We address the ambiguities in the super-resolution problem under translation. We demonstrate that combinations of low-resolution images at different scales can be used to make the super-resolution problem well posed. Such differences in scale can be achieved using sensors with different pixel sizes (as demonstrated here) or by varying the effective pixel size through changes in optical magnification (e.g., using a zoom lens). We show that images acquired with pairwise coprime pixel sizes lead to a system with a stable inverse, and furthermore, that super-resolution images can be reconstructed efficiently using Fourier domain techniques or iterative least squares methods. Our mathematical analysis provides an expression for the expected error of the least squares reconstruction for large signals assuming i.i.d. noise that elucidates the noise-resolution tradeoff. These results are validated through both one- and two-dimensional experiments that leverage charge-coupled device (CCD) hardware binning to explore reconstructions over a large range of effective pixel sizes. Finally, two-dimensional reconstructions for a series of targets are used to demonstrate the advantages of multiscale super-resolution, and implications of these results for common imaging systems are discussed.

翻译：我们解决了平移不变性下超分辨率问题中的模糊性。研究表明，不同尺度的低分辨率图像组合可使超分辨率问题具有适定性。这种尺度差异可通过不同像素尺寸的传感器（本文已验证）或通过改变光学放大倍数（如使用变焦镜头）调整有效像素尺寸来实现。我们证明，采用两两互质像素尺寸采集的图像可构建具有稳定逆变换的系统，且通过傅里叶域技术或迭代最小二乘法可高效重建超分辨率图像。数学分析给出了在大信号且噪声独立同分布假设下最小二乘重建的期望误差表达式，阐明了噪声-分辨率权衡关系。通过一维和二维实验验证了上述结果，实验利用电荷耦合器件（CCD）硬件像素合并技术探索了大范围有效像素尺寸下的重建效果。最后，以系列目标物的二维重建为例，论证了多尺度超分辨率的优势，并讨论了这些结果对常见成像系统的启示。