As I was reading the following comment extracted from the NPR blog entry on Compressive Sensing I could not help but think how some highly paid technicians can make themselves so pompous just because what they are doing is important, not because they have a deeper understanding of how things work. That is probably the reason TV series like House are having so much success: we collectively crave for the intelligent bastard to get the right diagnostic...at least once, even if it is in the alternate reality of TV. The comment reads:
I am a Pediatric ICU MD. Lets say that I am caring your your child, Ms. Norris, and I feel she is improved but would like an MRI to be certain all is well. I offer you 2 choices for this test for your little darling. 1. A shorter MRI in which much of the image is a "guess" (the word used in the story) or 2. A longer test in which the image is actually that of your child. Which would you choose?
I think this is why it is important to define "guess" and why we collectively need to make a more obvious difference between Compressive Sensing reconstructions and inpainting: In the first type of reconstruction, acquisition is performed in a manner were incoherence is key ( for MRI, sampling is performed in the Fourier space while imaging natural scenes that are sparse in wavelet/curvelets .., for audio, sampling is performed in the real space while the signal is sparse in the Fourier space) whereas in the second reconstruction, one is indeed guessing some elements that have been missing in the coherent acquisition. In the second reconstruction case, the statement of the commenter is indeed worthy of concern and has been the subject of a previous entry. However, in the case of MRI the former applies. Going back to the comment, I could not but remember this Alec Baldwin's jaw breaking monologue featured below. I am using the words jaw breaking because when you watch the movie for the first time, the tirade is totally unexpected, a little bit like when you have lived your whole life thinking Nyquist was the only game in town and compressive sensing barges in .
Similarly, would CT specialists also have the same reaction if one were to mention to them that the Fast Back Projection algorithm is not optimal (see Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?) ? I am thinking yes but that's just me.
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