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Signal reconstruction in compressive sensing involves finding a sparsesolution that satisfies a set of linear constraints. Several approaches to thisproblem have been considered in existing reconstruction algorithms. They eachprovide a trade-off between reconstruction capabilities and requiredcomputation time. In an attempt to push the limits for this trade-off, weconsider a smoothed l0 norm (SL0) algorithm in a noiseless setup. We argue thatusing a set of carefully chosen parameters in our proposed adaptive SL0algorithm may result in significantly better reconstruction capabilities interms of phase transition while retaining the same required computation time asexisting SL0 algorithms. A large set of simulations further support this claim.Simulations even reveal that the theoretical l1 curve may be surpassed in majorparts of the phase space.

Improving Smoothed l0 Norm in Compressive Sensing Using Adaptive Parameter Selection