A signal processing technique is presented for significantly sharpening the resolution of ultrasonic B-scan images, similar to those acquired in the nondestructive evaluation of girth welds in oil/gas pipelines. This enhancement allows a much improved estimate of the exact size of any detected anomaly in the weld, such that fracture mechanics can be used to gauge the probability of weld failure. The algorithm is based on the synthetic aperture focusing technique, combined with a variation of Wiener filtering and autoregressive spectral extrapolation. A numerical model of the transducer is used to construct a set of appropriate reference spectra for the deconvolution operation, and accounts for the dependence of a beam's frequency spectrum on the position of a flaw relative to the transmitter. Simulated and experimental B-scan images are used to provide an estimate of the improvement in resolution.