Total variation (TV) methods have been proposed to improve the image quality in count-reduced images, by reducing the variation between neighboring pixels. Although very easy to implement and fast to compute, TV-based methods may lead to a loss of texture information when applied to images with complex textures, such as high-resolution abdominal CT images. Here, we investigate the use of another regularization approach in the context of medical images based on multiresolution transformations. One such transformation is the shearlet transform, which is optimally sparse for images that are C2 except for discontinuities along C2 curves, and has better directional sensitivity than most other, related, wavelet transform approaches. We propose to solve the convex problem using the split-Bregman (augmented Lagrangian) approach. One of the primary advantages of the split-Bregman approach, is that the shearlet transform can easily be incorporated into the sparse-view CT reconstruction. The required sparsity prior is the l1 norm of the shearlet coefficients. Results are shown for this method in comparison to the same framework with TV as the regularization term on simulated data. The noise-resolution performance is investigated at different contrast levels. At equal image noise, TV-based regularization outperforms shearlet-based regularization. However, when image texture is analyzed on measured mouse data, shearlets outperform TV, which suffers from staircasing effects. Our results show that there are benefits in using shearlets in CT imaging: texture is reconstructed more accurately compared to when TV is used, without biasing the image towards a piecewise constant image model. However, due to the larger support of the basis functions, our results suggest that uncareful usage of shearlets may lead to wavy artifacts, which can be equally unwanted as staircasing effects.