In recent years, the Discrete Tchebichef Transform (DTT) has gained popularity as a signal processing tool for image and video compression due to its efficient coding and decorrelation properties. However, in the context of real-time applications and embedded systems, it is critical to develop approximate algorithms with reduced complexity and energy consumption. While three DTT approximations have been proposed to date, there is still room for further improvements. To address this gap, we propose two new low-complexity DTT approximations that employ a modified deviation metric, resulting in better compression efficiency and reduced complexity. We validate our proposed methods by implementing them on the Xilinx Virtex-6 XC6VSX475T-1FF1759-2 Field Programmable Gate Array (FPGA) through rapid prototyping. Our proposed transformations exhibit superior performance in terms of hardware resources and energy consumption, particularly for 1D 8 inputs. Furthermore, compared to the state-of-the-art DTT approximations in image compression, our proposed transformations demonstrate a quality gain of up to 2 dB. Overall, our proposed approximations provide a promising trade-off between image quality, hardware resources, and energy consumption, making them ideal for real-time applications and embedded systems.