铁道学报
鐵道學報
철도학보
2014年
9期
52-59
,共8页
压缩感知%图像修复%K-奇异值分解%稀疏度自适应%正则化正交匹配追踪(ROMP)
壓縮感知%圖像脩複%K-奇異值分解%稀疏度自適應%正則化正交匹配追蹤(ROMP)
압축감지%도상수복%K-기이치분해%희소도자괄응%정칙화정교필배추종(ROMP)
compressive sensing%image inpainting%K-SVD(Singular Value Decomposition)%sparsity adaptive%ROMP(Regularized Orthogonal Matching Pursuit)
压缩感知理论利用信号的稀疏特性，能够以较少的采样数据恢复出完整的信号。本文基于压缩感知理论，提出一种稀疏度自适应图像修复算法。有别于传统的图像修复方法，本文首先根据大量样本数据进行K-奇异值分解(K-SVD)字典训练，用训练得到的超完备字典取代正交基函数；然后根据图像的退化模型对感知矩阵加以约束；最后针对二维破损图像稀疏度未知问题，在重构阶段提出了一种稀疏度自适应正则化正交匹配追踪算法(SA-ROMP)实现破损图像修复。本文引入的超完备字典能够自适应地根据训练样本进行特征提取，具有更强的稀疏表示能力。重构阶段的 SA-ROMP算法在迭代过程中利用 logistic回归函数获取阈值，再通过阈值对残差与感知矩阵的相关系数进行判定，能够自适应选择原子候选集的个数。图像修复实验结果验证了本文算法的可行性，并且修复效果明显优于其他同类算法。
壓縮感知理論利用信號的稀疏特性，能夠以較少的採樣數據恢複齣完整的信號。本文基于壓縮感知理論，提齣一種稀疏度自適應圖像脩複算法。有彆于傳統的圖像脩複方法，本文首先根據大量樣本數據進行K-奇異值分解(K-SVD)字典訓練，用訓練得到的超完備字典取代正交基函數；然後根據圖像的退化模型對感知矩陣加以約束；最後針對二維破損圖像稀疏度未知問題，在重構階段提齣瞭一種稀疏度自適應正則化正交匹配追蹤算法(SA-ROMP)實現破損圖像脩複。本文引入的超完備字典能夠自適應地根據訓練樣本進行特徵提取，具有更彊的稀疏錶示能力。重構階段的 SA-ROMP算法在迭代過程中利用 logistic迴歸函數穫取閾值，再通過閾值對殘差與感知矩陣的相關繫數進行判定，能夠自適應選擇原子候選集的箇數。圖像脩複實驗結果驗證瞭本文算法的可行性，併且脩複效果明顯優于其他同類算法。
압축감지이론이용신호적희소특성，능구이교소적채양수거회복출완정적신호。본문기우압축감지이론，제출일충희소도자괄응도상수복산법。유별우전통적도상수복방법，본문수선근거대량양본수거진행K-기이치분해(K-SVD)자전훈련，용훈련득도적초완비자전취대정교기함수；연후근거도상적퇴화모형대감지구진가이약속；최후침대이유파손도상희소도미지문제，재중구계단제출료일충희소도자괄응정칙화정교필배추종산법(SA-ROMP)실현파손도상수복。본문인입적초완비자전능구자괄응지근거훈련양본진행특정제취，구유경강적희소표시능력。중구계단적 SA-ROMP산법재질대과정중이용 logistic회귀함수획취역치，재통과역치대잔차여감지구진적상관계수진행판정，능구자괄응선택원자후선집적개수。도상수복실험결과험증료본문산법적가행성，병차수복효과명현우우기타동류산법。
The compressive sensing theory describes that it can reconstruct the original signal from a small a-mount of sampling data by making use of the sparse feature of the signal.In this paper,we firstly proposed a sparsity adaptive algorithm for image inpainting based on compressive sensing.Different from traditional image inpainting methods,we firstly replaced the orthogonal-basis function by the over complete dictionary which was trained by K-SVD dictionary learning based on a large number of samples and then restrained the sensing ma-trix according to the image degeneration model.Finally,aiming at the unsolved sparse problems with two-di-mensional damaged images,we proposed the Sparsity Adaptive Regularized Orthogonal Matching Pursuit (SA-ROMP)algorithm in the reconstruction phase to realize inpainting of damaged images.The introduced over complete dictionary extracts features adaptively and provides a better sparsity extension.The SA-ROMP algo-rithm uses the logistic regression function to set the threshold in the process of iteration and determines the number of atoms and candidate atoms adaptively by estimating the relevance between iterative residues and sensing matrix.Comparison of experimental results shows that the proposed algorithm is feasible and better than other similar algorithms.
