Solving ill-posed inverse problems using iterative deep neural networks

We propose a partially learned approach for the solution of ill posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularization theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularizing functional. The method results in a gradient-like iterative scheme, where the "gradient" component is learned using a convolutional network that includes the gradients of the data discrepancy and regularizer as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against FBP and TV reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the TV reconstruction while being significantly faster, giving reconstructions of 512 x 512 volumes in about 0.4 seconds using a single GPU

Waste heat recovery from a high temperature diesel engine

2017 Fall.Includes bibliographical references.Government-mandated improvements in fuel economy and emissions from internal combustion engines (ICEs) are driving innovation in engine efficiency. Though incremental efficiency gains have been achieved, most combustion engines are still only 30-40% efficient at best, with most of the remaining fuel energy being rejected to the environment as waste heat through engine coolant and exhaust gases. Attempts have been made to harness this waste heat and use it to drive a Rankine cycle and produce additional work to improve efficiency. Research on waste heat recovery (WHR) demonstrates that it is possible to improve overall efficiency by converting wasted heat into usable work, but relative gains in overall efficiency are typically minimal (~5-8%) and often do not justify the cost and space requirements of a WHR system. The primary limitation of the current state-of-the-art in WHR is the low temperature of the engine coolant (~90°C), which minimizes the WHR from a heat source that represents between 20% and 30% of the fuel energy. The current research proposes increasing the engine coolant temperature to improve the utilization of coolant waste heat as one possible path to achieving greater WHR system effectiveness. An experiment was performed to evaluate the effects of running a diesel engine at elevated coolant temperatures and to estimate the efficiency benefits. An energy balance was performed on a modified 3-cylinder diesel engine at six different coolant temperatures (90°C, 100°C, 125°C, 150°C, 175°C, and 200°C) to determine the change in quantity and quality of waste heat as the coolant temperature increased. The waste heat was measured using the flow rates and temperature differences of the coolant, engine oil, and exhaust flow streams into and out of the engine. Custom cooling and engine oil systems were fabricated to provide adequate adjustment to achieve target coolant and oil temperatures and large enough temperature differences across the engine to reduce uncertainty. Changes to exhaust emissions were recorded using a 5-gas analyzer. The engine condition was also monitored throughout the tests by engine compression testing, oil analysis, and a complete teardown and inspection after testing was completed. The integrity of the head gasket seal proved to be a significant problem and leakage of engine coolant into the combustion chamber was detected when testing ended. The post-test teardown revealed problems with oil breakdown at locations where temperatures were highest, with accompanying component wear. The results from the experiment were then used as inputs for a WHR system model using ethanol as the working fluid, which provided estimates of system output and improvement in efficiency. Thermodynamic models were created for eight different WHR systems with coolant temperatures of 90°C, 150°C, 175°C, and 200°C and condenser temperatures of 60°C and 90°C at a single operating point of 3100 rpm and 24 N-m of torque. The models estimated that WHR output for both condenser temperatures would increase by over 100% when the coolant temperature was increased from 90°C to 200°C. This increased WHR output translated to relative efficiency gains as high as 31.0% for the 60°C condenser temperature and 24.2% for the 90°C condenser temperature over the baseline engine efficiency at 90°C. Individual heat exchanger models were created to estimate the footprint for a WHR system for each of the eight systems. When the coolant temperature increased from 90°C to 200°C, the total heat exchanger volume increased from 16.6 × 103 cm3 to 17.1 × 103 cm3 with a 60°C condenser temperature, but decreased from 15.1 × 103 cm3 to 14.2 × 103 cm3 with a 90°C condenser temperature. For all cases, increasing the coolant temperature resulted in an improvement in the efficiency gain for each cubic meter of heat exchanger volume required. Additionally, the engine oil coolers represented a significant portion of the required heat exchanger volume due to abnormally low engine oil temperatures during the experiment (~80°C). Future studies should focus on allowing the engine oil to reach higher operating temperatures which would decrease the heat rejected to the engine oil and reduce the heat duty for the oil coolers resulting in reduced oil cooler volume

A modified fuzzy C means algorithm for shading correction in craniofacial CBCT images

CBCT images suffer from acute shading artifacts primarily due to scatter. Numerous image-domain correction algorithms have been proposed in the literature that use patient-specific planning CT images to estimate shading contributions in CBCT images. However, in the context of radiosurgery applications such as gamma knife, planning images are often acquired through MRI which impedes the use of polynomial fitting approaches for shading correction. We present a new shading correction approach that is independent of planning CT images. Our algorithm is based on the assumption that true CBCT images follow a uniform volumetric intensity distribution per material, and scatter perturbs this uniform texture by contributing cupping and shading artifacts in the image domain. The framework is a combination of fuzzy C-means coupled with a neighborhood regularization term and Otsu's method. Experimental results on artificially simulated craniofacial CBCT images are provided to demonstrate the effectiveness of our algorithm. Spatial non-uniformity is reduced from 16% to 7% in soft tissue and from 44% to 8% in bone regions. With shading-correction, thresholding based segmentation accuracy for bone pixels is improved from 85% to 91% when compared to thresholding without shading-correction. The proposed algorithm is thus practical and qualifies as a plug and play extension into any CBCT reconstruction software for shading correction.Comment: 15 pages, published in CMBEBIH 201

Task adapted reconstruction for inverse problems

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as appropriate estimators (non-randomized decision rules) in statistical estimation problems. The implementation makes use of (deep) neural networks to provide a differentiable parametrization of the family of estimators for both steps. These networks are combined and jointly trained against suitable supervised training data in order to minimize a joint differentiable loss function, resulting in an end-to-end task adapted reconstruction method. The suggested framework is generic, yet adaptable, with a plug-and-play structure for adjusting both the inverse problem and the task at hand. More precisely, the data model (forward operator and statistical model of the noise) associated with the inverse problem is exchangeable, e.g., by using neural network architecture given by a learned iterative method. Furthermore, any task that is encodable as a trainable neural network can be used. The approach is demonstrated on joint tomographic image reconstruction, classification and joint tomographic image reconstruction segmentation