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

TL;DR

This paper compares progressive and random projection methods for compressive capture of high-dimensional visual signals, revealing that random projections excel mainly for higher-dimensional data, and introduces a fast, hardware-independent effectiveness measurement.

Contribution

It provides the first empirical comparison of lossy linear sensing strategies for various visual signals, highlighting the conditions where random projections outperform progressive methods.

Findings

Random projections outperform progressive methods for higher-dimensional signals.

A fast, hardware-independent measure of capture effectiveness is introduced.

The study suggests further research into adaptive and non-linear projection methods.

Abstract

Computational photography involves sophisticated capture methods. A new trend is to capture projection of higher dimensional visual signals such as videos, multi-spectral data and lightfields on lower dimensional sensors. Carefully designed capture methods exploit the sparsity of the underlying signal in a transformed domain to reduce the number of measurements and use an appropriate reconstruction method. Traditional progressive methods may capture successively more detail using a sequence of simple projection basis, such as DCT or wavelets and employ straightforward backprojection for reconstruction. Randomized projection methods do not use any specific sequence and use L0 minimization for reconstruction. In this paper, we analyze the statistical properties of natural images, videos, multi-spectral data and light-fields and compare the effectiveness of progressive and random projections. We define effectiveness by plotting reconstruction SNR against compression factor. The key idea is a procedure to measure best-case effectiveness that is fast, independent of specific hardware and independent of the reconstruction procedure. We believe this is the first empirical study to compare different lossy capture strategies without the complication of hardware or reconstruction ambiguity. The scope is limited to linear non-adaptive sensing. The results show that random projections produce significant advantages over other projections only for higher dimensional signals, and suggest more research to nascent adaptive and non-linear projection methods.