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

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


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.


[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.