A transmission matrix (TM) describes the linear relationship between input and output when a coherent wavefront passes through a scattering medium. Measurement of the TM enables numerous applications, such as focusing light and image reconstruction. However, measuring TM continues to be very challenging due to its large dimension. The state-of-the-art methods, including phase-shifting holography and double phase retrieval, require significant amounts of measurements, and the subsequent data processing is often slow and computationally intensive. In this thesis, we propose a solution for transmission matrix recovery, called 3PointTM, that uses a minimal number of measurements per pixel for TM recovery. As a result, 3PointTM reduces the measurement budget by a factor of two, as compared to phase-shifting holography. This enables the acquisition of TMs at high resolutions and with low computational complexity. We validate our approach on both real and simulated data, and in particular demonstrate focusing of light and image reconstruction on dense scattering media in high SNR settings at 4X reduced complexity.