# magni.cs.reconstruction.sl0 package¶

Subpackage providing implementations of Smoothed l0 Norm (SL0).

The implementations provided are the original SL0 reconstruction algorithm and a modified SL0 reconstruction algorithm. The algorithm used depends on the ‘algorithm’ configuration option: ‘std’ refers to the original algorithm while ‘mod’ (default) refers to the modified algorithm.

## Routine listings¶

config
Configger providing configuration options for this subpackage.
run(y, A)
Run the specified SL0 reconstruction algorithm.

Notes

See _algorithm for documentation of run.

Implementations of the original SL0 reconstruction algorithm [1] and a modified Sl0 reconstruction algorithm [3] are available. It is also possible to configure the subpackage to provide customised versions of the SL0 reconstruction algorithm. The projection algorithm [1] is used for small delta (< 0.55) whereas the contraint elimination algorithm [2] is used for large delta (>= 0.55) which merely affects the computation time.

References

 [1] (1, 2) H. Mohimani, M. Babaie-Zadeh, and C. Jutten, “A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed l0 Norm”, IEEE Transactions on Signal Processing, vol. 57, no. 1, pp. 289-301, Jan. 2009.
 [2] Z. Cui, H. Zhang, and W. Lu, “An Improved Smoothed l0-norm Algorithm Based on Multiparameter Approximation Function”, in 12th IEEE International Conference on Communication Technology (ICCT), Nanjing, China, Nov. 11-14, 2011, pp. 942-945.
 [3] C. S. Oxvig, P. S. Pedersen, T. Arildsen, and T. Larsen, “Surpassing the Theoretical 1-norm Phase Transition in Compressive Sensing by Tuning the Smoothed l0 Algorithm”, in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, Canada, May 26-31, 2013, pp. 6019-6023.