X-ray computed tomography (CT) is an important technique for noninvasive clinical diagnosis and nondestructive testing. In many applications a number of image processing steps are needed before the image features are available. One of these processing steps is image segmentation, which generates the edge and the structural features of the regions of interest. The conventional flow is to first reconstruct images and then apply image segmentation methods on reconstructed images. In contrast, an emerging technique obtains the tomographic image and segmentation simultaneously, which is especially useful in the case of limited data. An iterative method for simultaneous reconstruction and segmentation (SRS) with Mumford-Shah model has been proposed, which not only regularizes the ill-posed tomographic reconstruction problem, but also produces the image segmentation at the same time. The Mumford-Shah model is both mathematically and computationally challenging. In this paper, we propose an asynchronous ray-parallel algorithm of the SRS method and accelerate it using field-programmable gate array (FPGA) devices, which drastically improves the energy efficiency. Experimental results show that the FPGA implementation achieves a 1:2× speedup with an energy efficiency as great as 58×, over the GPU implementation.
The starting point for this paper is the well known equivalence between convolution filtering with a rescaled Gaussian and the solution of the heat equation. In the first sections we analyze the equivalence between multiscale convolution filtering, linear smoothing methods based on continuous wavelet transforms and the solutions of linear diffusion equations. I.e. we determine a wavelet ψ, resp. a convolution filter φ, which is associated
with a given linear diffusion equation ut = Pu and vice versa. This approach has an extension to non-linear smoothing techniques. The main result of this paper is the derivation of a differential equation, whose solution is equivalent to non-linear multi-scale smoothing based on soft shrinkage methods applied to Fourier or continuous wavelet transforms.
Conference Committee Involvement (1)
Wavelet Applications in Industrial Processing II
27 October 2004 | Philadelphia, Pennsylvania, United States
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