# Difference between revisions of "Graph Filterbanks"

## General Information

• This website provides source code for two-channel wavelet transforms on graphs.
• Publications describing these transforms can be found at:
• Email: kumarsun at usc dot edu

## Installation

• The code is written in Matlab(c) version R2011a.
• To install the code, simply unpack the directory in a Matlab folder.

## How to run demos

• Demo 1 implements a 2-dimensional graph-QMF filterbank on an 8-connected graph-formulation of any 2D digital image.
• For a K-level wavelet-tree decomposition, the algorithm automatically crops the input image into a square image of size multiple of 2^K.
• The output is graph wavelet-coefficients ordered in the image format as shown

• To run the demo, execute any of the following commands:

1 filterbanks on a default image and parameters

```  [wav_coeffs] = QMF_filterbank_demo_1();
```

2 filterbanks on a given image

```  filename = 'sample1.jpg';
filetype = 'jpeg';
[wav_coeffs] = QMF_filterbank_demo_1(filename,filetype);
```

3 filterbanks on a given image with optional parameters

```  opt = struct('max_level',3,'filterlen',20,'nnz_factor',1);
filename = 'sample1.jpg';
filetype = 'jpeg';
[wav_coeffs] = QMF_filterbank_demo_1(filename,filetype,opt);
% where max_level is the number of decomposition level,
% filterlen is length of approximated FIR Meyer kernel
% nnz_factor is the fraction of non-zero high-pass coefficients used in reconstruction

```
• Demo 2 implements a 2-dimensional graph-QMF filterbank on the Minnesota traffic graph.
• To run the demo, execute in Matlab
```  [wav_coeffs, channel_info] = QMF_filterbank_demo_2();
% where wav_coeffs are the output wavelet coefficients ordered as a vector
% channel_info(i).name is the name of subband,
% channel_info(i).nodes is the set of indices of wavelet coefficients in the ith subband.
```

## Contact

• Comments, questions or concerns should be directed to: Sunil K. Narang (kumarsun at usc dot edu)

## Related Publications

• S. K. Narang and Antonio Ortega, "Perfect Reconstruction Two-Channel Wavelet Filter-Banks For Graph Structured Data", In IEEE Transactions of Signal Processing, also available at Tech. Rep. arXiv:1106.3693v3
• S.K. Narang and A. Ortega, "Downsampling Graphs Using Spectral Theory",IEEE Intl. Conf. on Acoustics, Speech and Signal Processing (ICASSP'11), PDF format, Poster

## Acknowledgements

• This work was supported by NSF under grant CCF-1018977