A Deterministic Compressive Sensing Approach for Compressed Domain Image Analysis

Compressive sensing (CS) is a signal processing technique for acquiring sparse signals at sampling rates much lower than the Nyquist rate. Traditionally to avoid generation of large sensing matrices for images, the columns or rows are compressed in the sensing phase. This increases the number of matrix multiplication operations and results in a compressed image with a different aspect ratio than the original uncompressed image. To overcome these issues, in this paper, we investigate a 2D deterministic sensing technique that maintains both the aspect ratio and the morphology of the image. We use a linear filtering-based measurement matrix. Through this paper, we demonstrate that deterministic CS will preserve the features and there by enable analysis of the images such as detection and identification of objects in the compressed domain without the need to perform a computationally expensive reconstruction. In order to demonstrate this, images obtained by infra-red electro-optic camera on an airborne platform (low resolution), LandSat (medium resolution) and multispectral images (high resolution) are chosen. Features of chosen objects from an uncompressed image are compared with those of corresponding objects in the compressed image using template matching to demonstrate that image analysis can be done in the compressed domain. Frobenius norm-based structural similarity analysis for the images at different levels of compression is presented to demonstrate the similarity in structure. Robustness of the deterministic CS technique is demonstrated through template matching using SURF algorithm.