The most common cancer among women is breast cancer. The survival prognosis and rate of breast cancer differ considerably according to the stage of cancer. Treatment is more efficient if detected early because the progression to a higher stage can be avoided. Digital mammograms are used to identify breast cancer in the early stage. Low contrast mammogram images are usually affected by Poisson noise. In the present work, an improved L₀ gradient minimization smoothing method is proposed. Experiments performed on the DDSM (Digital Database for Screening Mammography) images show that the proposed method is better in sharpening major edges. Further the performance metrics such as peak signal to noise ratio (PSNR), mean square error (MSE) and structural similarity index measure (SSIM) values show that proposed method provides better performance as compared with different existing methods.