CAJ | 학술논문

变分图像分解，通过极小化能量泛函将图像分解为不同的特征分量，可以被应用到图像的恢复和重建。提出了变分框架下的多尺度图像恢复和重建的思想。基于这种思想，首先提出了一个单参数的（BV ，G ，E ）三元变分分解模型，并且理论分析了参数与不同特征分量的尺度的关系。然后将此模型的参数选为一个二进制序列，得到多尺度的（BV ，G ，E ）变分分解。该多尺度变分分解可以将图像分解为一序列图像结构、纹理和噪声。证明了此多尺度分解的收敛性并且基于对偶理论和交替迭代算法给出了其数值求解方法。最后将提出的多尺度的（BV ，G ，E ）变分分解应用到图像恢复和重建，实验结果证实了理论分析的正确性，显示了将此模型进行图像多尺度恢复和重建的有效性，和与一些其他分解模型相比较的优越性。
변분도상분해，통과겁소화능량범함장도상분해위불동적특정분량，가이피응용도도상적회복화중건。제출료변분광가하적다척도도상회복화중건적사상。기우저충사상，수선제출료일개단삼수적（BV ，G ，E ）삼원변분분해모형，병차이론분석료삼수여불동특정분량적척도적관계。연후장차모형적삼수선위일개이진제서렬，득도다척도적（BV ，G ，E ）변분분해。해다척도변분분해가이장도상분해위일서렬도상결구、문리화조성。증명료차다척도분해적수렴성병차기우대우이론화교체질대산법급출료기수치구해방법。최후장제출적다척도적（BV ，G ，E ）변분분해응용도도상회복화중건，실험결과증실료이론분석적정학성，현시료장차모형진행도상다척도회복화중건적유효성，화여일사기타분해모형상비교적우월성。
By minimizing the energy functional ,we can obtain the variational image decomposition which decomposes image into different characteristic components ,and can be used for image restoration and reconstruction .An idea of multiscale image restoration and reconstruction in the framework of variation is proposed .Based on this idea ,firstly ,a single-parameter (BV ,G ,E ) trituple decomposition model is proposed ,and the relationship between the parameter and the scale of each component is studied the-oretically .And then ,by replacing the parameter with a binary sequence ,we achieve a multiscale (BV ,G ,E) decomposition which can decompose an image into a sequence of image structure ,texture and noise .The convergence of this multiscale decomposition is proved ,and an efficient numerical method based on the duality theory and alternate iteration algorithm is introduced to solve it .At last ,the proposed multiscale (BV ,G ,E ) decomposition is applied for image restoration and reconstruction .Numerical results sup-port the theoretical results and show that the proposed model is efficient for multiscale image restoration and reconstruction ,and is superior to some other decomposition models .