As a sparse signal recovery algorithm, compressed sensing is particularly useful when the data has low-complexity and samples are rare, which matches perfectly with the task of quantum phase estimation (QPE). In this talk I will present a new Heisenberg-limited QPE algorithm for early fault-tolerant quantum computers based on compressed sensing. More specifically, given many copies of a proper initial state and queries to a specific unitary matrix, our algorithm is able to recover the phase with a total runtime $\mathcal{O}(\epsilon^{-1}\text{poly}\log (\epsilon^{-1}))$, where $\epsilon$ is the desired accuracy. Moreover, the maximal runtime satisfies $T_{\max}\epsilon \ll \pi$, which is comparable to the state-of-the-art algorithms, and our algorithm is also robust against certain amount of noise from sampling and state preparation. [\url{arXiv:2306.07008}]