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- All Subjects: Machine Learning
- Creators: Turaga, Pavan
Classification in machine learning is quite crucial to solve many problems that the world is presented with today. Therefore, it is key to understand one’s problem and develop an efficient model to achieve a solution. One technique to achieve greater model selection and thus further ease in problem solving is estimation of the Bayes Error Rate. This paper provides the development and analysis of two methods used to estimate the Bayes Error Rate on a given set of data to evaluate performance. The first method takes a “global” approach, looking at the data as a whole, and the second is more “local”—partitioning the data at the outset and then building up to a Bayes Error Estimation of the whole. It is found that one of the methods provides an accurate estimation of the true Bayes Error Rate when the dataset is at high dimension, while the other method provides accurate estimation at large sample size. This second conclusion, in particular, can have significant ramifications on “big data” problems, as one would be able to clarify the distribution with an accurate estimation of the Bayes Error Rate by using this method.
For each of these cases, I present a feasible image restoration pipeline to correct for their particular limitations. For the pinhole camera, I present an early pipeline to allow for practical pinhole photography by reducing noise levels caused by low-light imaging, enhancing exposure levels, and sharpening the blur caused by the pinhole. For lensless cameras, we explore a neural network architecture that performs joint image reconstruction and point spread function (PSF) estimation to robustly recover images captured with multiple PSFs from different cameras. Using adversarial learning, this approach achieves improved reconstruction results that do not require explicit knowledge of the PSF at test-time and shows an added improvement in the reconstruction model’s ability to generalize to variations in the camera’s PSF. This allows lensless cameras to be utilized in a wider range of applications that require multiple cameras without the need to explicitly train a separate model for each new camera. For UDCs, we utilize a multi-stage approach to correct for low light transmission, blur, and haze. This pipeline uses a PyNET deep neural network architecture to perform a majority of the restoration, while additionally using a traditional optimization approach which is then fused in a learned manner in the second stage to improve high-frequency features. I show results from this novel fusion approach that is on-par with the state of the art.
It is observed that the performance of the algorithm with regards to the kernels used are consistent with the theoretical performance of the kernel as presented in a previous work. The theoretical approach has also been automated in this work and the various implementation challenges have been addressed.