#### Optimal Coded Sampling for Temporal Super-Resolution

Proc. CVPR 2010

We propose coded sampling that address these issues: using N cameras it allows N times temporal super-resolution while allowing N/2 times more light compared to an equivalent high speed camera.

Conventional low frame rate cameras result in blur and/or aliasing in images while capturing fast dynamic events. Multiple low speed cameras have been used previously with staggered sampling to increase the temporal resolution. However, previous approaches are inefficient: they either use small integration time for each camera which does not provide light benefit, or use large integration time in a way that requires solving a big ill-posed linear system. We propose coded sampling that address these issues: using N cameras it allows N times temporal super-resolution while allowing N/2 times more light compared to an equivalent high speed camera. In addition, it results in a well-posed linear system which can be solved independently for each frame, avoiding reconstruction artifacts and significantly reducing the computational time and memory. Our proposed sampling uses optimal multiplexing code considering additive Gaussian noise to achieve the maximum possible SNR in the recovered video. We show how to implement coded sampling on off-the-shelf machine vision cameras. We also propose a new class of invertible codes that allow continuous blur in captured frames, leading to an easier hardware implementation. Joint work with Amit Agrawal, Mohit Gupta, Ashok Veeraraghavan and Srinivasa Narasimhan

Proc. CVPR 2010

Suppose we have N cameras each running at frame rate f. How can we use them to get a video with frame rate N*f? There are several sampling schemes possible.

Point Sampling: Reduce the exposure time of each camera to 1/Nf and stagger the start of integration.

Pros:

- The interleaved video automatically gives a higher frame rate video. Blur is avoided becasue each camera captures a sharp image. N cameras give a frame rate increase of N. No post-processing required.

Cons:

- No light benefit compared to an equivalent high speed camera running at frame rate Nf

Box Sampling: Use larger exposure time for each camera (1/f) and stagger the start of integration. The interleaved video removes aliasing. But every frame has motion blur.

Pros:

- More light (N times) compared to an equivalent high speed camera running at frame rate Nf

Cons:

- Box blur supppress high frequency content leading to ill-posed system. Noise is increased in reconstruction. Requires solving a big linear system. Dififcult to get N times increase in frame rate with N cameras.

Coded Sampling (Ours): Use larger exposure time for each camera (1/f), but temporally modulate every frame. Each camera has a different code, but the code is same for all frames of a given camera.

Pros:

- Mre light (N/2 times) compared to an equivalent high speed camera running at frame rate Nf.

- Easy to get N times increase in frame rate with N cameras.

- Codes can be chosen to get the maximum possible SNR in reconstruction.

- Coded blur leads to well-posed system which can be solved independently for each set of N output frames. This allows streaming reconstruction with low computational complexity (solving only a N by N linear system).

Cons:

- N/2 times more light instead of N times more light in each camera compared to box sampling

Figure 1: Comparison of box sampling with coded sampling. Four captured frames (one from each camera) are shown, both for box sampling and coded sampling. Notice the coded blur in frames corresponding to coded blur. The box sampling can be thought of having a code of all ones. For coded sampling, using 4 input frames, we can get 4 output frames by solving a 4 by 4 linear system for each pixel. This is because coded sampling is frame independent.

Note that reconstrcuted frames are sharp with low noise. Thus, coded sampling allows streaming output with low computation. On the other hand, for box sampling, one needs to solve a much bigger linear system (of several frames). Since box sampling is ill-posed it leads to increased noise. By using regularization, noise can be reduced, but blur is increased in the output.

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