Manifold optimization based method for non-smooth 3D image completion of tensor low-rank models

Abstract

The invention discloses a tensor low-rank model non-smooth three-dimensional image completion method based on manifold optimization. The manifold optimization is used to combine the tensor Q-kernel norm TQN and the orthogonality in the low-rank completion non-smooth three-dimensional image. The projection basis is set as a learnable image-dependent optimization variable, and the data-dependent orthogonal projection basis is updated. The input is the restricted observation image sample of the non-smooth 3D image under the action of the projection operator, and the output is the non-smooth to be restored. Low-rank 3D images, thereby efficiently realizing low-rank restoration of non-smooth 3D images. The invention is used for low-rank image restoration, improves the applicability of image completion, and improves the low-rank completion effect of non-smooth three-dimensional images.

Description

technical field [0001] The invention belongs to the technical fields of pattern recognition, machine learning, artificial intelligence and image processing, and relates to a low-rank completion method for image data, in particular to a non-smooth three-dimensional image completion method based on a manifold-optimized tensor low-rank model. Background technique [0002] With the rapid development of data science, high-dimensional data has been widely used, and the corresponding structure information of high-dimensional matrices (that is, tensors) for storing data is becoming more and more complex, which makes it difficult to process data recovery and other tasks. , existing low-rank tensor recovery models face more challenges. The commonly used data recovery method is based on the original tensor data The low-rank features of , thus according to some restricted observation samples To restore the original data, the corresponding model is as follows: [0003] [0004] w...

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Problems solved by technology

[0008] For this limitation, Kernfeld et al. hope to extract the signal features in the non-smooth direction by changing the discrete Fourier matrix in t-SVD into an arbitrary reversible linear operator. From this point of view, Kernfeld and Lu et al. proposed Using a fixed invertible matrix to replace the direction of the Fourier matrix, Kernfeld et al. proposed a TNN-C (Cosine) minimization model using the property that the Toeplitz-plus-Hankel matrix can be diagonalized by the discrete cosine matrix, but the discrete The cosine matrix is ​​still based on trigonometric functions, and there is still the problem of insignificant features for non-smooth images; Song et al. replaced the Fourier matrix with the Dobesy wavelet transform matrix and proposed a TTNN (Wavelet) minimization model. The wavelet base matrix considers Spatial structure information, but there is still a problem of poor adaptability to severely disordered image arrangements; Jiang et al. referred to the Framelet transformation matrix in image processing and proposed a F-TNN (Framelet) minimization model. They pointed out that redundant The projection base can better capture the features of the original image, but this will seriously increase the computational complexity

In summary, the above three models aim to solve the problem of restoration of non-smooth 3D images, but there is a lack of scientific and reasonable prior explanations for each projection basis that replaces the discrete Fourier matrix in TNN in the restoration of non-smooth 3D images, and The method of manually setting the projection base makes the application scenarios very limited, and the existing technology has great limitations in the completion of non-smooth 3D images

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