Intertwined Digital Rays in Discrete Radon Projections Pooled over Adjacent Prime Sized Arrays

Abstract

Abstract. Digital projections are image intensity sums taken along directed rays that sample whole pixel values at periodic locations along the ray. For 2D square arrays with sides of prime length, the Discrete Radon Transform (DRT) is very efficient at reconstructing digital images from their digital projections. The periodic gaps in digital rays complicate the use of the DRT for efficient reconstruction of tomographic images from real projection data, where there are no gaps along the projection direction. A new approach to bridge this gap problem is to pool DRT digital projections obtained over a variety of prime sized arrays. The digital gaps are then partially filled by a staggered overlap of discrete sample positions to better approximate a continuous projection ray. This paper identifies primes that have similar and distinct DRT pixel sampling patterns for the rays in digital projections. The projections are effectively pooled by combining several images, each reconstructed at a fixed scale, but using projections that are interpolated over different prime sized arrays. The basis for the pooled image reconstruction approach is outlined and we demonstrate the principle of this mechanism works.

The discrete Radon transform: a more efficient approach to image reconstruction?

“…For a p × p image [where p is prime], only p + 1 projections with p samples are required. Svalbe et al in [14][15][16] have developed many methods to map sampled continuous projection data to the discrete projections of the FRT; this is the only step in the inversion process where errors are introduced. The incorporation of the Haar filter to pre-condition the real projection data values 3,4 is an avenue which has not yet been fully explored.…”

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

“…These orientations are a subset of the Farey series for F N , as shown in Figure 2(c). The subset of Farey fractions (a/b) that are selected at each prime size p has its own interesting behaviour, as discussed in [15]. The FRT has robust, efficient real-space and Fourier-space reconstruction algorithms based on simple addition.…”

Generalised finite radon transform for N×N images

“…1a and b. The FRT has found application in tomographic reconstruction [2,16,17], image compression [7,15], image denoising [18], image representation [3], blind blur deconvolution [4], watermarking [19,5], encrypted and robust data transmission [5,6]. An adaptive FRT for a sliding and zooming window was developed in [20] to facilitate the location of small linear features and for object tracking.…”