Table 1 Different sufficient conditions related to k1, k2, and q
From: Non-convex block-sparse compressed sensing with coherent tight frames
k1 | k2 | q=0.1 | q=0.5 | q=0.7 | q=1 |
|---|---|---|---|---|---|
k | 3k | δk+1.43θk,3k<1 | δk+1.21θk,3k<1 | δk+1.13θk,3k<1 | δk+1.02θk,3k<1 |
k | 4k | δk+1.63θk,4k<1 | δk+1.2θk,4k<1 | δk+1.12θk,4k<1 | δk+θk,4k<1 |
\(\frac {5}{4}k\) | \(\frac {11}{4}k\) | \(\delta _{k}+1.49\theta _{\frac {5}{4}k,\frac {11}{4}k}<1\) | \(\delta _{k}+1.28\theta _{\frac {5}{4}k,\frac {11}{4}k}<1\) | \(\delta _{k}+1.09\theta _{\frac {5}{4}k,\frac {11}{4}k}<1\) | \(\delta _{k}+0.78\theta _{\frac {5}{4}k,\frac {11}{4}k}<1\) |
\(\frac {3}{2}k\) | \(\frac {7}{2}k\) | \(\delta _{k}+1.41\theta _{\frac {3}{2}k,\frac {7}{2}k}<1\) | \(\delta _{k}+1.19\theta _{\frac {3}{2}k,\frac {7}{2}k}<1\) | \(\delta _{k}+0.96\theta _{\frac {3}{2}k,\frac {7}{2}k}<1\) | \(\delta _{k}+0.61\theta _{\frac {3}{2}k,\frac {7}{2}k}<1\) |
2k | 5k | δk+1.37θ2k,5k<1 | δk+1.07θ2k,5k<1 | δk+0.79θ2k,5k<1 | δk+0.4θ2k,5k<1 |