A data-driven framework for artefact suppression in non-destructive testing data is proposed in this paper. The framework consists of two stages for dimensionality reduction through (1) a principal component analysis and (2) an autoencoder. The first stage reduces the dimensionality of the input data. This allows the architecture of the autoencoder to be relatively shallow, which means that the deep learning model is fast to train and does not need as much training data. The output of the autoencoder contains artefact information (originating from structural features) and is projected back to the original domain. This is subtracted from the input data in order to isolate defect and noise information. The framework trains on defect-free experimental data and it does not require a large amount of training data. An optimisation approach to arrive at a near-optimal framework architecture is also proposed. An ultrasonic phased-array imaging application is used to illustrate the methodology and compared against the state-of-the-art deep learning approach to suppressing artefacts. The proposed method proves to be effective at suppressing artefacts leading to a good defect detection and characterisation performance.