Telehealth has shown potential to improve access to health-care cost-effectively in respiratory illness. However, it has failed to live up to expectation, in part because of poor objective measures of symptoms such as cough events, which could lead to early diagnosis or prevention. Considering the burden that these conditions constitute for national health systems, an effort is needed to foster telehealth potential by developing low cost technology for efficient monitoring and analysis of cough events. This paper, proposes the use of local Hu moments as a robust feature set for automatic cough detection in smartphone-acquired audio signals. The final system feeds a k-Nearest Neighbors classifier with the extracted features. To properly evaluate the system in a diversity of noisy backgrounds, we contaminated real cough audio data with a variety of sounds including noise from both indoor and outdoor environments, and non-cough events (sneeze, laugh, speech, etc.). The created database allows flexible settings of Signal to Noise Ratio (SNR) levels between background sounds and events (cough and non-cough). This evaluation was complemented using real patient data from an outpatient clinic. The system is able to detect cough events with high sensitivity (up to 88.51%) and specificity (up to 99.77%) in a variety of noisy environments, overcoming other state-of-the-art audio features. Our proposal paves the way for ubiquitous cough monitoring with minimal disruption in daily activities.