A method of encoding a digital media image, the method comprising: tiling the image into blocks; applying a reversible overlap operator across at least some of the boundaries between the blocks, the reversible overlap operator being unit determinant; and applying a reversible block transform to the blocks, wherein the applying the reversible overlap operator comprises applying a reversible Hadamard network, applying a reversible block rotation, applying a reversible scaling operator, applying another reversible block rotation, and applying a reversible inverse Hadamard network; wherein the reversible overlap operator is created from orthogonal matrices U1, U2, V1 and V2 that correspond to a linear phase filter structure, wherein the component corresponding to U2 receives inputs s_i from U1, component corresponding to V2 receives inputs s_j from V1, and component V1 receives the negated inputs of U1, wherein creating the reversible overlap operator includes providing a decomposed filter F, F = I J J 2 − I 2 U 1 0 0 V 1 s 1 s 2 ⋱ s M U 2 0 0 V 2 I 2 J J 2 − I J = 0 0 1 0 1 0 0 ⋰ 1 0 0; where I is the identity matrix, and further includes deriving lossless realizations for U1, U2, V1 and V2 and deriving a lossless realization for the inputs matrix; wherein deriving lossless realizations for U1, U2, V1 and V2 includes making stages in the matrices unit determinant based on a factor of 0.5; wherein deriving a lossless realization of the component matrices is based on lifting steps; and wherein deriving the lossless realization of the inputs matrix comprises realizing the matrix in a plurality of lifting steps, wherein the inputs matrix is reformulated to comprise a shear matrix, wherein scaling factors in the inputs matrix are distributed to lifting steps of the shear matrix, wherein the last lifting step of the first matrix is combined with the first shear lifting step and the first lifting step of the last matrix is combined with the first shear lifting step, and wherein inverse operations are canceled from the resulting expression. tiling the image into blocks; applying a reversible overlap operator across at least some of the boundaries between the blocks, the reversible overlap operator being unit determinant; and applying a reversible block transform to the blocks, wherein the applying the reversible overlap operator comprises applying a reversible Hadamard network, applying a reversible block rotation, applying a reversible scaling operator, applying another reversible block rotation, and applying a reversible inverse Hadamard network; wherein the reversible overlap operator is created from orthogonal matrices U1, U2, V1 and V2 that correspond to a linear phase filter structure, wherein the component corresponding to U2 receives inputs s_i from U1, component corresponding to V2 receives inputs s_j from V1, and component V1 receives the negated inputs of U1, wherein creating the reversible overlap operator includes providing a decomposed filter F, F = I J J 2 − I 2 U 1 0 0 V 1 s 1 s 2 ⋱ s M U 2 0 0 V 2 I 2 J J 2 − I J = 0 0 1 0 1 0 0 ⋰ 1 0 0; where I is the identity matrix, and further includes deriving lossless realizations for U1, U2, V1 and V2 and deriving a lossless realization for the inputs matrix; wherein deriving lossless realizations for U1, U2, V1 and V2 includes making stages in the matrices unit determinant based on a factor of 0.5; wherein deriving a lossless realization of the component matrices is based on lifting steps; and wherein deriving the lossless realization of the inputs matrix comprises realizing the matrix in a plurality of lifting steps, wherein the inputs matrix is reformulated to comprise a shear matrix, wherein scaling factors in the inputs matrix are distributed to lifting steps of the shear matrix, wherein the last lifting step of the first matrix is combined with the first shear lifting step and the first lifting step of the last matrix is combined with the first shear lifting step, and wherein inverse operations are canceled from the resulting expression.