CCRB_Software

Software for Constrained Cramér-Rao bounds with application to hyperspectral super-resolution

This MATLAB software reproduces the results from the following papers:

@inproceedings{prevost2019performance,
  title={Performance bounds for coupled CP model in the framework of hyperspectral super-resolution},
  author={Prevost, Cl{\'e}mence and Usevich, Konstantin and Comon, Pierre and Haardt, Martin and Brie, David},
  booktitle={2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)},
  pages={201--205},
  year={2019},
  organization={IEEE}
}

Incoming

Acknowledgements

Uncoupled ALS algorithm is courtesy of R. Bro. Coupled ALS algorithms STEREO and Blind-STEREO are courtesy of C. Kanatsoulis. If you want to use this software for publication, please cite the following papers:

@inproceedings{bro1998multi,
  title={Multi-way analysis in the food industry-models, algorithms, and applications},
  author={Bro, Rasmus},
  booktitle={MRI, EPG and EMA,” Proc ICSLP 2000},
  year={1998},
  organization={Citeseer}
}

@article{kanatsoulis2018hyperspectral,
  title={Hyperspectral super-resolution: A coupled tensor factorization approach},
  author={Kanatsoulis, Charilaos I and Fu, Xiao and Sidiropoulos, Nicholas D and Ma, Wing-Kin},
  journal={IEEE Transactions on Signal Processing},
  volume={66},
  number={24},
  pages={6503--6517},
  year={2018},
  publisher={IEEE}
}

Content

demo.m : demo file with minimal requirements.
/data : contains simulations results, for speed purpose. These results can also be obtained in the demo files.
/demos : contains demo files that produce tables and figures (including main.m)
/figures : where the figures are saved
/images : contains illustrative figures for this README.md
/src : contains helpful files to run the demos

Minimal requirements

In order to run the demo file and reproduce the figures, you will need to:

Download and install Tensorlab 3.0: https://www.tensorlab.net

Demo file

A demo with minimal requirements is available. To proceed, please run the demo.m file.

Generate the model

$\begin{align*} \begin{cases} {\mathcal{Y}}_1 &= [\![\mathbf{A}_1,\mathbf{B}_1,\mathbf{C}_1]\!] + \mathcal{E}_1,\\ {\mathcal{Y}}_2 &= [\![\mathbf{A}_2,\mathbf{B}_2,\mathbf{C}_2]\!] + \mathcal{E}_2,\\ \end{cases} \end{align*} \begin{align*} \quad\text{ s. to }\mathbf{A}_1 = \mathbf{P}\mathbf{A}_2\cdot\mathbf{\alpha}^{-1}, \mathbf{B}_1 = \mathbf{Q}\mathbf{B}_2\cdot\mathbf{\beta}^{-1},\nonumber\\ \mathbf{C}_2 =\mathbf{R}\mathbf{C}_1\cdot(\mathbf{\alpha\beta})^{-1}\nonumber \end{align*}$

### Calculate the Cramér-Rao bounds

We compute the following lower bounds:

Uncoupled CRB;
Fully-coupled CCRB;
Blind-CCRB;

for the following parameters:

$\begin{align*} {\widetilde{\mathbf{\theta}}}^{T} &= \begin{bmatrix}\text{vec}({(\mathbf{A}_2)_{2:I,:}})^{T} & \text{vec}({(\mathbf{B}_2)_{2:J,:}})^{T} & \text{vec}(\mathbf{C}_1)^{T}\end{bmatrix}, \\ {\widetilde{\mathbf{\phi}}}^{T} &= \begin{bmatrix}\text{vec}({(\mathbf{A}_1)_{2:I_H,:}})^{T} & \text{vec}({(\mathbf{B}_1)_{2:J_H,:}})^{T} & \text{vec}(\mathbf{C}_2)^{T}\end{bmatrix}. \end{align*}$

### Run the algorithms

We run the following algorithms:

Uncoupled ALS;
STEREO;
Blind-STEREO;

on our model. The number of realizations, as well as the maximum number of iterations, can be user-specified in the Pre-allocation section of the file. We compute the MSE provided by each algorithm and compare it to the bounds.

### Display the results

We plot the bounds and total MSEs as a function of the noise on the first tensor (HSI).

## Reproduce figures from the paper

To do so, you need to run the main.m file. Here, a menu is available and allows you to choose which figure or table you want to generate. Each number in the table below corresponds to a set of figures.

Number	Content
1	produces Figure 1 from CAMSAP paper
2	produces Fig. 1 and 4 from preprint
3	produces Fig. 2 and 5 from preprint
4	produces Fig. 3 from preprint
5	produces Fig. 6 from preprint
6	produces Fig. 8, 9 and 10 from preprint
7	produces Fig. 11 and 12 from preprint
8	produces Fig. 13 and 14 from preprint
9	produces Fig. 15 and 16 from preprint

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