Many useful tasks in data science and machine learning applications can be written as simple variations of matrix multiplication. However, users have difficulty performing such tasks as existing matrix/vector libraries support only a limited class of computations hand-tuned for each unique hardware platform. Users can alternatively write the task as a simple nested loop but current compilers are not sophisticated enough to generate fast code for the task written in this way. To address these issues, we extend an open-source compiler to recognize and optimize these matrix multiplication-like tasks. Our framework, called Amulet, uses both database-style and compiler optimization techniques to generate fast code tailored to its execution environment. We show through experiments that Amulet achieves speedups on a variety of matrix multiplication-like tasks compared to existing compilers. For large matrices Amulet typically performs within 15% of hand-tuned matrix multiplication libraries, while handling a much broader class of computations.
Conebeam CT using a circular trajectory is quite often used for various applications due to its relative simple geometry. For conebeam geometry, Feldkamp, Davis and Kress algorithm is regarded as the standard reconstruction method, but this algorithm suffers from so-called conebeam artifacts as the cone angle increases. Various model-based iterative reconstruction methods have been developed to reduce the cone-beam artifacts, but these algorithms usually require multiple applications of computational expensive forward and backprojections. In this paper, we develop a novel deep learning approach for accurate conebeam artifact removal. In particular, our deep network, designed on the differentiated backprojection domain, performs a data-driven inversion of an ill-posed deconvolution problem associated with the Hilbert transform. The reconstruction results along the coronal and sagittal directions are then combined using a spectral blending technique to minimize the spectral leakage. Experimental results show that our method outperforms the existing iterative methods despite significantly reduced runtime complexity.
In many applications requiring multiple inputs to obtain a desired output, if any of the input data is missing, it often introduces large amounts of bias. Although many techniques have been developed for imputing missing data, the image imputation is still difficult due to complicated nature of natural images. To address this problem, here we proposed a novel framework for missing image data imputation, called Collaborative Generative Adversarial Network (CollaGAN). CollaGAN converts an image imputation problem to a multi-domain images-to-image translation task so that a single generator and discriminator network can successfully estimate the missing data using the remaining clean data set. We demonstrate that CollaGAN produces the images with a higher visual quality compared to the existing competing approaches in various image imputation tasks.