Breast ultrasound is gaining interest as an alternative to mammography. To improve its diagnostic value, full waveform inversion methods are developed. These methods aim for reconstructing speed of sound maps of the breast. When the inversion is performed in the frequency domain, computation time is reduced by limiting the number of frequency components at the cost of retrieving noisy images. To compensate for the lack of frequency information and to reduce the noise in the reconstruction, we propose two solutions. First, we select the frequency components randomly out of the entire available bandwidth for each source-receiver combination separately. Next, a regularization method is applied that takes advantage of the sparseness of the reconstructed contrast in the wavelet domain.