  A signal is sparse in one of its representation domain if the number of
nonzero coefficients in that domain is much smaller than the total number of
coefficients. Sparse signals can be reconstructed from a very reduced set of
measurements/observations. The topic of this paper are conditions for the
unique reconstruction of sparse signals from a reduced set of observations.
After the basic definitions are introduced, the unique reconstruction
conditions are reviewed using the spark, restricted isometry, and coherence of
the measurement matrix. Uniqueness of the reconstruction of signals sparse in
the discrete Fourier domain (DFT), as the most important signal transformation
domain, is considered as well.
