In this thesis, we investigate a sparse basis for ultrasound images, so that we can use sparse regularization in imaging. Actually, there are few previous researches explicitly demonstrating that medical ultrasound images can be sparsified for some dictionary. We consider various orthogonal transforms such as wavelet transforms, cosine transforms and wave atom transforms. Then, we perform those transforms on various ultrasound images and analyzes their sparsity. These ultrasound images include the images of two computer ultrasound phantoms and beamformed ultrasound images with good quality from real people. We looked at sparsity of the true pre-beamformed images, as well as beamformed images. We also consider constructing a specific ultrasound image dictionary using the K-SVD algorithm. We observed that, the pre-beamformed images hardly haVe no sparse basis, and the sparsity of beamformed images will only increase slightly if we use different 1D-DWT in each direction. We also found that the wide overdetermined dictionary generated by K-SVD significantly increases sparsity. After this, we simulate the ultrasound image reconstruction from the ultrasound RF measurements, and we analyze the effects of the different sparse spaces on the reconstruction performance. We observed that, the L1-regularization can work for ultrasound imaging better than L2-regularization, but the orthogonal transforms as well as the dictionary do not improve the reconstruction image quality much.