A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Universal distributed sensing via random projections
Proceedings of the 5th international conference on Information processing in sensor networks
Compressed sensing and Bayesian experimental design
Proceedings of the 25th international conference on Machine learning
Optimized Projections for Compressed Sensing
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Where computer vision needs help from computer science
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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The theory of compressed sensing tells a dramatic story that sparse signals can be reconstructed near-perfectly from a small number of random measurements. However, recent work has found the story to be more complicated. For example, the projections based on principal component analysis work better than random projections for some images while the reverse is true for other images. Which feature of images makes such a distinction and what is the optimal set of projections for natural images? In this paper, we attempt to answer these questions with a novel formulation of compressed sensing. In particular, we find that bandwise random projections in which more projections are allocated to low spatial frequencies are near-optimal for natural images and demonstrate using experimental results that the bandwise random projections outperform other kinds of projections in image reconstruction.