Computed tomography (CT) is a popular type of medical imaging that generates images of the internal structure of an object based on projection scans of the object from several angles. There are numerous methods to reconstruct the original shape of the target object from scans, but they are still dependent on the number of angles and iterations. To overcome the drawbacks of iterative reconstruction approaches like the algebraic reconstruction technique (ART), while the recovery is slightly impacted from a random noise (small amount of ℓ2 norm error) and projection scans (small amount of ℓ1 norm error) as well, we propose a medical image reconstruction methodology using the properties of sparse coding. It is a very powerful matrix factorization method which each pixel point is represented as a linear combination of a small number of basis vectors.