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A deep learning framework is presented that transforms the task of MR image reconstruction from randomly undersampled k-space data into pixel classification. A DL network was trained to remove incoherent undersampling artifacts from MR images. The underlying, fully sampled, target image was represented as a discrete quantized image. The quantization step enables the design of a convolutional neural network (CNN) that can classify each pixel in the input image to a discrete quantized level. The reconstructed image quality of the proposed DL classification model was compared with conventional compressed sensing (CS) and a DL regression model. The reconstructed images using the DL classification model outperformed the state-of-the-art compressed sensing and DL regression models with a similar number of parameters assessed using quantitative measures. The experiments reveal that the proposed deep learning method is robust to noise and is able to reconstruct high-quality images in low SNR scenarios where conventional CS reconstructions and DL regression networks perform poorly. A generic design framework for transforming MR image reconstruction into pixel classification is developed. The proposed method can be easily incorporated into other DL-based image reconstruction methods.