Spectroscopic imaging - scanning tunneling microscope studies of quasiparticle interference in the high temperature superconductor Bi2 Sr2 CaCu2 O8+sigma as a function hole density and temperature are presented. Its is found that the momentum space source of low energy Bogoliubov excitations is restricted to a region that falls rapidly as the hole density falls to zero. This region agrees well with a strongly correlated generalization of Luttinger's theorem relating the momentum space area of low energy excitations to the electron density. Excitations to higher energies, whose momentum space source would be outside this restricted region without correlations, lack the properties of Bogoliubov quasiparticles and instead locally break translational and rotational symmetries. These real space excitations are demonstrated to be the pseudogap states. An intimate relationship between the Bogoliubov excitation gap and the pseudogap is found. As the temperature increases, the quasiparticle interference patterns persist above the superconducting transition temperature revealing them to be the spectroscopic signature of phase fluctuations. Although the Bogoliubov excitation gap evolves with temperature, both the restricted region in momentum space occupied by the quasiparticles and the real space pseudogap excitation structure does not. The generalized Luttinger's theorem provides a unified framework for understanding the properties of the cuprates at low hole densities in terms of strong correlations.