以時頻分析的方法實現超分辨率

Abstract

當影像取樣的頻率太低時，影像就會發生混疊(aliasing)。傳統上，我們認為混疊是無用的並且使用抗混疊(anti-aliasing)濾波器將其消除。然而，這也消除了其中的資訊。事實上，混疊中也包含了影像高頻成分中的資訊，利用於超分辨率(super-resolution)的應用中。我們對同一個風景的一組影像擷取高頻資訊，並建立高解析度無混疊的影像。通常不同影像之間存在一些小位移，蘊含了對於風景些微不同的資訊。 超分辨率影像重建可以被表示成一個偏移量未知的多頻道取樣問題。在這篇論文中，我們專注在運算這些偏移量，因為這是高解析度重建的必要條件。Vandewalle, Susstrunk和Vetterli提出了一個基於傅立葉轉換的頻域方法。一對影像的配準參數可以利用頻譜中沒有發生混疊的部分求得。然而，這個方法無法用在完全混疊的信號上。在這篇論文中，我們利用加伯轉換(Gabor transform)將其延伸到時頻域。理論上，我們的演算法會有更好的結果，因為頻域方法只是時頻域方法的一個特例。實驗的結果也的確證明了我們的方法在處理真實信號和影像時，的確有比較好的表現。

Aliasing in images occurs when an image is sampled at a too low sampling rate. Conventionally, we consider aliasing useless and cancel it with an anti-aliasing filter. However, this also destroyed the information. In fact, aliasing also conveys useful information about the high frequency content of the image, which is exploited in super-resolution applications. We use a set of input images of the same scene to extract such high frequency information and create a higher resolution aliasing-free image. Typically, there is a small shift between the different images, such that they contain slightly different information about the scene. Super-resolution image reconstruction can be formulated as a multichannel sampling problem with unknown offsets. This thesis concentrates on the computation of these offsets, as they are an essential prerequisite for an accurate high resolution reconstruction. A frequency domain approach based on Fourier transform is proposed by Vandewalle, Susstrunk, and Vetterli. The registration parameters between a pair of signals are computed using the aliasing-free part of the spectrum. However, the method cannot work for totally-aliased signals. In this thesis, we extend the concept to the time-frequency domain, based on Gabor transform. Theoretically, our algorithm will perform better, since the frequency domain approach is simply a special case of the time-frequency domain approach. The experiment results show that the performance indeed increases when dealing with real signals and images.