05 Fakultät Informatik, Elektrotechnik und Informationstechnik
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Item Open Access Stochastic neural networks : components, analysis, limitations(2022) Neugebauer, Florian; Polian, Ilia (Prof. Dr.)Stochastic computing (SC) promises an area and power-efficient alternative to conventional binary implementations of many important arithmetic functions. SC achieves this by employing a stream-based number format called Stochastic numbers (SNs), which enables bit-sequential computations, in contrast to conventional binary computations that are performed on entire words at once. An SN encodes a value probabilistically with equal weight for every bit in the stream. This encoding results in approximate computations, causing a trade-off between power consumption, area and computation accuracy. The prime example for efficient computation in SC is multiplication, which can be performed with only a single gate. SC is therefore an attractive alternative to conventional binary implementations in applications that contain a large number of basic arithmetic operations and are able to tolerate the approximate nature of SC. The most widely considered class of applications in this regard is neural networks (NNs), with convolutional neural networks (CNNs) as the prime target for SC. In recent years, steady advances have been made in the implementation of SC-based CNNs (SCNNs). At the same time however, a number of challenges have been identified as well: SCNNs need to handle large amounts of data, which has to be converted from conventional binary format into SNs. This conversion is hardware intensive and takes up a significant portion of a stochastic circuit's area, especially if the SNs have to be generated independently of each other. Furthermore, some commonly used functions in CNNs, such as max-pooling, have no exact corresponding SC implementation, which reduces the accuracy of SCNNs. The first part of this work proposes solutions to these challenges by introducing new stochastic components: A new stochastic number generator (SNG) that is able to generate a large number of SNs at the same time and a stochastic maximum circuit that enables an accurate implementation of max-pooling operations in SCNNs. In addition, the first part of this work presents a detailed investigation of the behaviour of an SCNN and its components under timing errors. The error tolerance of SC is often quoted as one of its advantages, stemming from the fact that any single bit of an SN contributes only very little to its value. In contrast, bits in conventional binary formats have different weights and can contribute as much as 50\% of a number's value. SC is therefore a candidate for extreme low-power systems, as it could potentially tolerate timing errors that appear in such environments. While the error tolerance of SC image processing systems has been demonstrated before, a detailed investigation into SCNNs in this regard has been missing so far. It will be shown that SC is not error tolerant in general, but rather that SC components behave differently even if they implement the same function, and that error tolerance of an SC system further depends on the error model. In the second part of this work, a theoretical analysis into the accuracy and limitations of SC systems is presented. An existing framework to analyse and manage the accuracy of combinational stochastic circuits is extended to cover sequential circuits. This framework enables a designer to predict the effect of small design changes on the accuracy of a circuit and determine important parameters such as SN length without extensive simulations. It will further be shown that the functions that are possible to implement in SC are limited. Due to the probabilistic nature of SC, some arithmetic functions suffer from a small bias when implemented as a stochastic circuit, including the max-pooling function in SCNNs.Item Open Access Scatter and beam hardening correction for high-resolution CT in near real-time based on a fast Monte Carlo photon transport model(2022) Alsaffar, Ammar; Simon, Sven (Prof. Dr.-Ing.)Computed tomography (CT) is a powerful non-destructive testing (NDT) technique. It provides inception about the inner of the scanned object and is widely used for industrial and medical applications. However, this technique suffers from severe quality degradation artifacts. Among these artifacts, the scatter and the beam hardening (BH) causes severe quality degradation of the reconstructed CT images. The scatter results from the change in the direction, or the direction and the energy of the photon penetrating the object, while the beam hardening results from the polychromatic nature of the X-ray source. When photons of different energies penetrate through the object, low-energy photons are more easily absorbed than high-energy photons. This results in the hardening of the X-ray beam which causes the non-linear relation between the propagation path length and the attenuation of the beam. These kinds of artifacts are the major source of the cupping and the streak artifacts that highly degrades the quality of the computed tomography imaging. The presence of the cupping and the streak artifacts reduce the contrast of this image and the contrast-to-noise and cause distortion of the grey values. As a consequence important analysis of the results from the computed tomography technique is affected, e.g., the detectability of voids and cracks is reduced by the reduction of the contrast and affects the dimensional measurement. Monte Carlo (MC) simulation is considered the most accurate approach for scatter estimation. However, the existing MC estimators are computationally expensive, especially for the considered high-resolution flat-panel CT. In this work, a muli-GPU photon forward projection model and an iterative scatter correction algorithm were implemented. The Monte Carlo model has been highly accelerated and extensively verified using several experimental and simulated examples. The implemented model describes the physics within the 1 keV to 1 MeV range using multiple controllable key parameters. Based on this model, scatter computation for a single projection can be completed within a range of a few seconds under well-defined model parameters. Smoothing and interpolation are performed on the estimated scatter to accelerate the scatter calculation without compromising accuracy too much compared to measured near scatter-free projection images. Combining the scatter estimation with the filtered backprojection (FBP), scatter correction is performed effectively in an iterative manner. In order to evaluate the proposed MC model, extensive experiments have been conducted on the simulated data and real-world high-resolution flat-panel CT. Compared to the state-of-the-art MC simulators, the proposed MC model achieved a 15× acceleration on a single GPU in comparison to the GPU implementation of the Penelope simulator (MCGPU) utilizing several acceleration techniques, and a 202× speed-up on a multi-GPU system comparing to the multi-threaded state-of-the-art EGSnrc MC simulator. Furthermore, it is shown that for high-resolution images, scatter correction with sufficient accuracy is accomplished within one to three iterations using a FBP and the proposed fast MC photon transport model. Moreover, a fast and accurate BH correction method that requires no prior knowledge of the materials and corrects first and higher-order BH artifacts has been implemented. In the first step, a wide sweep of the material is performed based on an experimentally measured look-up table to obtain the closest estimate of the material. Then the non-linearity effect of the BH is corrected by adding the difference between the estimated monochromatic and the polychromatic simulated projections of the segmented image. The estimated monochromatic projection is simulated by selecting the energy from the polychromatic spectrum which produces the lowest mean square error (MSE) with the BH-corrupted projection from the scanner. While the polychromatic projection is accurately estimated using the least square estimation (LSE) method by minimizing the difference between the experimental projection and the linear combination of simulated polychromatic projections using different spectra of different filtration. As a result, an accurate non-linearity correction term is derived that leads to an accurate BH correction result. To evaluate the proposed BH correction method, extensive experiments have been conducted on real-world CT data. Compared to the state-of-the-art empirical BH correction method, the experiments show that the proposed method can highly reduce the BH artifacts without prior knowledge of the materials. In summary, the lack of the availability of fast and computationally efficient methods to correct the major artifacts in CT images, i.e., scatter and beam hardening, has motivated this work in which efficient and fast algorithms have been implemented to correct these artifacts. The correction of these artifacts has led to better visualization of the CT images, a higher contrast-to-noise ratio, and improved contrast. Supported by multiple experimental examples, it is shown that the scatter corrected images, using the proposed method, resample the near artifacts-free reference images acquired experimentally within a reasonable time. On the other hand, the application of the proposed BH correction method after the correction of the scatter artifacts results in the complete removal of the rest cupping and streak artifacts that were degrading the scatter-corrected images and improved the contrast-to-noise (CNR) ratio of the scatter-corrected images. Moreover, assessments of the correction quality of the CT images have been performed using the software Volume Graphics VGSTUDIO MAX. Better surface determination can be derived from the artifacts-corrected images. In addition, enhancing the contrast by correcting these artifacts results in an improved detectability of voids and cracks in several concrete examples. This supports the efficiency of the implemented artifacts correction methods in this work.