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A single-shot method to reconstruct the transverse self-wakefields acting on a beam, based only on screen images, is introduced. By employing numerical optimization with certain approximations, a relatively high-dimensional parameter space is efficiently explored to determine the multipole components of the transverse-wakefield topology up to desired order. The reconstruction technique complements simulations, which are able to directly describe the wakefield composition based on experimental conditions. The technique is applied to representative simulation results as a benchmark, and also to experimental data on wakefield observations driven in dielectric-lined structures.