Study on Dynamical Super-resolution Algorithm in Uniform/Log-polar Coordinate System

各种补偿相机抖动或被摄体运动引起的图像模糊的技术已经发展起来。然而，当模糊宽度较长或亮度较暗时，这些传统方法就不能很好地工作。在这项研究中，我们提出了一种新的方法，使我们能够清晰地补偿大的模糊。它是基于这样的想法，即捕获的图像能够有宽带的组成部分，通过曝光倍增与亮度调制的光移动的主题。为了评估我们提出的方法的有效性，我们用LED灯进行了一些亮度调制的实验，结果表明，当捕获的图像包含较大的模糊时，所提出的方法在信噪比上比传统的亮度恒定的方法有更好的性能。此外，我们还研究了什么像素阵列有利于主体的各种运动。我们认为，视场中心附近以均匀结构为主，而外围以对数极结构为主，因此它们与视网膜的感受野具有相同的结构。在这次讨论中，我们发现了一个函数对傅里叶变换具有不可变性，它被称为“自傅里叶函数（SFF）”。作为SFF的一种，我们提出了“广义梳状函数（GCF）”，它由沿横向轴等间隔但按比例扩展的脉冲组成。在这项研究中，我们提出了一种新的自傅立叶图像（SFI），通过将GCF扩展到二维形式。数值算例表明，可以构造具有任意核函数的SFI，并满足傅里叶变换的不变性。

Various technologies for compensating the image blur caused by a camera shake or a subject motion have been developed. These conventional methods, however, do not work well when the blur width is long or the brightness is dark. In this study, we have proposed a new method that enables us to compensate clearly even the large blur. It is based on the idea that the captured image is able to have wideband components by exposing multiply to the moving subject with the brightness modulated light. To evaluate the effectiveness of our proposed method, we have carried out some experiments with LED lights for the brightness modulation and have showed the proposed method provides better performance in SNR than the conventional one with a constant brightness when the captured image involves a large blur.Additionally, we have investigated what pixel array works advantageously to various motions of the subject. It is expected that a uniform structure is dominant near the center of the viewing field, but a log-polar structure is dominant in the peripheral, so they have same structure with the receptive field of the retina. During this discussion, we discovered a functions that has unchangeability to the Fourier transform and that is called "self-Fourier function (SFF)." As one of SFF's, we have proposed "generalized comb function (GCF)" that consists of equally spaced but proportionally expanded pulses along the transversal axis. In this study, we have presented a novel self-Fourier image (SFI) made by expanding the GCF to a two-dimensional form. Some numerical examples show that the SFI with an arbitrary kernel function can be constructed and satisfies unchangeability to the Fourier transform.