Dual photography: https://www.youtube.com/watch?v=D4p4XUZYfp4 https://www.youtube.com/watch?v=mgJlwdTVGL0 On Thu, Mar 29, 2018 at 11:55 PM, Henry Baker <hbaker1@pipeline.com> wrote:
At 09:21 PM 3/29/2018, Keith F. Lynch wrote:
Henry Baker <hbaker1@pipeline.com> wrote:
There's also nothing special about using a *point* of light! One could illuminate the picture to be scanned with a long sequence of random 2D patterns of light, with the single-pixel sensor converting its *average* taken over the entire scene into a time-varying signal whose next value would be the *average over the entire scene* of the light pattern reflected from the next random pattern, and so on.
For greatest efficiency, the 2D patterns should be Costas arrays.
If I recall correctly, an image from a multiple-pinhole camera can be disambiguated only if the pinholes form a Costas array.
Actually, simple classical orthogonality works just fine.
If you have a rectangular array of pixels, the various arrays created by putting exactly one "1" into an array with all 0's, form a basis for the vector space. So a raster scan simply enumerates the basis vectors in a convenient ordering.
But there are lots of other bases, including those generated by the inverse Fourier transform of these raster scan bases.
So any set of patterns which are linearly independent can be utilized, hence the interest in random arrays, which are with very high probability independent.
You could do even better with Singular Value Decomposition of the image (as an approximation to the pixel array), but that would require a priori knowledge of the image(s) to be scanned.
BTW, standard MPEG encoding breaks an image into little 8x8 blocks, and MPEG approximates the DCT of these blocks, so if we were concerned only with an 8x8 image we could approximate it directly (and optically) by quickly running through ~64=8*8 special DCT-type patterns.
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