小波轉換及其理論為近幾年來相當熱門的研究主題之一，目前小波轉換已被廣泛地應用在信號處理、影像和音訊處理、通信系統以及應用數學等不同的研究領域。由於小波轉換具有極佳的時域−頻域分析功能以及多重解析的特性，因此非常適合運用在影像解析度強化上。本論文研究主題為小波轉換在影像解析度強化處理之應用，並針對影像解析度強化提出一套以小波轉換為基礎的基本處理架構。
本論文提出一個在小波域上之影像解析度強化演算法，用來估算小波域上的高頻係數。此方法根據小波係數在臨近係數之間的關係使用了一個模形函式，且利用未向下取樣之離散小波轉換去估算未知的詳細係數。實驗結果顯示，此方法的表現不管在主觀視覺或客觀數據都優於其他傳統影像插補演算法。

Wavelet transform and its theory is one of the most exciting developments in the last decade. In fact, the wavelet transform has been developed independently for various fields such as signal processing, image processing, audio processing, communication, and applied mathematics. Due to the wavelet representation has characteristics of the efficient time-frequency localization and the multi-resolution analysis, the wavelet transforms are suitable for processing the image resolution enhancement. Therefore, this thesis focuses on the study of wavelet-based image resolution enhancement and proposes a framework of image resolution enhancement using wavelet transform.
This thesis proposed a wavelet-domain image resolution enhancement algorithm which is based on the estimation of detail wavelet coefficients at high resolution scales. The method exploits shape function according to wavelet coefficient correlation in a local neighborhood sense and employs undecimated discrete wavelet transform to estimate the unknown detail coefficients. Results show that the proposed method is considerably superior to conventional image interpolation techniques, both in objective and subjective terms.

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