Fig. 2.

Construction of the structured matrix lifting 𝒯 (f̂) considered in this work. From a rectangular array of the Fourier coefficients f̂ [k_x, k_y] of a continuous domain image f(x, y), the weighted arrays k_x f̂ [k_x, k_y] and k_y f̂ [k_x, k_y] are constructed. The matrices 𝒯_x(f̂) and 𝒯_y(f̂) are then obtained by extracting all vectorized patches from the weighted arrays, and loading these into the rows of 𝒯_x(f̂) and 𝒯_y(f̂). The resulting matrices 𝒯_x(f̂) and 𝒯_y(f̂) have a block Toeplitz with Toeplitz blocks structure. Finally 𝒯 (f̂) is formed by vertically concatenating the blocks 𝒯_x(f̂) and 𝒯_y(f̂).