本文選題：圖像復原 + 正則化��； 參考：《光子學報》2017年04期

【摘要】：傅里葉域與小波域的聯合去模糊算法在低噪聲時具有優(yōu)越的恢復效果,但是這種聯合去模糊算法并不適用于含噪聲的模糊圖像.為了解決這一問題,本文將先驗約束分別引入傅里葉域的去模糊步驟和小波域的去噪步驟.在傅里葉域,用矩陣形式表示目標函數.對目標函數添加平滑約束并且通過噪聲水平和模糊圖像高頻信息計算得到平滑約束項的濾波系數.同樣方式,在小波域對小波域目標函數添加能量約束,實現小波域目標函數的正則化過程.分析傅里葉域的噪聲放大程度,通過傅里葉域的濾波系數計算得到小波域能量約束的濾波系數.傅里葉域的平滑約束可以抑制濾波過程中噪聲的產生,小波域的能量約束可以提高小波域濾波的魯棒性.仿真實驗表明,改進的算法相比于原始算法具有更好的魯棒性,可以有效提高圖像的恢復質量.對于噪聲標準差為0.010.1的模糊圖像,改進算法恢復圖像峰值信噪比比原始算法恢復圖像的峰值信噪比高1左右.并且改進算法對于高斯型點擴散函數誤差具有魯棒性,當點擴散函數估計方差與實際方差相差0.4時,改進算法的恢復效果仍優(yōu)于原始算法.
[Abstract]:The joint de-blurring algorithm in Fourier domain and wavelet domain has a superior recovery effect at low noise, but this joint de-blurring algorithm is not suitable for fuzzy images with noise. In order to solve this problem a priori constraint is introduced into the steps of deblurring in Fourier domain and denoising in wavelet domain respectively. In Fourier domain, the objective function is expressed in matrix form. The smoothing constraint is added to the objective function and the filtering coefficient of the smoothing constraint is obtained by calculating the noise level and the high frequency information of the blurred image. In the same way, the energy constraint is added to the objective function in the wavelet domain to realize the regularization process of the objective function in the wavelet domain. The degree of noise amplification in Fourier domain is analyzed and the filter coefficient of energy constraint in wavelet domain is obtained by calculating the filter coefficient in Fourier domain. The smoothing constraint in Fourier domain can suppress the noise in the filtering process, and the energy constraint in wavelet domain can improve the robustness of filtering in wavelet domain. Simulation results show that the improved algorithm is more robust than the original algorithm and can effectively improve the quality of image restoration. For a fuzzy image with a noise standard deviation of 0.010.1, the improved algorithm is about 1 higher than the original algorithm in restoring the peak signal-to-noise ratio (PSNR) of the image. The improved algorithm is robust to the error of Gao Si type point diffusion function. When the estimated variance of the point diffusion function is 0.4 different from the actual variance, the improved algorithm is still better than the original algorithm.
【作者單位】： 中國科學院光電研究院計算光學成像技術重點實驗室;中國科學院大學;
【基金】：國家自然科學基金(No.61505219)資助~~
【分類號】：TP391.41

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