In this section, we compare the performance of T-LARS and Kronecker-OMP to obtain $K$-sparse representations of our 3D MRI brain image, $Y$, $175\xd7150\xd710$ voxels by solving the $L0$ constrained sparse tensor least-squares problem. We also obtained similar K-sparse representations using T-LARS by solving the $L1$ optimization problem. Table 2 summarizes our results for the five experiments described in section 5.2. In all experiments, the algorithms were stopped when the number of nonzero coefficients $K$ reached **13**, **125**, which is 5% of the number of elements in $Y$. We note that in Table 2, the number of iterations for $L1$ optimization problems is larger than K because, as shown in algorithm 2 at each iteration T-LARS could either add or remove nonzero coefficients to or from the solution.

Table 2:

Experiment . | Image Size . | Optimization Problem . | Dictionary Type . | Number of Iterations . | Computation Time (sec) K-OMP . | Computation Time (sec) T-LARS . |
---|---|---|---|---|---|---|

1 | 175 $\xd7$ 150 $\xd7$ 10 | $L0$ | Fixed | 13,125 | 20,144 | 434 |

2 | 32 $\xd7$ 32 $\xd7$ 10 $\xd7$ 36 | $L0$ | Learned $\Phi KOMP$ | 13,125 | 25,002 | 394 |

3 | 32 $\xd7$ 32 $\xd7$ 10 $\xd7$ 36 | $L0$ | Learned $\Phi TLARS$ | 13,125 | 22,646 | 400 |

4 | 175 $\xd7$ 150 $\xd7$ 10 | $L1$ | Fixed | 14,216 | -- | 495 |

5 | 32 $\xd7$ 32 $\xd7$ 10 $\xd7$ 36 | $L1$ | Learned $\Phi TLARS$ | 14,856 | -- | 490 |

Experiment . | Image Size . | Optimization Problem . | Dictionary Type . | Number of Iterations . | Computation Time (sec) K-OMP . | Computation Time (sec) T-LARS . |
---|---|---|---|---|---|---|

1 | 175 $\xd7$ 150 $\xd7$ 10 | $L0$ | Fixed | 13,125 | 20,144 | 434 |

2 | 32 $\xd7$ 32 $\xd7$ 10 $\xd7$ 36 | $L0$ | Learned $\Phi KOMP$ | 13,125 | 25,002 | 394 |

3 | 32 $\xd7$ 32 $\xd7$ 10 $\xd7$ 36 | $L0$ | Learned $\Phi TLARS$ | 13,125 | 22,646 | 400 |

4 | 175 $\xd7$ 150 $\xd7$ 10 | $L1$ | Fixed | 14,216 | -- | 495 |

5 | 32 $\xd7$ 32 $\xd7$ 10 $\xd7$ 36 | $L1$ | Learned $\Phi TLARS$ | 14,856 | -- | 490 |

This site uses cookies. By continuing to use our website, you are agreeing to our privacy policy.