Comparison of Short Exposure, Traditional
Camera and Coded Exposure Camera
Figures
in the top row shows the timing diagram for a short exposure,
traditional camera and coded exposure camera. In a traditional camera,
the shutter is open for the entire duration of time. In a coded
exposure camera, the shutter is fluttered
open and close according to a binary pseudorandom sequence within a single exposure time. The
sequence is chosen so that the resulting motion blur PSF has a flat
frequency spectrum and maximizes the minimum of the DFT magnitudes. For
a traditional camera, the PSF corresponds to a box filter which has
zeros in the frequency spectrum, making the inverse filtering
illposed. The fluttering in the coded exposure camera makes the
deconvolution wellposed.
In a traditional camera, motion
blurring results in a continuous smear as compared to replicas in a
coded exposure camera. The high spatial frequencies are preserved in
coded exposure. Deconvolution by solving a simple linear system gives
the output image free of any ringing and deconvolution artifacts.
Compare it with the ground truth static image of the object captured
separately. In contrast, traditional deblurring results in large noise
and banding artifacts. We also show the result using RichardsonLucy
algorithm (Matlab implementation) which reduces noise but smooth out
the image, reducing its sharpness.

Figures in the last row show
the covariance matrix of the noise in the deblurred image
assuming Gaussian noise in the input for traditional and coded exposure
camera. These matrices are for a representative case of an object 300
pixels wide moving horizontally and getting blurred by 52 pixels.
If the motion blur system is written as a linear system Ax=b, the
covariance matrix is proportional to inv(A'*A).
Notice the bar on the side which shows the range of values. The covariance matrix for flat blur has large diagonal and subdiagonal entries, which results in its poor performance in terms of noise and artifacts. Using coded exposure, the offdiagonal entires are significantly reduced in the covariance matrix. The largest value for traditional camera is 9270.9 corresponding to noise amplification of 39.67 dB. For coded exposure, the largest value is 77.6 corresponding to noise amplification of only 18.9 dB. 