Quantitative sodium MRI is a unique tool for assessing tissue viability noninvasively. A major obstacle to widespread clinical applications of sodium MRI is low sensitivity, which leads to low spatial resolution even with long scan times. We present a novel method for reconstruction of high-resolution sodium maps from noisy, limited k-space data. The proposed method has been validated using simulated and experimental data, producing high-SNR and high-resolution tissue sodium concentration maps. These high-resolution maps were also shown to improve the detection of tumor responses to radiation therapy.