The study of thermoacoustic oscillations is of great importance for pollutant emission reduction and for designing hydrogen-based burner systems. The authors developed a high-resolution method for accurate measurement of those oscillations based on the detection of the line-of-sight refractive index gradients. This method, called Heterodyne Background Oriented Schlieren, suffers from a drop in accuracy when both vertical and horizontal gradients are detected simultaneously. In addition, it is not always possible to record both gradients due to the environmental conditions of the experiment. To overcome these limitations, a machine-learning-based approach has been developed. Based on supervised training of a deep neural network using bidirectional data, we demonstrate the ability to reconstruct a bidirectional gradient field from the knowledge of the unidirectional gradient field alone. As a result, for multidirectional or limited-view observations, knowledge of the gradient behavior in only one direction is sufficient for a complete gradient characterization in the case of turbulent reactive flows.