The gradient of standard full waveform inversion (FWI) attempts to map the residuals in the data to perturbations in the model. Such perturbations include smooth background updates from the transmission components and high wavenumber updates from the reflection components. A new optimization approach is used to update the background and perturbed velocity, simultaneously. We also use a more efficient scattering angle filter to enhance the large scattering angle for the background velocity update and enhance the small scattering angle for the perturbed velocity update. This efficient implementation of the filter is fast and requires less memory. Thus, the new FWI procedure updates mainly along the wave-path for both diving and reflected waves in the initial stages. At the same time, it updates the perturbation with mainly reflections (filtering the diving waves). An application to Marmousi model shows that this method converges starting with a linearly increasing velocity, and with data free of frequencies below 4 Hz.