sLRMF

MATLAB code for Stable Nonconvex Statistical Estimation for Simultaneous Low-rank and Smooth Data.

The package contains the synthetic experiments used in the manuscript, supplementary numerical studies, and real-data demonstrations for images, hyperspectral compressed imaging, traffic time-series imputation, and video background/foreground separation.

Requirements

• MATLAB R2021a or later.
• Image Processing Toolbox is required by the image examples and several TV-based baselines.
• Manopt and matrix-sensing utilities needed by the simulation scripts are included under simulations/tools/.

Set MATLAB's Current Folder to the repository root before running the scripts below. Do not recursively add the whole repository to the MATLAB path; each entry script adds only the folders it needs.

Directory structure

sLRMF_code/
├── README.md
├── methods/
│   ├── LRMF.m
│   ├── sLRMF.m
│   ├── synthetic/
│   └── baselines/
├── simulations/
│   ├── demo_test.m
│   ├── main/
│   ├── supplementary/
│   └── tools/
├── applications/
│   ├── README.md
│   ├── image/
│   │   ├── README.md
│   │   ├── data/
│   │   └── methods/
│   ├── hyperspectral/
│   ├── traffic/
│   ├── video/
│   └── shared/
└── results/
    ├── main/
    ├── supplementary/
    └── applications/

Main-paper simulations

The main figure scripts are in simulations/main/.

Manuscript result	Script	Main output
Figure 2(a,b)	figure2_linear_convergence.m	figure2_errors.pdf, figure2_log_gaps.pdf
Figure 3(a)	figure3a_smoothness_dependent_error.m	figure3a_smoothness_dependent_error.pdf
Figure 3(b)	figure3b_smoothness_applications.m	figure3b_smoothness_applications.pdf
Figure 3(c)	figure3c_smoothness_other_methods.m	figure3c_smoothness_other_methods.pdf
Figure 4	figure4_oracle_scaling.m	figure4_oracle_scaling.pdf

Example:

run('simulations/main/figure3a_smoothness_dependent_error.m');
run('simulations/main/figure3b_smoothness_applications.m');
run('simulations/main/figure3c_smoothness_other_methods.m');

Each Figure 3 script saves both the plotted figure and its numerical results under results/main/. Experiment parameters and Monte Carlo repetition counts are defined near the top of each script.

Supplementary simulations

See simulations/supplementary/README.md. The supplementary folders contain:

• convergence experiments for sensing, completion, and robust PCA;
• smoothness-dependent errors in multiple norms;
• norm-specific effective-smoothness experiments;
• regularization studies and experiments associated with Theorems 6 and 7.

Outputs are written to results/supplementary/.

Real-data applications

Image examples

run('applications/image/demo_image_denoising.m');
run('applications/image/demo_image_sensing.m');
run('applications/image/demo_image_inpainting.m');
run('applications/image/demo_image_outlier_removal.m');

Three sample images are included under applications/image/data/. These scripts are single-image demonstrations; they are not the full BSD300 batch aggregation reported in the manuscript.

Hyperspectral, traffic, and video examples

run('applications/hyperspectral/demo_hsi_compressed_imaging.m');
run('applications/traffic/demo_traffic_time_series_imputation.m');
run('applications/video/demo_video_background_modeling.m');

The HSI and traffic datasets are not redistributed because of their size; download and preparation instructions are provided in the corresponding data/README.md files. A 20-frame airport video example and foreground mask are included in applications/video/data/ so that the video workflow can be run directly.

See applications/README.md for the application-to-manuscript mapping and output locations.

Results

Running a script writes results under results/; files with matching names are overwritten. Most scripts save PDF figures and MAT files, and some application runners also save CSV summaries and PNG previews.

The included third-party Manopt and sensing utilities retain their original license and author notices.