According to one embodiment, an image processing apparatus includes first and second computation portions, a selection portion, a projection portion, and a weighted averaging portion. The first computation portion is configured to obtain magnitudes of correlations between a first vector and plural basis vectors. The selection portion is configured to select basis vectors from the plural basis vectors. The projection portion is configured to select a second region, obtain a first projection vector by projecting the first vector onto a subspace formed by the selected basis vectors and obtain a second projection vector for each second region by projecting a second vector onto the subspace. The second computation portion is configured to compute a distance between the first and second projection vectors. The weighted averaging portion is configured to weighted average a pixel value of the second pixel to obtain an output pixel value of a first pixel.