Related Papers on Tensor Sparsity

 

[1] Qi Xie, Qian Zhao, Deyu Meng, Zongben Xu. Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery,  accepted in IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017.

[2] Dong Zeng, Qi Xie, Wenfei Cao, Jiahui Lin, Shanli Zhang, Jing Huang, Zhaoying Bian, Deyu Meng, Zongben Xu, Zhengrong Liang, Wufan Chen, and Jianhua Ma. Low-dose dynamic cerebral perfusion computed tomography reconstruction via Kronecker-basis-representation tensor sparsity regularization. Accepted by IEEE Transactions on Medical Image, 2017.

[3] Qi Xie, Qian Zhao, Deyu Meng, Zongben Xu, Shuhang Gu, Wangmeng Zuo and Lei Zhang. Multispectral images denoising by intrinsic tensor sparsity regularizationIEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016. [supplementary material[Matlab code]

[4] Qian Zhao, Deyu Meng, Xu Kong, Qi Xie, Wenfei Cao, Yao Wang, Zongben Xu. A Novel Sparsity Measure for Tensor Recovery, ICCV, 2015. [supplementary material]

[5] Yi Peng, Deyu Meng, Zongben Xu, Chenqiang Gao, Yi Yang, Biao Zhang. Decomposable Nonlocal Tensor Dictionary Learning for Multispectral Image DenoisingSupplementary Material, CVPR, 2014. Matlab code.

[6] Wenfei Cao, Yao Wang, Jian Sun, Deyu Meng, Can Yang, Andrzej Cichocki, Zongben Xu. Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements. IEEE Transactions on Image Processing, 2016.[Demo code]

More Experimental Results on ITS-based Methods

 More experimental results on our submission "Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery"


1. MSI Denoising Results

1.1. MSI denoising results at each band of MSI chart and stuffed toy, (a) The clean image; (b) The noisy images corrupted by Gaussian noise with variance v = 0:2, (c)-(m) The restored image obtained by the 11 utilized MSI denoising methods

1.2. MSI denoising results at two bands (400nm and 700nm) of MSI egyptian_statue_ms, (a) The clean image; (b) The noisy images corrupted by Gaussian noise with variance v = 0:2, (c)-(m) The restored image obtained by the 11 utilized MSI denoising methods

1.3. MSI denoising results at two bands (400nm and 700nm) of MSI feathers, (a) The clean image; (b) The noisy images corrupted by Gaussian noise with variance v = 0:2, (c)-(m) The restored image obtained by the 11 utilized MSI denoising methods

1.4. Average performance of 9 competing methods with respect to 4 PQIs and v (the variance of noise) is setting
to be 0.10, 0.15, 0.20, 0.25 and 0.30. For both settings, the results are obtained by averaging through the 32 scenes in Columbia MSI Database

                             

2. MSI Completion Results

2.1. MSI completion results at each band of MSI fake and real lemons, (a) The clean image; (b) The corresponding sampled images with sampling rate 10%, (c)-(j) The restored image obtained by the 8 utilized MSI denoising methods

2.2.  Kronecker bases obtained by ITS-TC from the corresponding sampled images of MSI fake and real lemons with sampling rate 10%, and the combination result of a part of bases obtained by ITS-TC

2.3. MSI completion results at a band (700nm) of MSI cloth, (a) The clean image; (b) The corresponding sampled images with sampling rate 10%, (c)-(j) The restored image obtained by the 8 utilized MSI denoising methods, (k) First 6 Kronecker bases obtained by ITS-TC; (l) Combination result of the first 10, 100 and 1000 bases obtained by ITS-TC, respectively.

 

2.4. MSI completion results at a band (700nm) of MSI jelly beans, (a) The clean image; (b) The corresponding sampled images with sampling rate 10%, (c)-(j) The restored image obtained by the 8 utilized MSI denoising methods, (k) First 6 Kronecker bases obtained by ITS-TC; (l) Combination result of the first 10, 100 and 1000 bases obtained by ITS-TC, respectively.

 

2.5. MSI completion results at a band (700nm) of MSIwatercolor, (a) The clean image; (b) The corresponding sampled images with sampling rate 10%, (c)-(j) The restored image obtained by the 8 utilized MSI denoising methods

 

3. Background Subtraction Results

3.1. From left to right: original video frames, background and foreground extracted by all competing methods.

Proof for Theorem 1 in our submission "Intrinsic Tensor Sparsity Regularization and Its
Applications to Tensor Recvery":

The proof is listed in Proof File.

 

Matlab Codes