X-ray computed tomography reconstruction has evolved over 40 years for medical, security, and industrial applications. Compared to traditional analytic reconstruction techniques such as filtered back projection (FBP), statistical reconstruction algorithms like alternating minimization (AM) provide improved image quality and can incorporate prior information. Increasing patient safety through reduced radiation dose results in fewer measured photons. Penalized AM is a powerful tool for maintaining image quality with less data, but the weight of penalty must be chosen carefully. If the penalty weight is too low, noise may not be suppressed and artifacts may be exhibited, such as those due to sharp discontinuities in attenuation at edges of dense material. If the penalty weight is higher, noise and artifacts may be reduced, but at the expense of introducing bias into the reconstruction. These contradicting requirements for the weight of the penalty limit our ability to improve reconstructed image quality in a low dose scenario. In this paper, we develop a new algorithm called wavelet regularized alternating minimization (wav-AM) by introducing a second penalty term on wavelet coefficients. By solving this dual domain optimization problem, we are able to perform 3D reconstruction of scanned baggage with low X-ray photon intensity. A medical imaging application of the wav-AM algorithm will be provided to illustrate the performance in image quality improvement. Evaluation of these real data reconstructions show reduced noise and artifacts without biasing the estimated attenuation of objects of known attenuation. The wav-AM algorithm features guaranteed convergence and increases the computational burden compared to the usual penalized AM algorithm only negligibly, even though we are solving a dual domain optimization problem.