In this paper, a missing image data reconstruction method based on an adaptive inverse projection via sparse representation is proposed. The proposed method utilizes sparse representation for obtaining low-dimensional subspaces that approximate target textures including missing areas. Then, by using the obtained low-dimensional subspaces, inverse projection for reconstructing missing areas can be derived to solve the problem of not being able to directly estimate missing intensities. Furthermore, in this approach, the proposed method monitors errors caused by the derived inverse projection, and the low-dimensional subspaces optimal for target textures are adaptively selected. Therefore, we can apply adaptive inverse projection via sparse representation to target missing textures, i.e., their adaptive reconstruction becomes feasible. The proposed method also introduces some schemes for color processing into the calculation of subspaces on the basis of sparse representation and attempts to avoid spurious color caused in the reconstruction results. Consequently, successful reconstruction of missing areas by the proposed method can be expected. Experimental results show impressive improvement of our reconstruction method over previously reported reconstruction methods.