A medical system (20) includes a shaft (22) configured for insertion into an intra-body cavity, such as a cardiac chamber； multiple ultrasound transducers (48), which are distributed over splines that form a basket catheter (40) at a distal end of the shaft, the transducers being configured to transmit ultrasonic signals in the intra-body cavity and to receive echo signals in response to the ultrasonic signals； and a processor (41) 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.
