Even the simplest environmental stimuli elicit responses in large populations of neurons in early sensory cortical areas. How these distributed responses are read out by subsequent processing stages to mediate behavior remains unknown. Here we used voltage-sensitive dye imaging to measure directly population responses in the primary visual cortex (V1) of monkeys performing a demanding visual detection task. We then evaluated the ability of different decoding rules to detect the target from the measured neural responses. We found that small visual targets elicit widespread responses in V1, and that response variability at distant sites is highly correlated. These correlations render most previously proposed decoding rules inefficient relative to one that uses spatially antagonistic center-surround summation. This optimal decoder consistently outperformed the monkey in the detection task, demonstrating the sensitivity of our techniques. Overall, our results suggest an unexpected role for inhibitory mechanisms in efficient decoding of neural population responses.