The general tensor-based methods can recover missing values of multidimensional images by exploiting the low-rankness on the pixel level. However, especially when considerable pixels of an image are missing, the low-rankness is not reliable on the pixel level, resulting in some details losing in their results, which hinders the performance of subsequent image applications (e.g., image recognition and segmentation). In this article, we suggest a novel multiscale feature (MSF) tensorization by exploiting the MSFs of multidimensional images, which not only helps to recover the missing values on a higher level, that is, the feature level but also benefits subsequent image applications. By exploiting the low-rankness of the resulting MSF tensor constructed by the new tensorization, we propose the convex and nonconvex MSF tensor train rank minimization (MSF-TT) to conjointly recover the MSF tensor and the corresponding original tensor in a unified framework. We develop the alternating directional method of multipliers (ADMMs) to solve the convex MSF-TT and the proximal alternating minimization (PAM) to solve the nonconvex MSF-TT. Moreover, we establish the theoretical guarantee of convergence for the PAM algorithm. Numerical examples of real-world multidimensional images show that the proposed MSF-TT outperforms other compared approaches in image recovery and the recovered MSF tensor can benefit the subsequent image recognition.

中文翻译：

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用于多维图像恢复的多尺度特征张量序列秩最小化。

一般基于张量的方法可以通过利用像素级别的低秩来恢复多维图像的缺失值。然而，特别是当图像中有相当多的像素丢失时，低秩在像素级别上是不可靠的，导致其结果中丢失了一些细节，这阻碍了后续图像应​​用（例如图像识别和分割）的性能。在本文中，我们通过利用多维图像的 MSF，提出了一种新颖的多尺度特征 (MSF) 张量化，这不仅有助于在更高级别（即特征级别）上恢复缺失值，而且有利于后续图像应​​用。通过利用由新张量化构建的结果 MSF 张量的低秩，我们提出了凸和非凸 MSF 张量序列秩最小化 (MSF-TT)，以在统一框架中联合恢复 MSF 张量和相应的原始张量。我们开发了交替定向乘法器 (ADMM) 来解决凸 MSF-TT 和近端交替最小化 (PAM) 来解决非凸 MSF-TT。此外，我们为PAM算法建立了收敛的理论保证。真实世界多维图像的数值示例表明，所提出的 MSF-TT 在图像恢复方面优于其他比较方法，并且恢复的 MSF 张量有利于后续的图像识别。我们开发了交替定向乘法器 (ADMM) 来解决凸 MSF-TT 和近端交替最小化 (PAM) 来解决非凸 MSF-TT。此外，我们为PAM算法建立了收敛的理论保证。真实世界多维图像的数值示例表明，所提出的 MSF-TT 在图像恢复方面优于其他比较方法，并且恢复的 MSF 张量有利于后续的图像识别。我们开发了交替定向乘法器 (ADMM) 来解决凸 MSF-TT 和近端交替最小化 (PAM) 来解决非凸 MSF-TT。此外，我们为PAM算法建立了收敛的理论保证。真实世界多维图像的数值示例表明，所提出的 MSF-TT 在图像恢复方面优于其他比较方法，并且恢复的 MSF 张量有利于后续的图像识别。