Least squares signal reconstruction under normalized autocorrelation constraints

A constrained optimization method is used to reconstruct signals from their noisy linear transforms. In this approach the fit error energy is minimized over a set of signals whose first few normalized autocorrelation coefficients are larger than specified constraint values. This provides another method of introducing regularization to the least squares signal reconstruction. By choosing the constraint values larger more regularization can be obtained. Significant computational saving is gained by solving the corresponding dual optimization problem in the actual computation of the reconstruction. Comparison of the results of this and other approaches leads us to the conclusion that although the proposed approach requires more computation, it provides better reconstructions