In this chapter I introduce the theory behind the LSJIMP method. The chapter is divided into three sections. In section I motivate the LSJIMP inverse problem in general. In Section , I go on to outline my particular implementation of LSJIMP. In section , I show how, in a laterally-homogeneous earth, to create prestack time-domain images of pegleg multiples that are directly comparable, both in terms of kinematics and amplitudes, to the image of the primaries. In a heterogeneous earth, peglegs ``split'' into multiple arrivals. To account for this phenonmenon, in section I introduce the HEMNO (Heterogeneous Earth NMO Operator) equation, which can independently image each leg of split peglegs in a moderately heterogeneous earth.