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 pseudo-random 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 ill-posed. The fluttering in the coded exposure camera makes the deconvolution well-posed.

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 Richardson-Lucy algorithm (Matlab implementation) which reduces noise but smooth out the image, reducing its sharpness.

Short Exposure Image

Blurred image using Traditional Camera

Blurred image using Coded Exposure Camera

Deblurred image by solving a linear system

Deblurred image by solving a linear system

Deblurred image using Richardson-Lucy

Ground truth static image of the scene

Output Noise Covariance Matrix

Output Noise Covariance Matrix

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 sub-diagonal entries, which results in its poor performance in terms of noise and artifacts. Using coded exposure, the off-diagonal 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.