Random Teoplitz / Circulant / Convolution
Sensing matrix A = [Downsample]*[Circulant Matrix]
Note that a Toeplitz matrix can be turned into a circulant matrix by adding zeros. Also, multiplying with a circulant matrix is equivalent to circular convolution with its first row.
Benefits for Compressive Sensing
- Easy to realize by hardware.
- Effective encoding. The compression ratio is as good as i.i.d. Gaussian random matrices.
- Faster decoding.
Performance comparisons: See here or this paper.
1D Matlab Demo: Version 2010/05/29, Download Link.
To install, (i) download and install YALL1; (ii) put yall1.m in the search path, and then the demo is ready to run.