Coded Aperture (CA) imaging has recently been used in nuclear medicine, but still, there is no commercial SPECT imaging camera based on CA for cancer detection. The literature is rich in examples of using the CA for planar and thin 3D imaging. However, thick 3D reconstruction is still challenging for small lesion detection. This paper presents the results of mosaic modified uniformly redundant array (MURA) mask/antimask CA combined with a maximum-likelihood expectation-maximization (MLEM) algorithm. The MLEM is an iterative algorithm applied to a mosaic MURA CA mask/antimask for 3D anthropomorphic breast phantom reconstruction, slice by slice. The difference between the mask and the antimask suppresses the background noise to enhance the quality of reconstructed images. Furthermore, all reconstructed slices are stacked to form a 3D breast phantom image from single-projection data. The results of phantom reconstruction with 8 mm, 6 mm, 4 mm, and 3 mm lesions are presented. Moreover, the proposed SPECT imaging camera can reconstruct a 3D breast phantom from single-projection data of the patient’s scanning. To assess the quality of lesions in the reconstructed images, the contrast-to-background ratio (CBR), the peak signal-to-noise ratio (PSNR) and mean square error (MSE) were measured.