A signal processor in a touch-sensitive apparatus generates a 2D representation of touch interaction on a touch surface by tomographic processing. The signal processor generates observed values for detection lines that correspond to signal propagation paths across the touch surface. The observed values correspond to sampling points in a sample space defined by a first dimension representing a rotation angle of the detection line on the touch surface and a second dimension representing a distance of the detection line from a predetermined origin on the touch surface. The signal processor processes the observed values, by interpolation in the sample space, to generate estimated values for matched sampling points in the sample space using a tomographic reconstruction function.