In this section, we compare the performance of T-LARS and Kronecker-OMP to obtain $K$-sparse representations of our 3D PET-CT brain image, $Y$, $180×160×10$ 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 3 summarizes our results for the five experiments. In all experiments, the algorithms were stopped when the number of nonzero coefficients $K$ reached 14,400, 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 3:
Summary of Experimental Results for Our 3D PET-CT Brain Image.
ExperimentImage SizeOptimization ProblemDictionary TypeIterationsNumber of K-OMPComputation Time (sec) T-LARS
180 $×$ 160 $×$ 10 $L0$ Fixed 14,400 29,529 505
32 $×$ 32 $×$ 10 $×$ 42 $L0$ Learned $ΦKOMP$ 14,400 33,453 476
32 $×$ 32 $×$ 10 $×$ 42 $L0$ Learned $ΦTLARS$ 14,400 31,083 490
180 $×$ 160 $×$ 10 $L1$ Fixed 16,059 – 591
32 $×$ 32 $×$ 10 $×$ 42 $L1$ Learned $ΦTLARS$ 18,995 – 744
ExperimentImage SizeOptimization ProblemDictionary TypeIterationsNumber of K-OMPComputation Time (sec) T-LARS
180 $×$ 160 $×$ 10 $L0$ Fixed 14,400 29,529 505
32 $×$ 32 $×$ 10 $×$ 42 $L0$ Learned $ΦKOMP$ 14,400 33,453 476
32 $×$ 32 $×$ 10 $×$ 42 $L0$ Learned $ΦTLARS$ 14,400 31,083 490
180 $×$ 160 $×$ 10 $L1$ Fixed 16,059 – 591
32 $×$ 32 $×$ 10 $×$ 42 $L1$ Learned $ΦTLARS$ 18,995 – 744

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