Example of a simple CS reconstruction problem. (a) The Shepp-Logan phantom test image. (b) The sampling geometry from which Fourier coefficients are sampled along 22 approximately radial lines. (c) The zero-filling result, where non-sampled coefficients are set to zero and an inverse Fourier transformation is applied. (d) Reconstruction obtained using CS methods. The reconstruction is an exact replica of the image in (a). We also tested all sampling geometries of Table
1 on this image. For sampling geometries using 20.3% of the total samples, reconstructions gave values well-above 40 dB (50-60 dB) which are excellent (e.g., see Figure
5). It is interesting to note that stochastic geometries perform significantly better than deterministic geometries at higher sampling rates. For example, random sampling on PDF gave over 90 dB reconstructions while the SLP geometry gave reconstructions of less than 60 dB. Again, all of these reconstructions are excellent. The lack of perfect-reconstruction for our geometries comes from the use of Wavelet transform in our method. As it is well-known, and also demonstrated here, the standard TV-norm is the best fit for this example.