In that example he's not blurring in the usual sense, he's replacing the whole image by a single average value.
Blurring is mathematically a convolutions product of an image that can be represented as a function f and a kernel g. The key fact is that the Fourier transform of f.g is the product of the Fourier transforms of f and g. So if you know g, or can guess what it is, you can solve for f knowing f.g and g, since everything is linear. (Some blurs might not be linear transforms but the usual gaussian blur is)
Information can be lost in two ways : 1/ quantization of the data due to storage in a limited number of bits, 2/ truncation of the blur at the image edges. So blurs cannot be fully reversed, but some information can be recovered. That might be enough to identify the information that was concealed in the first place. See the Wikipedia article on deconvolution for examples.
Blurring is mathematically a convolutions product of an image that can be represented as a function f and a kernel g. The key fact is that the Fourier transform of f.g is the product of the Fourier transforms of f and g. So if you know g, or can guess what it is, you can solve for f knowing f.g and g, since everything is linear. (Some blurs might not be linear transforms but the usual gaussian blur is)
Information can be lost in two ways : 1/ quantization of the data due to storage in a limited number of bits, 2/ truncation of the blur at the image edges. So blurs cannot be fully reversed, but some information can be recovered. That might be enough to identify the information that was concealed in the first place. See the Wikipedia article on deconvolution for examples.