High-resolution Electrocorticography (HR-ECoG) has emerged as a key strategic technology for recording localized neural activity with high temporal and spatial resolution with potential applications in brain-computer interfaces (BCI), and seizure detection for epilepsy. However, HR-ECoG has 400 times the resolution of conventional ECoG, making it a challenge to process, transmit and store the HR-ECoG data. Therefore, simple and efficient compression algorithms are vital for the feasibility of implantable wireless medical devices for HR-ECoG recordings. In this paper, following the observation that HR-ECoG signals have both high spatial and temporal correlations similar to video/image signals, various compression methods suitable for video/image- compression based on motion estimation, discrete cosine transform (DCT) and discrete wavelet transform (DWT)- are investigated for compressing HR-ECoG data. We first simplify these methods to satisfy the low-power requirements for implantable devices. Then, we demonstrate that spatiotemporal compression methods produce up to 46% more data reduction on HR-ECoG data than compression methods using only spatial compression do. We further show that this data reduction can be achieved with low hardware complexity. In particular, among the methods investigated, spatiotemporal compression using DCT-based methods provide the best trade-off between hardware complexity and compression performance, and thus we conclude that DCT-based compression is a promising solution for ultralow-power implantable devices for HR-ECoG.