Many fault detection filters have been developed to detect and identify sensor and actuator faults by using analytical redundancy. An approach to further reconstruct sensor and actuator faults from the residual generated by the fault detection filter is proposed. The transfer matrix from the faults to the residual is derived in terms of the eigenvalues of the fault detection filter associated with the detection spaces of the faults and the invariant zeros of the faults. For each fault, all possible fault reconstruction processes are derived and parameterized by applying a projector to the transfer matrix and taking inverse. Then, the optimal fault reconstruction process is determined by minimizing the ratio of the H 2 norm of the projected transfer matrix from the disturbance over the H 2 norm of the projected transfer matrix from the fault. For the existence of the fault reconstruction process, the invariant zeros of the fault have to be in the left-half plane. Furthermore, for reconstructing a sensor fault, the system has to be detectable with respect to the other sensors.