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[D] Conditions for a convolution to be bijective?

Setting: I have a convolution of Image I and kernel w, J=conv2D(I,w). I is an image I of size nxn with c channels, while w is a cxcx3x3 matrix, therefore we have c 3×3 filters that can be applied to the image. We use zero-padding so that J has the same dimensionality of I.

What properties does w have to fulfill for the convolution to be invertible? It is clear that at least one such w exists, because 1×1 convolutions are a subset of 3×3 convolutions and since we have c filters, we can encode the identity, which is invertible. It is not enough for the filters to be independent, because as the input has 9c dimensions, we can still loose information.

submitted by /u/Ulfgardleo
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Toronto AI is a social and collaborative hub to unite AI innovators of Toronto and surrounding areas. We explore AI technologies in digital art and music, healthcare, marketing, fintech, vr, robotics and more. Toronto AI was founded by Dave MacDonald and Patrick O'Mara.