Fundamentals of digital image processing
Fundamentals of digital image processing
Strong formulations for mixed integer programming: a survey
Mathematical Programming: Series A and B
On the Inverse Hough Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hough Transform from the Radon Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
Short Communication: A note on exact image reconstruction from a limited number of projections
Journal of Visual Communication and Image Representation
Reconstruction from limited-angle projections based on δ - u spectrum analysis
IEEE Transactions on Image Processing
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A new method for the exact reconstruction of any gray-scale image from its projections is proposed. The original image is projected into several view angles and the projection samples are stored in an accumulator array. In order to reconstruct the image, the accumulator array is considered as an accumulation of sinusoidal contributions each one corresponding to a certain pixel of the original image. The proposed method defines conditions for the necessary number of projections and the density of ray samples on the projection axis. These conditions insure that, for each pixel, there is at least one sample in the accumulator array where only this particular pixel contributes. This characteristic projection sample is used during the reconstruction phase to determine the coordinates and the gray-scale value of the corresponding image pixel. A variation of the method is also proposed where the reconstruction is performed using a limited number of projection samples in certain view angles. Specifically, the number of necessary samples equals at most the overall number of pixels in the original image. This approach leads to a significant reduction of memory and processing time requirements since it provides exact image reconstruction using one projection sample per pixel.