Cylindrical Fast Backprojection (CFBP) is a novel image reconstruction algorithm developed at PNNL that radically increases the efficiency of normal backprojection techniques and is ideally suited to microwave and millimeter-wave imaging systems based on scanned linear arrays such as current and next-generation cylindrical body scanners in common use for aviation security screening. This method achieves its gains in efficiency by separating a full backprojection into a sequence of three steps, range focusing, vertical focusing, and lateral focusing, with intermediate results saved and used to avoid repetitive multidimensional computation. This invention is a critical enabling technology that will allow efficient image reconstruction in next-generation body scanners - the CFBP algorithm allows imaging results to be presented within a fraction of a second after the scan is complete.