In this paper, we develop an efficient bit allocation strategy for subband-based image coding systems. More specifically, our objective is to design a new optimization algorithm based on a rate-distortion optimality criterion. To this end, we consider the uniform scalar quantization of a class of mixed distributed sources following a Bernoulli-Generalized Gaussian distribution. This model appears to be particularly well-adapted for image data which have a sparse representation in a wavelet basis. In this context, we propose new approximations of the entropy and the distortion functions by using piecewise affine and exponential forms, respectively. Thanks to these approximations, we reformulate the bit allocation problem as a convex optimization one. Solving the resulting problem allows us to derive the optimal quantization step for each subband. Experimental results show the benefits that can be drawn from the proposed bit allocation method in a typical transform-based coding application.