A medical system includes a shaft, multiple ultrasound transducers and a processor. The shaft is configured for insertion into an intra-body cavity of a patient. The multiple ultrasound transducers, which are distributed over splines that form a basket catheter at a distal end of the shaft, are configured to transmit ultrasonic signals in the intra-body cavity and to receive echo signals in response to the ultrasonic signals. The processor is configured to calculate a surface of the intra-body cavity by processing the echo signals using an ellipsoidal back-projection method, which reconstructs ultrasound-wave reflecting surfaces by performing at least one of applying back-projection summation over sub-sets of scattered echo signals distributed over respective sub-sets of constructed ellipsoids and applying a non-linear minimum operator over each of the sub-sets of distributed echo signals to generate a respective minimum value for each sub-set.