Quantum State Tomography (QST) is a fundamental tool for quantum signal processing. However, in real noisy quantum devices construction of the state's density matrix via QST can utilize a large amount of resources. Here, we discuss some signal processing techniques that are currently applied to this resource issue, and implement on current quantum chips a modification that can assist in reducing resources. An application of QST to quantum entanglement distillation is provided for further insight.