Minimising Acquisition Maximising Inference—A Demonstration on Print Error Detection

Is it possible to detect a feature in an image without ever being able to look at it? Images are known to be very redundant in spatial domain. When transformed to bases like Discrete Cosine Transform (DCT) or wavelets, they acquire a sparser (more effective) representation. Compressed Sensing is a technique which proposes simultaneous acquisition and compression of any signal by taking very few random linear measurements (M) instead of uniform samples at more than twice the bandwidth frequency (Shannon-Nyquist theorem). The quality of reconstruction directly relates with M, which should be above a certain threshold (determined by the level of sparsity, k) for a reliable recovery. Since these measurements can non-adaptively reconstruct the signal to a faithful extent using purely analyticalmethodslikeBasisPursuit,MatchingPursuit,Iterativethresholding,etc.,wecanbeassured that these compressed samples contain enough information about any relevant macro-level feature contained in the (image) signal. Thus if we choose to deliberately acquire an even lower number of measurements-inordertothwartthepossibilityofacomprehensiblereconstruction,buthighenough to infer whether a relevant feature exists in an image - we can achieve accurate image classification while preserving its privacy. Through the print error detection problem, it is demonstrated that such a novel system can be implemented in practise.