Projections onto the range of the exponential Radon transform and reconstruction algorithms

In recent articles Metz and Pan have introduced a large class of methods for inverting the exponential Radon transform that are parametrized by a function ω of two variables. We show that when ω satisfies a certain constraint, the corresponding inversion method uses projection to the range of the transform. The addition of another constraint on ω makes this projection orthogonal with respect to a weighted inner product. Their quasi-optimal algorithm uses the projection that is orthogonal with respect to the ordinary inner product.