Image reconstruction of steel reinforcing bars in concrete using Fourier-domain interpolation applied to a sparsely populated data set

High-resolution image generation of bars in concrete using a single coil scanning inductive sensor is a time consuming process. This paper presents a method of generating the image using a sparsely populated data set (SPDS), obtained from a reduced number of scan lines, whose use is justifies by an analysis of the sensor spatial frequency response. Three methods are discussed: linear and cubic spline interpolation in the spatial domain, and Fourier interpolation, all of which are applied to an SPDS. Data for the SPDS are provided from a widely spaced scanning regime implemented in both the x and y-axes. Interpolated values are then synthesized to obtain high-resolution images. The Fourier-based method employs zero padding in the spatial frequency domain and inverse Fourier transformation to obtain higher resolution data in the time/spatial domain. In general, the results obtained by the linear interpolation algorithm are unacceptable since they do not represent the point-spread function of the sensor. The results obtained by the cubic spline and Fourier methods are very satisfactory, with the deviation from the results obtained by the standard high-resolution image generation process being very small. However, the cubic spline method is cumbersome to implement, requiring the computation of a large number of unique polynomials. In contrast, the Fourier algorithm is efficient, straightforward to code and yields an ideal band-limited interpolation. Experiments show that this new methodology is faster than the traditional scanning protocol by at least a factor of 10; a large area scan of 0.5 m2 can thus be produced in 12 min, rather than 2 h. In the future, this technique could be applied to widely spaced solid-state arrays, requiring a fraction of a second for image synthesis.