FAMILIES OF ORTHOGONAL 2-DIMENSIONAL WAVELETS

We construct orthonormal wavelet bases of L(2)(R(2)) with compact supp ort for dilation matrices of determinant 2. The key idea is to describ e the set H-2 of all two-dimensional (2D) scaling coefficients satisfy ing the orthogonality condition as an implicit function. This set incl udes the scaling coefficients for induced 1D wavelets. We compute the tangent space of H-2 at H-N, the scaling coefficients for induced 1D D aubechies wavelets. The structure of the tangent space allows us to bu ild nonseparable wavelets by starting at H-N and tracing H along its t angent lines. Various families of compactly supported orthogonal 2D wa velets for the quincunx grid are explicitly given.