Abstract-We demonstrate an algorithm, relevant to tomography sensor systems, to obtain images from the parallel reconstruction of essentially localized elements at different scales. This is achieved by combining methodology to reconstruct images from limited and/or truncated data, with the time-frequency capabilities of the Wavelet Transform. Multi-scale, as well as time-frequency, localization properties of the separable twodimensional wavelet transform are exploited as an approach for faster reconstruction. The speed up is realized not only by reducing the computation load on a single processor, but also by achieving the parallel reconstruction of several tiled blocks. With tiled-block image reconstruction by wavelet-based, parallel filtered back-projection we measure more than 36 times gain in speed, compared to standard filtered back-projection.Index Terms-image reconstruction, computed tomography, data processing algorithms, parallel processing, wavelet transform.
I. INTRODUCTIONCROSS many applications, it is common to identify the need of information about an object, without altering its physical structure. Fortunately, there are numerous methods allowing radiation, either emitted or transmitted, to be employed to obtain cross-sectional images characterizing the inner structure of an object. The mathematical foundation behind such an approach was developed by Johann Radon in 1917 [1] and several decades later, in 1972, experimentally implemented by Hounsfield [2] resulting in the demonstration of the first Computed Tomography (CT) scanner.The main motivation for this work was the existing body of knowledge and achievements on the reconstruction of reduced-area full-resolution images, originally encouraged by the radiation dose exposure reduction in medical imaging and where the Wavelet Transform (WT), along its different representations, proved to be an effective tool given its timefrequency localization capabilities [4], [5]. Such research has been commonly named as Wavelet-based local reconstruction, and has been reported to be useful in other application areas such as Nano and Micro Tomography [6], [7]; Terahertz Tomography [8], and Dental Radiology [9].Of special interest is the 2D fast wavelet transform (2D FWT), employed in [5] and [10]. In addition to achieving local Manuscript received October 15, 2015. Jorge Guevara Escobedo (jorge.guevaraescobedo@manchester.ac.uk) and Krikor B. Ozanyan (k.ozanyan@manchester.ac.uk) are with the School of Electrical and Electronic Engineering, The University of Manchester, M13 9PL, Manchester, UK. JGE wishes to acknowledge the financial support of Consejo Nacional de Ciencia y Tecnología (CONACyT), Mexico, for a doctoral studentship.reconstruction, it allows projection data to be processed in a multi-resolution scheme. Such a feature proves to be of great benefit, when realizing its similarities with the parallel algorithm proposed in [11]. In that algorithm, a frequential decomposition of projection data is performed with the aim to back-project every componen...