In this section, we call the pick-l algorithms introduced in Section 2 and 3 as simply the (basic) pick-l and the optimized pick-l algorithms respectively.
The optimized pick-l algorithm provides a tighter, or at least the same, upper bound of α k than the basic pick-l algorithm introduced in (11).
Therefore, the optimized pick-l algorithm, which is (15), provides a tighter or at least the same upper bound than the basic pick-l algorithm.
In summary, the optimized pick-l algorithm provides better or at least equal upper bound on α k to the basic pick-l algorithm, with additional complexity.
Table 4 demonstrates that when l=3 and k=4,5,…,8, the optimized pick-l algorithm provided tighter upper bounds on α k than the basic pick-l algorithm.
Additionally, we provided the exact α k values obtained from TSA in order to check how tight the bounds obtained from the basic pick-l and the optimized pick-l are.
We compared the basic pick-l algorithm introduced in Section 2 to the optimized pick-l algorithm in Section 3 on Gaussian sensing matrices 28×40 and 40×50 for l=3 and k=4,5,…,8.
In terms of the execution time, the optimized pick-l algorithm, which computes (15), was around 1.7 and 4.4 times slower than the basic pick-l on 28×40 and 40×50 Gaussian matrix respectively.
Hence, the optimal value of (15), which is the result from the optimized pick-l, can be smaller than or equal to that of (11), which is the basic pick-l.
