MPR-Flow: Efficient Inverse Problem Solving for Sequential Measurements

Many real-world imaging techniques rely on combining multiple measurements acquired sequentially. The final image can then be obtained by solving an inverse problem that accounts for the physical model of the acquisition process. In many applications, it is essential to minimize the number of data acquisitions to avoid multiplying time-consuming, costly, or risky procedures. Being able to obtain the best possible reconstruction as measurements are acquired is thus critical to avoid unnecessary acquisitions. In this setting, each reconstruction can be a useful computation state for the next step. With this in mind, we introduce Measurement-Progressive Reconstruction Flow (MPR-Flow), a plug-and-play flow solver that exploits continuity at two scales. First, across acquisition stages, previous reconstructions are used as a prior to speed up the reconstruction. Second, across solver iterations, the re-noising step is constrained so that well-measured regions are pre- served. MPR-Flow needs no retraining, nor any changes in the prior. Experiments on simulated and real datasets show that it outperforms state-of-the-art flow-based inverse solvers in terms of reconstruction quality and acquisition time.