The accuracy of initial conditions is an important driver of the forecast skill of numerical weather prediction models. Increases in the quantity of available measurements, in particular high-resolution remote sensing observational data products from satellites, are valuable inputs for improving those initial condition estimates. However, the data assimilation methods used for integrating observations into forecast models are computationally expensive. This makes incorporating dense observations into operational forecast systems challenging, and it is often prohibitively time-consuming. As a result, large quantities of data are discarded and not used for state initialization. We demonstrate, using the Lorenz-96 system for testing, that a simple machine learning method can be trained to assimilate high-resolution data. Using it to do so improves both initial conditions and forecast accuracy. Compared to using the Ensemble Kalman Filter with high-resolution observations ignored, our augmented method has an average root-mean-squared error reduced by 15%. Ensemble forecasts using initial conditions generated by the augmented method are more accurate and reliable at up to 10 days of forecast lead time.