The tunable Q-factor wavelet transform (TQWT) is a fully-discrete wavelet transform for which the Q-factor,
Q, of the underlying wavelet and the asymptotic redundancy (over-sampling rate), r, of the transform are easily
and independently specified. In particular, the specified parameters Q and r can be real-valued. Therefore,
by tuning Q, the oscillatory behavior of the wavelet can be chosen to match the oscillatory behavior of the
signal of interest, so as to enhance the sparsity of a sparse signal representation. The TQWT is well suited
to fast algorithms for sparsity-based inverse problems because it is a Parseval frame, easily invertible, and can
be efficiently implemented using radix-2 FFTs. The TQWT can also be used as an easily-invertible discrete
approximation of the continuous wavelet transform.