The continually expanding number of electric vehicles in circulation presents challenges in terms of end-of-life disposal, driving interest in the reuse of batteries for second-life applications. A key aspect of battery reuse is the quantification of the relative battery condition or state of health (SoH), to inform the subsequent battery application and to match batteries of similar capacity. Impedance spectroscopy has demonstrated potential for estimation of state of health, however, there is difficulty in interpreting results to estimate state of health reliably. This study proposes a model-free, convolutional-neural-network-based estimation scheme for the state of health of high-power lithium-ion batteries based on a dataset of impedance spectroscopy measurements from 13 end-of-first-life Nissan Leaf 2011 battery modules. As a baseline, this is compared with our previous approach, where parameters from a Randles equivalent circuit model (ECM) with and without dataset-specific adaptations to the ECM were extracted from the dataset to train a deep neural network refined using Bayesian hyperparameter optimisation. It is demonstrated that for a small dataset of 128 samples, the proposed method achieves good discrimination of high and low state of health batteries and superior prediction accuracy to the model-based approach by RMS error (1.974 SoH%) and peak error (4.935 SoH%) metrics without dataset-specific model adaptations to improve fit quality. This is accomplished while maintaining the competitive performance of the previous model-based approach when compared with previously proposed SoH estimation schemes.