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In this work, we introduce a new approach for medical image denoising. An innovative method is proposed to extend the concept of low-pass filtering to the sparse representation framework. A weight matrix is applied to the definition of the sparse coding optimization problem intended to reduce coefficients corresponding to atoms with higher frequency contents, which dominantly represent the image noise. In parallel, a new overcomplete Discrete Cosine Transform (DCT) dictionary is constructed to include both frequency and phase information, aiming to remove blocking artifacts without considering patch-overlap. The proposed denoising approach was applied on low-dose Computed Tomography (CT) phantoms. The resultant observations demonstrate qualitative and quantitative improvements, in terms of peak signal to noise ratio (PSNR), in comparison to some previous approaches.