In cardiac diffusion tensor magnetic resonance imaging (DT-MRI), low signal-to-noise ratio (SNR) inherently hampers the measurement accuracy of myocardium fiber structures. This paper presents a new method for filtering diffusion weighted (DW) images in cardiac DT-MRI. The method is based on sparse representation through using basis pursuit denoising (BPDN) algorithm allowing seeking overall sparest solution. It decomposes useful structures in DW images into sparsely representing atoms with Heaviside dictionary, while yielding nonsparse representation on noise, which leads to the separation of the noise from the image's useful structures. The proposed method is evaluated on both simulated and real cardiac DW images.