Reversible data hiding (RDH) based on prediction error expansion (PEE) needs a reliable predictor to forecast the pixel. The hidden information is inserted into the original cover image pixels using the Prediction Error (PE). To improve the accuracy of pixel predictions for cover images, there are a number of algorithms available in the literature. Based on the different gradient estimations, several academics have suggested prediction methods. More research on this gradient-based pixel prediction method is presented in this article. In order to improve exploration gradient estimates, we have looked at a number of local contexts surrounding the current pixel. It has been stated that experiments have been conducted to evaluate the effect of different neighborhood sizes on gradient estimation. Additionally, we investigate two methods for choosing paths according to gradient magnitudes. To incorporate the data into the initial pixels, a new embedding technique called Prediction Error Expansion has been suggested. In the context of reversible data concealment, experimental results point towards a better gradient based prediction employing an prediction embedding technique.