Sensitive and accurate detection of sulfur dioxide (SO2) from space is important for monitoring and estimating global sulfur emissions. Inspired by detection methods applied in the thermal infrared, we present here a new scheme to retrieve SO2 columns from satellite observations of ultraviolet back-scattered radiances. The retrieval is based on a measurement error covariance matrix to fully represent the SO2-free radiance variability, so that the SO2 slant column density is the only retrieved parameter of the algorithm. We demonstrate this approach, named COBRA, on measurements from the TROPOspheric Monitoring Instrument (TROPOMI) aboard the Sentinel-5 Precursor (S-5P) satellite. We show that the method reduces significantly both the noise and biases present in the current TROPOMI operational DOAS SO2 retrievals. The performance of this technique is also benchmarked against that of the principal component algorithm (PCA) approach. We find that the quality of the data is similar and even slightly better with the proposed COBRA approach. The ability of the algorithm to retrieve SO2 accurately is further supported by comparison with ground-based observations. We illustrate the great sensitivity of the method with a high-resolution global SO2 map, considering 2.5 years of TROPOMI data. In addition to the known sources, we detect many new SO2 emission hotspots worldwide. For the largest sources, we use the COBRA data to estimate SO2 emission rates. Results are comparable to other recently published TROPOMI-based SO2 emissions estimates, but the associated uncertainties are significantly lower than with the operational data. Next, for a limited number of weak sources, we demonstrate the potential of our data for quantifying SO2 emissions with a detection limit of about 8 kt yr−1, a factor of 4 better than the emissions derived from the Ozone Monitoring Instrument (OMI). We anticipate that the systematic use of our TROPOMI COBRA SO2 column data set at a global scale will allow missing sources to be identified and quantified and help improve SO2 emission inventories.