Deep Learning is a Machine Learning technique that is a more complex (deeper) version of the Neural Networks that were developed in the 80ies. As for all Machine Learning algorithms, the idea is to learn a function that links an input variable x to an output variable y from annotated samples, called the training set.
In image analysis, we usually use a particular class of neural networks, called « Convolutional Neural Networks » that take images as input variable. These networks consist in a large number of image convolutions (with variable parameters) and non-linearities that transform the image in many ways and learn all the parameters from the training set. The number of parameters is typically very large (in the millions).
Neural networks can be used for image classification (in this case x is an image and y is a class label), for segmentation (in this case x is an image and y a binary image) or image reconstruction/prediction. They usually require a large number of annotated data and the large number of parameters makes them tricky to train. This has – for a long time – been seen as an obstacle in the bioimaging field, where annotated image data tend to be scarce. However, they are considered to be the most powerful methods for classification of image data today.