The size of the lens itself does not necessarily impact image quality. The main factor in image quality is sensor size, and the size of each pixel on the sensor.

“The larger the sensor, the larger your pixels, which means the camera captures more light, which means a clearer and better the image.”
https://www.camerahouse.com.au/blog/best-action-cameras-for-low-light/

“[In a bigger sensor there is a] lower pixel density … pixels have a larger area to occupy on an image sensor. What this means to us is that each pixel is able to capture more light information, meaning better color depth for precision of color captured, greater dynamic range or amount of light intensity, meaning better and more accurate definition in light and dark areas of an image, and a much cleaner image. When talking about low light performance in cameras, it is the sensor that makes good performance possible.
That extra light captured by pixels on an image sensor with more surface area translates to better performance in low light scenarios and less digital noise.”
https://www.videomaker.com/article/f6/17249-the-image-sensors-role-in-video

“1/2.3-inch … is the smallest sensor that’s commonly used in cameras today, and is typically found in budget compacts. They usually offer between 16-20MP… For general snapshots taken in good lighting conditions, cameras using these sensors may deliver perfectly acceptable results, but otherwise they can struggle to hold on to highlight detail and may produce images with a grainy, noisy texture.”
http://www.techradar.com/how-to/sensor-sizes-explained-what-you-need-to-know

The Hawkeye Firefly cameras and the Xiaomi Yi HD camera all use 1/2.3” CMOS sensors.