The production of high-quality electron bunches in laser wakefield acceleration relies on the possibility of injecting ultra-low emittance bunches in the plasma wave. A new bunch injection scheme (resonant multi-pulse ionization, ReMPI) has been conceived and studied, in which electrons extracted by ionization are trapped by a large-amplitude plasma wave driven by a train of resonant ultrashort pulses. Such a train of pulses can be obtained in a very efficient, compact and stable way, by phase manipulation in the laser front-end. The ReMPI injection scheme relies on currently available laser technology and is being considered for the implementation of future compact x-ray free electron laser schemes. Simulations show that high-quality electron bunches with an energy of up to 5 GeV and a peak current exceeding 2 kA, with normalized emittance of below 0.1 mm × mrad and a slice energy spread of below 0.1%, can be obtained with a single stage.