In common radiography, image contrast is often limited due mainly to scattered x-rays and noise, decreasing the quantitative usefulness of x-ray images. Several scatter reduction methods based on software correction schemes have been extensively investigated in an attempt to overcome these difficulties, most of which are based on measurement, mathematical-physical modeling, or a combination of both. However, those methods require special equipment, system geometry, and extra manual work to measure scatter characteristics. In this study, we investigated a new software scheme for scatter correction based on a simple radiographic scattering model where the intensity of the scattered x-rays was directly estimated from a single x-ray image using a weighted l-norm contextual regularization framework. We implemented the proposed algorithm and performed a systematic simulation and experiment to demonstrate its viability. We also conducted some clinical image studies using patient's image data of breast and L-spine to verify the clinical effectiveness of the proposed scheme. Our results indicate that the degradation of image characteristics by scattered x-rays and noise was effectively recovered by using the proposed software scheme, thus improving radiographic visibility considerably. Graphical abstract The schematic illustrations of scatter suppression methods by using a an antiscatter grid and b a scatter estimation algorithm.