We present a novel framework for object-level 3D underwater reconstruction using imaging sonar sensors. We demonstrate that imaging sonar reconstruction is analogous to the problem of confocal non-line-of-sight (NLOS) reconstruction. Drawing upon this connection, we formulate the problem as one of solving for volumetric albedo, where the scene of interest is modeled as a directionless albedo field. After discretization, reconstruction reduces to a convex linear optimization problem, which we can augment with a variety of priors and regularization terms. We show how to solve the resulting regularized problems using the alternating direction method of multipliers (ADMM) algorithm. We demonstrate the effectiveness of the proposed approach in simulation and on real-world datasets collected in a controlled, test tank environment with several different sonar elevation apertures.