Unitary matrix for image processing

Question

Why usually consider unitary matrices to define image transforms?

Answer 1

1. We can transform back and forth without any matrix inversion, since for any unitary matrix A, $A^{-1}=A^*$ where * is the conjugate transpose.

2. Unitary matrices represent an orthogonal basis, which is useful in image processing.

Answer 2

Because, on a inner product space (i.e. Euclidean space, or Hilbert space in more generality) unitaries are precisely the linear isometric bijections. You want a bijection if you want not to lose information, and you want isometric if you want the distances in your image to be preserved. The linearity, together with the isometry, imply that orthogonality is preserved.