We present the latest progress of our computation method for critical currents in bulk YBCO samples from magnetic field measurements with Hall probe, based on discretization of the magnetization M and resolution of the linearized inverse Biot-Savart problem by QR inversion. While computationally harder than other linear/FFT methods, it is more robust in front of measurement errors, and allows the computation of detailed current maps without assuming any symmetry in the OXY plane. In particular, we are able to detect irregularities such as multiple domains, or the perturbation induced by a welding. If the current in the bulk sample is not homogenous along the OZ axis, we obtain the average along the OZ axis of the current density. Moreover, the inhomogeneity of the current along the vertical axis can be detected by the user by measuring the magnetic field on the side of the bulk sample and comparing it with that induced by the computed OZ-averaged current. Finally, we discuss what must be done in the measurement of the magnetic field and mathematical processing of the data to avoid numerical pitfalls, and discuss the limits to the computation of 3-dimensional current maps. © 2006 IOP Publishing Ltd.