  We propose a new algorithm to compute a shifted proper orthogonal
decomposition (sPOD) for systems dominated by multiple transport velocities.
The sPOD is a recently proposed mode decomposition technique which overcomes
the poor performance of classical methods like the proper orthogonal
decomposition (POD) for transport-dominated phenomena. This is achieved by
identifying the transport directions and velocities and by shifting the modes
in space to track the transports. Our new algorithm carries out a residual
minimization in which the main computational cost arises from solving a
nonlinear optimization problem scaling with the snapshot dimension. We apply
the algorithm to snapshot data from the simulation of a pulsed detonation
combuster and observe that very few sPOD modes are sufficient to obtain a good
approximation. For the same accuracy, the common POD needs ten times as many
modes and, in contrast to the sPOD modes, the POD modes do not reflect the
moving front profiles properly.
