  In this article, we develop a general method for constructing wavelets {|det
A_j|^{1/2} g(A_jx-x_{j,k}): j in J, k in K}, on irregular lattices of the form
X={x_{j,k} in R^d: j in J, k in K}, and with an arbitrary countable family of
invertible dxd matrices {A_j in GL_d(R): j in J} that do not necessarily have a
group structure. This wavelet construction is a particular case of general
atomic frame decompositions of L^2(R^d) developed in this article, that allow
other time frequency decompositions such as non-harmonic Gabor frames with
non-uniform covering of the Euclidean space R^d. Possible applications include
image and video compression, speech coding, image and digital data
transmission, image analysis, estimations and detection, and seismology.
