Table 1 Comparison results ( ∥x-x ∗ ∥ 2/ ∥x∥ 2 ) of randomly generated signals with length N = 256 and m = 64 uneven size blocks by mixed l 2 / l q method and l q method with four different values of q and two different sampling sizes r = M/k 0
From: On recovery of block-sparse signals via mixed l 2 /l q (0 < q ≤ 1) norm minimization
σ = 0.02 | σ = 0.05 | σ = 0.10 | |
|---|---|---|---|
k = 4,r = 3 | |||
Lasso | 0.535 ± 0.153 | 0.543 ± 0.153 | 0.572 ± 0.153 |
l q (q = 0.7) | 0.467 ± 0.184 | 0.458 ± 0.177 | 0.504 ± 0.209 |
l q (q = 0.5) | 0.472 ± 0.185 | 0.469 ± 0.206 | 0.507 ± 0.225 |
l q (q = 0.1) | 0.355 ± 0.243 | 0.364 ± 0.251 | 0.461 ± 0.253 |
Group Lasso | 0.283 ± 0.149 | 0.332 ± 0.175 | 0.426 ± 0.208 |
l 2/l q (q = 0.7) | 0.159 ± 0.125 | 0.189 ± 0.173 | 0.312 ± 0.268 |
l 2/l q (q = 0.5) | 0.145 ± 0.095 | 0.168 ± 0.117 | 0.313 ± 0.201 |
l 2/l q (q = 0.1) | 0.064 ± 0.042 | 0.118 ± 0.103 | 0.324 ± 0.263 |
k = 4,r = 4 | |||
Lasso | 0.363 ± 0.093 | 0.397 ± 0.106 | 0.421 ± 0.105 |
l q (q = 0.7) | 0.308 ± 0.112 | 0.327 ± 0.112 | 0.332 ± 0.102 |
l q (q = 0.5) | 0.307 ± 0.115 | 0.309 ± 0.105 | 0.320 ± 0.095 |
l q (q = 0.1) | 0.179 ± 0.083 | 0.177 ± 0.093 | 0.240 ± 0.112 |
Group Lasso | 0.193 ± 0.078 | 0.222 ± 0.064 | 0.306 ± 0.130 |
l 2/l q (q = 0.7) | 0.126 ± 0.060 | 0.130 ± 0.048 | 0.182 ± 0.061 |
l 2/l q (q = 0.5) | 0.112 ± 0.059 | 0.120 ± 0.063 | 0.156 ± 0.052 |
l 2/l q (q = 0.1) | 0.041 ± 0.032 | 0.062 ± 0.024 | 0.178 ± 0.099 |
k = 12,r = 3 | |||
Lasso | 0.419 ± 0.063 | 0.434 ± 0.059 | 0.444 ± 0.058 |
l q (q = 0.7) | 0.382 ± 0.064 | 0.397 ± 0.065 | 0.399 ± 0.062 |
l q (q = 0.5) | 0.359 ± 0.064 | 0.372 ± 0.063 | 0.374 ± 0.057 |
l q (q = 0.1) | 0.162 ± 0.040 | 0.183 ± 0.047 | 0.221 ± 0.051 |
Group Lasso | 0.244 ± 0.046 | 0.264 ± 0.052 | 0.291 ± 0.046 |
l 2/l q (q=0.7) | 0.164 ± 0.036 | 0.182 ± 0.048 | 0.198 ± 0.036 |
l 2/l q (q = 0.5) | 0.129 ± 0.039 | 0.148 ± 0.048 | 0.168 ± 0.034 |
l 2/l q (q = 0.1) | 0.042 ± 0.018 | 0.073 ± 0.018 | 0.154 ± 0.048 |
k = 12,r = 4 | |||
Lasso | 0.350 ± 0.040 | 0.362 ± 0.054 | 0.373 ± 0.048 |
l q (q = 0.7) | 0.330 ± 0.048 | 0.336 ± 0.053 | 0.333 ± 0.051 |
l q (q = 0.5) | 0.309 ± 0.049 | 0.313 ± 0.051 | 0.308 ± 0.050 |
l q (q = 0.1) | 0.138 ± 0.033 | 0.149 ± 0.023 | 0.189 ± 0.037 |
Group Lasso | 0.202 ± 0.030 | 0.214 ± 0.069 | 0.242 ± 0.038 |
l 2/l q (q = 0.7) | 0.143 ± 0.029 | 0.153 ± 0.028 | 0.175 ± 0.030 |
l 2/l q (q = 0.5) | 0.109 ± 0.029 | 0.124 ± 0.026 | 0.155 ± 0.027 |
l 2/l q (q = 0.1) | 0.038±0.014 | 0.069 ± 0.013 | 0.157 ± 0.041 |