Classical beamforming methods, based on Delay- And-Sum (DAS) require an extensive number of samples and delay calculations to obtain high-quality images. Compressed Beamforming (CB) proposes an alternative to DAS, based on compressed sensing, which aims at reducing the data rate. However, proposed CB approaches induce a computationally heavy measurement model that hampers their attractiveness for iterative image reconstruction. In this paper, a CB framework, applicable to either radio-frequency or in-phase quadrature data and for both plane wave and diverging wave compounding, is described. The proposed framework exploits a computationally light measurement model which leads to tractable reconstruction. It solves a convex problem and assumes sparsity in a waveletbased model to achieve high-quality image reconstruction from measurements acquired with only few transducer elements.