Digital breast tomosynthesis is a promising modality providing 3D cross sectional images of breast. However, reconstructing the image from few projections is still a challenging task. We introduce an anisotropic total variation regularized reconstruction method which exploits varying resolution along transverse and sagittal planes by adapting the weights of TV gradients. Moreover, we also investigate if non-convex ℓp quasinorm with p ∈ (0,1) can help to improve the performance of anisotropic TV in detecting micro calcifications and spheroidal masses. The contrast to noise ratio (CNR) for in-plane quality, full with at half maximum (FWHM) of artefact spread function (ASF) for resolution in the z-axis, signal difference to noise ratio (SdNR), and quality factor (QF) for a comprehensive evaluation were used in quantitative analyses and comparisons. For low contrast analysis, QF value of the proposed method for p = 0.9 is 0.18 whereas QF value of isotropic TV with ℓ1 and ℓ2 norms are 0.15 and 0.14, respectively. For high contrast features such as micro-calcifications, although the best CNR value changes with different p values, the majority of the best CNR values are calculated for values 0.8 and 0.9. Overall, the results show that the proposed method, anisotropic TV with non-convex ℓp quasinorm, outperforms isotropic TV with ℓ1 and ℓ2 norms by recovering small micro calcifications and spheroidal masses with higher CNR and increased depth resolution. The proposed method shows the best performance for p values of 0.8 ≤ p < 1.