  Signals sparse in a transformation domain can be recovered from a reduced set
of randomly positioned samples by using compressive sensing algorithms. Simple
re- construction algorithms are presented in the first part of the paper. The
missing samples manifest themselves as a noise in this reconstruction. Once the
reconstruction conditions for a sparse signal are met and the reconstruction is
achieved, the noise due to missing samples does not influence the results in a
direct way. It influences the possibility to recover a signal only. Additive
input noise will remain in the resulting reconstructed signal. The accuracy of
the recovery results is related to the additive input noise. Simple derivation
of this relation is presented. If a reconstruction algorithm for a sparse
signal is used in the reconstruction of a nonsparse signal then the noise due
to missing samples will remain and behave as an additive input noise. An exact
relation for the mean square error of this error is derived for the partial DFT
matrix case in this paper and presented in form of a theorem. It takes into
account very important fact that if all samples are available then the error
will be zero, for both sparse and nonsparse recovered signals. Theory is
illustrated and checked on statistical examples.
