In the Data_preprocessing folder:

The data doesn't work very well when we set the tubal-rank too low during data preprocessing.
When tubal-rank is 15, we can see that the rank approximation result has some new noise.
When tubal-rank is 32, we can get a good approximation result.

The CDF of singular values for the seismic data, compared with processed data.

Original data.

Processed data.

These figures are obtained by running the test_r_error.m in the Data_preprocessing folder.

Result:

The result of TNN algorithm and Tubal-Alt-Min algorithm:

data size: t * m * n: 300 * 120 * 80, tubal-rank:15.
RSE of TNN:6.1e-03. RSE of Tubal-Alt-Min:1.56e-02.

(a) Slice view of the original complete data.
(b) Slice view of reconstructed data using TNN.
(c) Slice view of reconstructed data using Tubal-Alt-Min.

run Tubal_Alt_Min.m to get the result.

The reconstruction error of TNN algorithm and Tubal-Alt-Min algorithm:

The figure shows the RSE of the Tubal-Alt-Min algorithm and TNN algorithm for varying frontal slice sampling rates from 80% to 98%.

run Tubal_TNN.m in the error folder to get the figure

Two m_files in the error folder:

Tubal_Alt_Min_error.m is used to calculate RSE in the case of different slice missing.
Tubal_TNN.m compared the recovery accuracy and convergence speed between Tubal_Alt_Min algorithm and TNN algorithm.
The TNN_solver folder is some functions of the TNN algorithm.

In the Plot_CDF folder:

the function of the test low-tubal-rank character of the seismic data in three different dimensions.

T_synthetic_tubal_rank_2.mat is a synthetic seismic data set of size: 64 * 64 * 256. Three dimensions are inline,crossline,time respectively.

The experimental data of size 326 * 431 * 531. The three dimensions are: time,inline and crossline. tubal-rank: 45.

The SeisPlot.zip is the toolbox to plot the seismic data. You should add path in MATLAB after decompression

Tubal-sampling result

data size:64 * 64 * 256, tubalrank:2.
tubal-sampling : 50%.

Tubal_Alt_Min algorithm result and TNN algorithm result:

Tubal_Alt_Min RSE = 1.289423e-15.TNN RSE = 1.475729e-04．

corrupted data

Tubal_Alt_Min recovery data

TNN recovery data

run Tubal_Alt_Min_TNN_tubal_sampling.m to get the result.

reconstruction error (RSE) under different tubal sampling rates:

run tubal_sampling_error.m to get the result.

GCG algorithm result：

GCG RSE:4.907527e-03.
GCG recovery data

run gcgexample.m in the GCGalgorithm folder to get the result.

conclusion:

tubal sampling: 70%. Tubal_Alt_Min RSE:5.504735e-16. TNN RSE:7.84263e-05. GCG RSE: 2.165258e-03.
tubal sampling: 30%. Tubal_Alt_Min RSE:4.928588e-07. TNN RSE:3.27454e-03. GCG RSE: 3.460236e-02.

YangletLiu / Seismic_Sensory_Data_Analysis