Sigma Delta quantization for images
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In this paper, we propose the first adaptive quantization method for direct digital image acquisition that yields a better information conversion rate than the state-of-the-art method in cameras. This new method allows a rich color-palette to be reconstructed by using extremely low bits for each pixel and therefore is beneficial for capturing scenes with high-contrast. The work is motivated by recent results on super-resolution for sparse signals, but is free from the usual separation requirement between spikes. We assume natural images are of small TV norms of order 1 or 2, and design an appropriate reconstruction algorithm that reduces the reconstruction error from the known O(√(P)) to O(√(s)) where P is the number of pixels and s is the number of edges in the image. Our numerical experiments confirm these theoretical findings and further show that a dramatic increase in the photo quality can be achieved when the photo is taken in a dark environment.
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