On the design of a sparsifying dictionary for compressive image feature extraction

Abstract

Compressive sensing is an alternative to Nyquist-rate sampling when the signal to be acquired is known to be sparse or compressible. A sparse signal has a small number of nonzero components compared to its total length. This property can either exist either in the sampling domain, i. e. time or space, or with respect to a transform basis. There is a parallel between representing a signal in a compressed domain and feature extraction. In both cases, there is an effort to reduce the amount of resources required to describe a large set of data. A given feature is often represented by a set of parameters, which only acquire a relevant value in a few points in the image plane. Although there are some works reported on feature extraction from compressed samples, none of them considers the implementation of the feature extractor as a part of the sensor itself. Our approach is to introduce a sparsifying dictionary, feasibly implementable at the focal plane, which describes the image in terms of features. This allows a standard reconstruction algorithm to directly recover the interesting image features, discarding the irrelevant information. In order to validate the approach, we have integrated a Harris-Stephens corner detector into the compressive sampling process. We have evaluated the accuracy of the reconstructed corners compared to applying the detector to a reconstructed image.