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

已经开发了用于补偿由相机抖动或被摄体运动引起的图像模糊的各种技术。然而，当模糊宽度较长或亮度较暗时，这些常规方法不能很好地工作。在这项研究中，我们提出了一种新的方法，使我们能够清楚地补偿，即使是大的模糊。这是基于这样的想法，即通过用亮度调制光对运动对象进行多次曝光，所捕获的图像能够具有宽带分量。为了评估我们所提出的方法的有效性，我们进行了一些实验与LED灯的亮度调制，并已表明，所提出的方法提供了更好的性能比传统的一个恒定的亮度时，捕获的图像涉及到一个大的模糊。此外，我们已经调查了什么样的像素阵列的作品有利于各种运动的主题。可以预期，在视野的中心附近，均匀结构占主导地位，但是在周边，对数极坐标结构占主导地位，因此它们与视网膜的感受野具有相同的结构。在讨论过程中，我们发现了一种对傅里叶变换具有不变性的函数，称为“自傅里叶函数”。作为SFF的一种，我们提出了“广义梳状函数（GCF）”，它由沿横轴沿着等间隔但成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）通过扩展的GCF的二维形式。数值算例表明，可以构造具有任意核函数的SFI，且SFI满足Fourier变换不变性。

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.