Thursday, July 14, 2011

Calibrating and Enhancing the Planar Fourier Capture Array ?

Laurent Duval sent me a link to the paper on the tiny camera we mentioned earlier, it's called the Planar Fourier Capture Array (PFCA). The article is: A Micro-Scale Camera Using Direct Fourier-Domain Scene Capture by  Patrick Gill, Changhyuk Lee, Dhon-Gue Lee, Albert Wang, and Alyosha Molnar. The abstract reads:
We demonstrate chip-scale (< 1 mm2) sensor, the Planar Fourier Capture Array (PFCA), capable of imaging the far field without any off-chip optics. The PFCA consists of an array of angle-sensitive pixels manufactured in a standard semiconductor process, each of which reports one component of a spatial 2D Fourier transform of the local light field. Thus, the sensor directly captures 2D Fourier transforms of scenes. The effective resolution of our prototype is approximately 400 pixels.

From the text of the paper:

To characterize the array, we presented a series of random calibration images to the sensor using a square CRT area 20 cm on a side, 22.86cm from the PFCA for an h of 31.7 at the square's corners.... We then use linear system identification tools [12] to reconstruct the kernel of each ASP (Fig. 6C). Afterwards, we presented various test images with an accumulation time of 15.7ms and  successfully reconstructed the images (Fig. 7B) up to the Nyquist Limit of our sensor, set by the highest-b design in our array....

Clearly, in light of what we now know about Compressive Sensing, some improvements could be entertained:

  • If I understand correctly, the colored tiles above show photodiodes with different spatial frequencies responses. The sampling is ordered so that the whole Fourier domain is covered up to the Nyquist limit. The use of Compressive Sensing could allow more of these pixels packed in the same space under the condition that the fewer pixels with a random set of frequencies were to be set on this plane. This could be done at the hardware level. In the meantime, however, given the data already gathered:
  • The calibration step could be improved as the transfer function for each pixel (ASP) is sparse in the Fourier domain. Sensing random patterns as trial function should yield good transfer functions using L_1 solvers.. 
  • Given the transfer functions of every ASP computed already, and as mentioned earlier, using an L_1 minimization solver could probably give a better looking Mona Lisa

Thanks Laurent, Dan and Alain for alerting me and pointing me to the paper.

No comments: