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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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