Table 1 Summary of sparse reconstruction methods
From: Robust compressive sensing of sparse signals: a review
Method | Optimization problem | SER for signal [dB] | SER for image [dB] | Time [s] |
|---|---|---|---|---|
LBP | \(\phantom {\dot {i}\!}\|\mathbf {y}-\mathsf {\Phi } \mathbf {x}\|_{\text {LL}_{2},\gamma }+\lambda \| \mathbf {x}\|_{1}\) | 24.0 | 20.7 | 10.58 |
LIHT | \(\phantom {\dot {i}\!}\|\mathbf {y}-\mathsf {\Phi } \mathbf {x}\|_{\text {LL}_{2},\gamma }~~\text {s.t.}~~\|\mathbf {x}\|_{0}\leq s \) | 24.0 | 19.4 | 2.13 |
R-Lasso | \(\frac {1}{2}\| \mathbf {y}-\mathsf {\Phi } \mathbf {x}-\mathbf {r}\|_{2}^{2} + \tau _{x}\| \mathbf {x}\|_{1} + \tau _{r}\|\mathbf {r}\|_{1}\) | 8.9 | 18.1 | 7.23 |
L-CD | \(\phantom {\dot {i}\!}\|\mathbf {y}- \mathsf {\Phi } \mathbf {x} \|_{\text {LL}_{2},\gamma } + \tau \|\mathbf {x}\|_{0} \) | 25.1 | 19.2 | 6522.7 |
ℓ 1-CD | ∥y−Φ x∥1+τ∥x∥0 | 28.2 | 20.3 | 3814.2 |
ℓ 1-LS | \(\frac {1}{2}\|\mathbf {y}-\mathsf {\Phi } \mathbf {x}\|_{2}^{2}+\lambda \| \mathbf {x}\|_{1}\) | –6.5 | 7.3 | 4.73 |
ℓ 1-LAD | ∥y−Φ x∥1+τ∥x∥1 | 16.9 | 19.6 | 7.05 |
HIHT | \(\sum _{i=1}^{M}\rho \big (\frac {y_{i}-\mathbf {\phi }_{i}^{T}\mathbf {x}}{\sigma }\big)~~\text {s.t.}~~\|\mathbf {x}\|_{0}\leq s\) | 25.1 | 19.4 | 90.78 |
ℓ 1-OMP | ∥y−Φ x∥1 s.t. ∥x∥0≤s | 24.1 | – | – |