Lossless Image Compression via Predictive Coding of Discrete Radon Projections

International audienceThis paper investigates predictive coding methods to compress images represented in the Radon domain as a set of projections. Both the correlation within and between discrete Radon projections at similar angles can be exploited to achieve lossless compression. The discrete Radon projections investigated here are those used to define the Mojette transform first presented by Guedon et al. [Psychovisual image coding via an exact discrete Radon transform, in: T.W. Lance (Ed.), Proceedings of the Visual Communications AND Image Processing (VCIP), May 1995, Taipei, Taiwan, pp. 562-572]. This work is further to the preliminary investigation presented by Autrusseau et al. [Lossless compression based on a discrete and exact radon transform: a preliminary study, in: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), vol. II, May 2006, Toulouse, France, pp. 425-428]. The 1D Mojette projections are re-arranged as two dimensional images, thus allowing the use of 2D image compression techniques onto the projections. Besides the compression capabilities, the Mojette transforms brings an interesting property: a tunable redundancy. As the Mojette transform is able to both compress and add redundancy, the proposed method can be viewed as a joint lossless source-channel coding technique for images. We present here the evolution of the compression ratio depending on the chosen redundancy

Fast Mojette Transform for Discrete Tomography

A new algorithm for reconstructing a two dimensional object from a set of one dimensional projected views is presented that is both computationally exact and experimentally practical. The algorithm has a computational complexity of O(n log2 n) with n = N^2 for an NxN image, is robust in the presence of noise and produces no artefacts in the reconstruction process, as is the case with conventional tomographic methods. The reconstruction process is approximation free because the object is assumed to be discrete and utilizes fully discrete Radon transforms. Noise in the projection data can be suppressed further by introducing redundancy in the reconstruction. The number of projections required for exact reconstruction and the response to noise can be controlled without comprising the digital nature of the algorithm. The digital projections are those of the Mojette Transform, a form of discrete linogram. A simple analytical mapping is developed that compacts these projections exactly into symmetric periodic slices within the Discrete Fourier Transform. A new digital angle set is constructed that allows the periodic slices to completely fill all of the objects Discrete Fourier space. Techniques are proposed to acquire these digital projections experimentally to enable fast and robust two dimensional reconstructions.Comment: 22 pages, 13 figures, Submitted to Elsevier Signal Processin

Redundant Image Representation via Multi-Scale Digital Radon Projection

International audienceA novel ordering of digital Radon projections co-efficients is presented here that enables progressive image reconstruc- tion from low resolution to full resolution. The digital Radon transform applied here is the Mojette transform first defined by Guedon et al. in [1]. The Mojette transform is a natural way to generate redundancy to any specified degree and has been demonstrated to be useful for redundant representation for robust data storage and transmission. Combining this with the wavelet transform facilitates compression, i.e., joint source-channel coding, along with the additional property of scalability

Lossless Image Compression and Selective Encryption Using a Discrete Radon Transform

International audienceIn this paper we propose a new joint encryption and loss- less compression technique designed for large images 1 . The proposed technique takes advantage of the Mojette transform properties, and can easily be included in a distributed storage architecture. The basic crypto-compression scheme presented is based on a cascade of Radon projection which enables fast encryption of a large amount of digital data. Standard encryp- tion techniques, such as AES, DES, 3DES, or IDEA can be applied to encrypt very small percentages of high resolution images. As the proposed scheme uses standard encryption, and only transmits uncorrelated data along with the encrypted part, this technique takes benefit of the security related to the chosen encryption standard, here, we assess its performances in terms of processing time and compression ratio

Quantised Angular Momentum Vectors and Projection Angle Distributions for Discrete Radon Transformations

International audienceA quantum mechanics based method is presented to generate sets of digital angles that may be well suited to describe projections on discrete grids. The resulting angle sets are an alternative to those derived using the Farey fractions from number theory. The Farey angles arise naturally through the definitions of the Mojette and Finite Radon Transforms. Often a subset of the Farey angles needs to be selected when reconstructing images from a limited number of views. The digital angles that result from the quantisation of angular momentum (QAM) vectors may provide an alternative way to select angle subsets. This paper seeks first to identify the important properties of digital angles sets and second to demonstrate that the QAM vectors are indeed a candidate set that fulfils these requirements. Of particular note is the rare occurrence of degeneracy in the QAM angles, particularly for the half-integral angular momenta angle sets

Serum osmolarity and haematocrit do not modify the association between the impedance index (Ht2/Z) and total body water in the very old: The Newcastle 85+ Study

Bioelectrical impedance is a non-invasive technique for the assessment of body composition; however, information on its accuracy in the very old (80+ years) is limited. We investigated whether the association between the impedance index and total body water (TBW) was modified by hydration status as assessed by haematocrit and serum osmolarity. This was a cross-sectional analysis of baseline data from the Newcastle 85+ Cohort Study. Anthropometric measurements [weight, height (Ht)] were taken and body mass index (BMI) calculated. Leg-to-leg bioimpedance was used to measure the impedance value (Z) and to estimate fat mass, fat free mass and TBW. The impedance index (Ht2/Z) was calculated. Blood haematocrit, haemoglobin, glucose, sodium, potassium, urea and creatinine concentrations were measured. Serum osmolarity was calculated using a validated prediction equation. 677 men and women aged 85 years were included. The average BMI of the population was 24.3±4.2kg/m2 and the prevalence of overweight and obesity was 32.6% and 9.5%, respectively. The impedance index was significantly associated with TBW in both men (n=274, r=0.76, p<0.001) and women (n=403, r=0.96, p<0.001); in regression models, the impedance index remained associated with TBW after adjustment for height, weight and gender, and further adjustment for serum osmolarity and haematocrit. The impedance index values increased with BMI and the relationship was not modified by hydration status in women (p=0.69) and only marginally in men (p=0.02). The association between the impedance index and TBW was not modified by hydration status, which may support the utilisation of leg-to-leg bioimpedance for the assessment of body composition in the very old

Recovering missing slices of the discrete fourier transform using ghosts

The discrete Fourier transform (DFT) underpins the solution to many inverse problems commonly possessing missing or unmeasured frequency information. This incomplete coverage of the Fourier space always produces systematic artifacts called Ghosts. In this paper, a fast and exact method for deconvolving cyclic artifacts caused by missing slices of the DFT using redundant image regions is presented. The slices discussed here originate from the exact partitioning of the Discrete Fourier Transform (DFT) space, under the projective Discrete Radon Transform, called the discrete Fourier slice theorem. The method has a computational complexity of O(n\log-{2}n) (for an n=N\times N image) and is constructed from a new cyclic theory of Ghosts. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. This paper concludes with an application to fast, exact, non-iterative image reconstruction from a highly asymmetric set of rational angle projections that give rise to sets of sparse slices within the DFT

Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with X-ray micro-CT

This paper reports on recent advances at the micro-computed tomography facility at the Australian National University. Since 2000 this facility has been a significant centre for developments in imaging hardware and associated software for image reconstruction, image analysis and image-based modelling. In 2010 a new instrument was constructed that utilises theoretically-exact image reconstruction based on helical scanning trajectories, allowing higher cone angles and thus better utilisation of the available X-ray flux. We discuss the technical hurdles that needed to be overcome to allow imaging with cone angles in excess of 60°. We also present dynamic tomography algorithms that enable the changes between one moment and the next to be reconstructed from a sparse set of projections, allowing higher speed imaging of time-varying samples. Researchers at the facility have also created a sizeable distributed-memory image analysis toolkit with capabilities ranging from tomographic image reconstruction to 3D shape characterisation. We show results from image registration and present some of the new imaging and experimental techniques that it enables. Finally, we discuss the crucial question of image segmentation and evaluate some recently proposed techniques for automated segmentation