  Compressive sensing claims that the sparse signals can be reconstructed
exactly from many fewer measurements than traditionally believed necessary. One
of issues ensuring the successful compressive sensing is to deal with the
sparsity-constraint optimization. Up to now, many excellent theories,
algorithms and software have been developed, for example, the so-called greedy
algorithm ant its variants, the sparse Bayesian algorithm, the convex
optimization methods, and so on. The formulations for them consist of two
terms, in which one is and the other is (, mostly, p=1 is adopted due to good
characteristic of the convex function) (NOTE: without the loss of generality,
itself is assumed to be sparse). It is noted that all of them specify the
sparsity constraint by the second term. Different from them, the developed
formulation in this paper consists of two terms where one is with () and the
other is . For each iteration the measurement matrix (linear operator) is
reweighed by determined by which is obtained in the previous iteration, so the
proposed method is called the iteratively reweighed operator algorithm (IROA).
Moreover, in order to save the computation time, another reweighed operation
has been carried out; in particular, the columns of corresponding to small have
been excluded out. Theoretical analysis and numerical simulations have shown
that the proposed method overcomes the published algorithms.
