In this section, we compare the performance of T-LARS and Kronecker-OMP to obtain $K$-sparse representations of our 3D MRI brain image, $Y$, $175×150×10$ 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 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:
Summary of Experimental Results for Our 3D MRI Brain Image.
ExperimentImage SizeOptimization ProblemDictionary TypeNumber of IterationsComputation Time (sec) K-OMPComputation Time (sec) T-LARS
175 $×$ 150 $×$ 10 $L0$ Fixed 13,125 20,144 434
32 $×$ 32 $×$ 10 $×$ 36 $L0$ Learned $ΦKOMP$ 13,125 25,002 394
32 $×$ 32 $×$ 10 $×$ 36 $L0$ Learned $ΦTLARS$ 13,125 22,646 400
175 $×$ 150 $×$ 10 $L1$ Fixed 14,216 -- 495
32 $×$ 32 $×$ 10 $×$ 36 $L1$ Learned $ΦTLARS$ 14,856 -- 490
ExperimentImage SizeOptimization ProblemDictionary TypeNumber of IterationsComputation Time (sec) K-OMPComputation Time (sec) T-LARS
175 $×$ 150 $×$ 10 $L0$ Fixed 13,125 20,144 434
32 $×$ 32 $×$ 10 $×$ 36 $L0$ Learned $ΦKOMP$ 13,125 25,002 394
32 $×$ 32 $×$ 10 $×$ 36 $L0$ Learned $ΦTLARS$ 13,125 22,646 400
175 $×$ 150 $×$ 10 $L1$ Fixed 14,216 -- 495
32 $×$ 32 $×$ 10 $×$ 36 $L1$ Learned $ΦTLARS$ 14,856 -- 490

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