Context. High-contrast imaging at optical wavelengths is limited by the modest correction of conventional near-IR optimized AO systems. We take advantage of new fast and low-readout-noise detectors to explore the potential of fast imaging coupled to post-processing techniques to detect faint companions of stars at small angular separations. Aims: We have focused on I-band direct imaging of the previously detected brown dwarf binary HD 130948 BC, attempting to spatially resolve the L2+L2 system considered as a benchmark for the determination of substellar objects dynamical masses. Methods: We used the lucky-imaging instrument FastCam at the 2.5-m Nordic Telescope to obtain quasi diffraction-limited images of HD 130948 with ~0.1" resolution. In order to improve the detectability of the faint binary in the vicinity of a bright (I = 5.19 ± 0.03) solar-type star, we implemented a post-processing technique based on wavelet transform filtering of the image, which allows us to strongly enhance the presence of point-like sources in regions where the primary halo generally dominates. Results: We detect for the first time the binary brown dwarf HD 130948 BC in the optical band I with a SNR ~ 9 at 2.561" ± 0.007" (46.5 AU) from HD 130948 A and confirm in two independent datasets (2008 May 29 and July 25) that the object is real, as opposed to time-varying residual speckles. We do not resolve the binary, which can be explained by astrometric results posterior to our observations, which predict a separation below the telescope resolution. We reach a contrast of ΔI = 11.30 ± 0.11 at this distance, and estimate a combined magnitude for this binary I = 16.49 ± 0.11 and a I - J color of 3.29 ± 0.13. At 1", we reach a detectability 10.5 mag fainter than the primary after image post-processing. Conclusions: We obtain on-sky validation of a technique based on speckle imaging and wavelet-transform post-processing, which improves the high-contrast capabilities of speckle imaging. The I - J color measured for the BD companion is slightly bluer, but still consistent with what is typically found for L2 dwarfs (~3.4-3.6).