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Computational photography involves sophisticated capture methods. A new trendis to capture projection of higher dimensional visual signals such as videos,multi-spectral data and lightfields on lower dimensional sensors. Carefullydesigned capture methods exploit the sparsity of the underlying signal in atransformed domain to reduce the number of measurements and use an appropriatereconstruction method. Traditional progressive methods may capture successivelymore detail using a sequence of simple projection basis, such as DCT orwavelets and employ straightforward backprojection for reconstruction.Randomized projection methods do not use any specific sequence and use L0minimization for reconstruction. In this paper, we analyze the statisticalproperties of natural images, videos, multi-spectral data and light-fields andcompare the effectiveness of progressive and random projections. We defineeffectiveness by plotting reconstruction SNR against compression factor. Thekey idea is a procedure to measure best-case effectiveness that is fast,independent of specific hardware and independent of the reconstructionprocedure. We believe this is the first empirical study to compare differentlossy capture strategies without the complication of hardware or reconstructionambiguity. The scope is limited to linear non-adaptive sensing. The resultsshow that random projections produce significant advantages over otherprojections only for higher dimensional signals, and suggest more research tonascent adaptive and non-linear projection methods.

Progressive versus Random Projections for Compressive Capture of Images, Lightfields and Higher Dimensional Visual Signals