We apply expectation‐conditional maximization either (ECME) hard thresholding algorithms to X‐ray computed tomography (CT) reconstruction, where we implement the sampling operator using the nonuniform fast Fourier transform (NUFFT). The measurements follow an underdetermined linear model, where the regression‐coefficient vector is a sum of an unknown deterministic sparse signal component and a zero‐mean white Gaussian component with an unknown variance. Our ECME schemes aim at maximizing this model’s likelihood function with respect to the sparse signal and variance of the random signal component. These schemes exploit signal sparsity in the discrete wavelet transform (DWT) domain and yield better reconstructions than the traditional filtered backprojection (FBP) approach, which is demonstrated via numerical examples. In contrast with FBP, our methods achieve artifact‐free reconstructions in undersampled and limited‐angle projection examples. We also compare the ECME schemes with a state‐of‐the‐art convex sparse signal reconstruction approach in terms of the reconstruction speed.