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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 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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