I am familiar with much of the mathematical background behind wavelets. However when implementing algorithms on a computer with wavelets I am less certain about whether I should be using continuous or discrete wavelets. In all reality everything on a computer is discrete of course, so it seems obvious that discrete wavelets are the right choice for digital signal processing. However according to wikipedia it is the continuous wavelet transform that is primarily used in (digital) image compression as well as a large number of other digital data processing activities. What are the pros and cons to consider when deciding whether to use an (approximate) continuous wavelet transform instead of an (exact) discrete wavelet transform for digital image or signal processing?
P.S. (Checking an assumption here) I am assuming continuous wavelet transforms are used in digital processing by simply taking the value of the continuous wavelet at evenly spaced points and using the resulting sequence for wavelet computations. Is this correct?
P.P.S. Usually wikipedia is pretty precise about mathematics, so I am assuming that the applications in the article on Continuous Wavelet Transforms are in fact applications of the Continuous Wavelet Transform. Certainly it mentions some that are specifically CWT so there is clearly some use of CWT in digital applications.