1. A touch-sensitive apparatus comprising: a panel configured to conduct signals from a plurality of incoupling ports to a plurality of outcoupling ports, thereby defining detection lines that extend across a non-circular touch surface on the panel between pairs of incoupling and outcoupling ports; at least one signal generator coupled to the incoupling ports to generate the signals; at least one signal detector coupled to the outcoupling ports to generate an output signal; and a signal processor configured to receive the output signal and: process the output signal to generate a set of observed values for at least a subset of the detection lines, wherein the observed values correspond to sampling points in a two-dimensional sample space, in which a first dimension is defined by an angle parameter that represents a rotation angle of the detection line in the plane of the panel and a second dimension is defined by a distance parameter that represents a distance of the detection line in the plane of the panel from a predetermined origin; process the observed values for the sampling points, by interpolation in the two-dimensional sample space, to generate estimated values for matched sampling points in the two-dimensional sample space, wherein the matched sampling points are arranged to form consecutive columns in the two-dimensional sample space, such that the columns extend in the second dimension and are spaced in the first dimension, and wherein at least a subset of the consecutive columns are non-equispaced and arranged to coincide with alignment lines that are defined by the locations of the sampling points in the two-dimensional sample space; and execute a tomographic reconstruction function on the estimated values for the matched sampling points to generate a two-dimensional representation of touch interaction on the touch surface.