Left : all methods used same undersampling mask Ht with Ht = H for all times.
CS-Residual: Least Squares Compressive Sensing (LS-CS) and Kalman Filtered Compressive Sensing (KF-CS) Back to Home
| Research description | Papers | Experiment Results | Code | Links |
We develop compressive sensing (CS) based algorithms for real-time dynamic MR image reconstruction or for single-pixel video imaging with real-time video display capabilities. Both these problems can be reformulated as a problem of causally and recursively reconstructing a time sequence of approximately sparse (compressible) signals, with unknown and time-varying sparsity patterns, from a small number of linear projection measurements at each time.
The key idea of LS-CS and KF-CS is to replace CS on the observation by CS on the LS / KF observation residual computed using the previous support estimate. If support changes slowly, the signal residual will be approximately much more sparse compared to the signal itself, and as a result these can achieve accurate reconstruction using much fewer measurements.
We obtain computable bounds for LS-CS for compressible sequences and show that these bounds are much smaller than those for simple CS, if the sparsity pattern changes are slow enough.
We also apply LS-CS and KF-CS algorithms for various types of dynamic MRI and video sequences demonstrate that our proposed algorithms significantly outperform existing approaches.
| MRI reconstruction | Video compression |
We focus on the case with: (1) compressible signals, (2) nosiy measurements. We use Basis Pursuit-Denoising (BPDN) for CS reconstruction.
We compared LS-CS and KF-CS with simple CS (doing CS for each frame seperately as in Lustig et al, MRM'07), CS-diff (doing CS on observation difference to recover signal difference as in Volkan Cevher et al, ECCV ’08), and two batch methods, Batch CS (a batch method as in M. Lustig et al, ISMRM' 06) and k-t-FOCUSS (another batch method as in H. Jung, et al, Magnetic Resonance in Medicine), using 35% observations. MR imaging with full kx and randomly selected ky coefficients was simulated and Gaussian noise was added. This undersampling scheme can be modeled as using an undersampling matrix Ht, which contains a single 1 at a different location in each row and all other entries are zero. Monte Carlo averaging was done.
Left : all methods used same undersampling mask Ht with Ht = H for all
times.
Right: LS-CS, KF-CS and Batch CS used a same undersampling mask Ht, with Ht different for each t. K-t-FOCUSS used a different mask from all other methods. It fully sampled the eight lowest spatial frequencies and randomly sampled high frequency data (as described in H. Jung, et al, Magnetic Resonance in Medicine).
We see that LS-CS and KF-CS outperform CS (BPDN) as well as come close to the performance of batch-CS method.
Reconstructions of 10th , 15th and 20th image frame (for time-varying Ht case)
Comparison of LS-CS and KF-CS with simple CS for a standard video compression sequence - foreman sequence. We used 50% random-Gaussian measurements corrupted by additive Gaussian noise with SNR = 50dB. We see that LS-CS and KF-CS significantly outperform CS (BPDN).
