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A convolutional neural network is a type of neural network commonly used for image processing, i.e., image recognition. Its general strategy regarding image-handling is inspired by processing of visual information within the brain and is currently a successful strategy in developing software with such capabilities regarding images.
A neural network is a type of artificial intelligence (AI) program modeled after the apparent microstructure of brain matter: a network consisting of links transferring data between nodes (termed neurons, both in the brain and in such software), the nodes processing/combining the data and passing it on through other such links to other nodes.
A convolutional neural network uses a particular kind of processing within the neurons, and uses particular types of patterns regarding exactly which neurons are linked together. Its specific techniques have worked well with the massive amount of interrelated processing necessary to extract recognizable concepts from the massive amount of data in an image (e.g., many thousand pixels). These particular convolution techniques were inspired by what has been discovered regarding the brain's vision processing.