  We consider a class of l0-minimization problems, which is to search for the
partial sparsest solution to an underdetermined linear system with additional
constraints. We introduce several concepts, including lp-induced norm (0 < p <
1), maximal scaled spark and scaled mutual coherence, to develop several new
uniqueness conditions for the partial sparsest solution to this class of
l0-minimization problems. A further improvement of some of these uniqueness
criteria have been also achieved through the so-called concepts such as maximal
scaled (sub)coherence rank.
