍入误差下的超分辨率与离散图像配准问题。以往方法将信号恢复建模为优化问题，本文聚焦低模糊情形，提出模糊、采样与量化操作类似计算机程序运算，具备可抽象为某种逻辑的形式。当间断点间最小距离介于采样间隔的1.5至2倍之间时，会出现最简单的干扰形式，称为‘混杂’。本文提出一种推理同一信号两组采样数据的方法，通常能正确恢复信号幅值，并讨论了间断点间距的边界估计方式。
原文摘要 · Abstract (English)
Discrete image registration can be a strategy to reconstruct signals from samples corrupted by blur and noise. We examine superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions which are subject to blur which is Gaussian or a mixture of Gaussians as well as to round-off errors. Previous approaches address the signal recovery problem as an optimization problem. We focus on a regime with low blur and suggest that the operations of blur, sampling, and quantization are not unlike the operation of a computer program and have an abstraction that can be studied with a type of logic. When the minimum distance between discontinuity points is between $1.5$ and 2 times the sampling interval, we can encounter the simplest form of a type of interference between discontinuity points that we call ``commingling.'' We describe a way to reason about two sets of samples of the same signal that will often result in the correct recovery of signal amplitudes. We also discuss ways to estimate bounds on the distances between discontinuity points.
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