Wavelet transform: How to compute the initial coefficients when only samples are available?
I remember that using the discrete samples was termed  "wavelet crime" by Gilbert Strang (Strang and Nguyen, Wavelets and Filter banks, 1996, pages 232 sq.), or "wavelet sin" by others. 

On prefiltering discrete signals to obtain "better" wavelet coefficients, here are some references I have in store:


Wavelet coefficient computation with optimal prefiltering, IEEE Trans. Signal Processing, 1994, Xia, X.-G. and Kuo, C.-C.J. and Zhang, Z.
On the initialization of the discrete wavelet transform algorithm, IEEE Signal Processing Letters, 1994, Abry and Flandrin
From the wavelet series to the discrete wavelet transform - the initialization, IEEE Trans. Signal Processing, 1996, Xiao-Ping Zhang and Li-Sheng Tian and Ying-Ning Peng
Sard-optimal prefilters for the fast wavelet transform, Numer. Algorithms, 1997, S. Ehrich
A new prefilter design for discrete multiwavelet transforms, IEEE Trans. Signal Processing, 1998, Xia, X.-G.
Quadrature prefilters for the discrete wavelet transform, IEEE Trans. Signal Processing, 2000, Johnson, B. R. and Kinsey, J. L.
Meaningful MRA initialization for discrete time series, Signal Processing, 2000, D. Veitch and M. S. Taqqu and P. Abry
Efficient Wavelet Prefilters with Optimal Time-Shifts, IEEE Trans. Signal Processing, 2003, Ericsson, S. and Grip, N.


It seems however that no prefiltering does not induce too much errors for compression, denoising, deconvolution. But for detection, or using multiple  different  wavelets at once (like with dual-tree wavelets, or unions of wavelet bases), or with multiwavelets, it is quite mandatory.