Contrast agent kinetic analysis has applications in medical diagnostics by helping to characterize the functional state of a tissue, and applications in drug discovery by offering insight into the behavior of the contrast agent itself. Contrast agent kinetic analysis is used often in conjunction with an imaging device that can measure noninvasively the concentration of the contrast agent, at one or more locations, as a function of time. The chapter describes the three major strategies for deconvolution, including strengths and weaknesses of each. The strategies include frequency domain strategy, analytical model strategy, and spatial-domain strategy. The chapter provides a novel approach to deconvolution termed physiologically-constrained deconvolution (PCD). PCD is based on the matrix strategy, but overcomes some of the limitations of this strategy by incorporating a priori physiologic information. The chapter demonstrates the application of the novel approach to measuring cardiac perfusion with both computer simulations and experimental data.