Treffer: Some theory and application in data sciences: one-dimensional phase retrieval and image noise level estimation

M.Phil. ; This thesis studies two problems in data science. First one is the one-dimensional phase retrieval problem. we prove that neither do gradient-based regularizations nor adding extra Fourier magnitude measurements than 2N −1 helps resolve ambiguities. We show that box relaxation to binary constraint is equivalent to the original problem. Some uniqueness and ambiguities problem are also discussed. Finally, we propose a denoising algorithm, which works as predicted. ; Another one is the image noise level estimation problem. We first review Marchenko–Pastur distribution and the spiked population model. Then, we apply this model to image noise level estimation. We discover that the small eigenvalues of the patch covariance matrices corresponding to the clean image are close to zero. Assuming all the small eigenvalues are with the same small values, we derive a proportional relation between eigenvalues and variances of the noisy images. Using this relation, we propose a new method for noise level estimation from a single noisy image contaminated by additive white Gaussian noise. A similar analysis is extended multiplicative noise. Experimental results show that our algorithm outperforms the state-of-art algorithms. ; 本文研究了兩個數據科學中的問題，首先是一維相位檢索。作者證明了基於梯度的正則化與多於2N-1經傅立葉轉換後的幅度測量均無助減少非單值性。此外，作者顯示受二值約束的相位檢索問題等價於其經鬆弛後的問題。唯一與非單值性亦是研究問題之一。最後，作者提出一個去雜訊算法，其功效與預測一樣。 ; 其次是估計圖像雜訊強度。作者首先回顧Marchenko–Pastur分佈和尖峰整體模型。然後，作者運用上述模型估計圖像雜訊強度。作者發現乾淨圖像的方塊協方差矩陣的小特徵值相當接近零，若假設所有小特徵值的數值相等，則得出特徵值與圖像雜訊方差之間的比例。作者利用此比例提出新方法，從加性高斯白雜訊污染的單個有雜訊圖像中估計雜訊水平。相乘雜訊亦有相似分析。實驗結果顯示本文的演算法優於現有算法。 ; Wong, Wing Hong. ; Thesis M.Phil. Chinese University of Hong Kong 2020. ; Includes bibliographical references (leaves 64-73). ; Abstracts also in Chinese. ; Title from PDF title page (viewed on January 5, 2022).