The Fourier transform in image processing is an important tool that allows observation of an image in the frequency-domain and due to which several difficult problems become very simple to analyze. The transform is used in a wide range of applications, such as image analysis, image filtering, image compression, etc. On the other hand, with the recent trend for data-driven approaches, deep-learning has arisen as a promising learning method that has had success in several computer vision areas, such as image classification, object detection, pedestrian detection, etc. Deep learning algorithms train a deep neural network on a large set of images to learn the parameters instead of using hand-tuned filters.

In this thesis, we propose to design a framework, inspired by both the Fourie...[ Read more ]

The Fourier transform in image processing is an important tool that allows observation of an image in the frequency-domain and due to which several difficult problems become very simple to analyze. The transform is used in a wide range of applications, such as image analysis, image filtering, image compression, etc. On the other hand, with the recent trend for data-driven approaches, deep-learning has arisen as a promising learning method that has had success in several computer vision areas, such as image classification, object detection, pedestrian detection, etc. Deep learning algorithms train a deep neural network on a large set of images to learn the parameters instead of using hand-tuned filters.

In this thesis, we propose to design a framework, inspired by both the Fourier transform and deep-learning methodology, to address two image reconstruction problems: multispectral demosaicking and low-dose computed tomography (LDCT) artifact reduction. In multispectral demosaicking, we need to reconstruct the original image from an overly downsampled image, whereas in LDCT artifact reduction, we need to reconstruct an artifact-free image from an artifact-induced image. Basically, in both these problems, we must restore the original component from a given noisy observation and thus require a proper investigation to understand the fundamental aspects of both problems. In view of this observation, in this thesis, we first analyze the both problems in the frequency-domain and then propose a solution that addresses both problems. Specifically, our proposed framework for each problem can be divided into two phases:

1. Frequency-domain analysis phase: With the help of frequency-domain analysis, we are able to identify the potential issues in the assumptions of each problem and then give a systematic analysis of why existing methods cannot produce a result with a sufficient level of quality.

2. Reconstruction phase: Based on the frequency-domain analysis, we first propose an algorithm based on an image-driven approach, which extracts information from the target image itself to address the problems. Later, a data-driven approach is incorporated into the proposed algorithm to further enhance its performance. In the data-driven approach, we first train a deep neural network on a large set of images and then address the problems with the learned parameters.

We first consider the problem of multispectral demosaicking in multispectral imaging, which is an extension of 3-band (or color) demosaicking. Color demosaicking is a process of interpolating the missing color samples in each band to reconstruct a full-color image, but in multispectral demosaicking each band is significantly undersampled due to the increment in the number of bands. Specifically, in the proposed framework, we demonstrate a frequency-domain analysis of the subsampled color-difference signal and observe that the conventional assumption of highly correlated spectral bands for estimating undersampled components is not precise. Instead, such a spectral correlation assumption is image dependent and rests on the aliasing interferences among the various color-difference spectra. To address this problem, we propose an image-driven approach, called the adaptive spectral-correlation-based demosaicking (ASCD) algorithm, that uses a novel anti-aliasing filter to suppress these interferences and then integrates it with an intra-prediction scheme to generate a more accurate prediction for the reconstructed image. The weights for the integration are obtained in the linear minimum mean square error (LMMSE) sense to produce an accurate reconstruction. Further, to enhance the accuracy of the reconstruction, we obtain the weights by a data-driven approach, namely the deep-learning approach. In this approach, we first train a deep neural network on a large set of images and then learn the weights accordingly.

In the second problem, we address the removal of artifacts in LDCT images. Computed tomography (CT) examination with a reduced radiation dose, known as low-dose CT (LDCT), has gained increasing attention from the medical community because it decreases the radiation exposure of patients. However, images obtained from LDCT reconstruction consist of severe artifacts that degrade the quality of the images for diagnostic tasks. Recently, a frequency-split technique, has been proposed to address a different issue of CT reconstruction by extracting the high-frequency components from both uncorrected and corrected images (obtained by an existing method). Given this, we propose an optimized frequency-split algorithm that first investigates the high-frequency and low-frequency component of both the uncorrected and corrected image and then integrates them optimally to generate a reduced artifact image. Our algorithm is optimal in the linear minimum mean square error (LMMSE) sense, and the optimal weights store the information on whether a pixel or block of pixels in the uncorrected image belongs to a desired or undesired edge and thus optimally reduces the artifacts. To further improve the accuracy of the proposed algorithm, we propose to include a clean prior image in the optimization framework, thus reducing the artifacts significantly. Experimental results demonstrate that the proposed algorithm, based on an optimized frequency-split-based technique, drastically reduces artifacts. Similar to our approach for multispectral demosaicking, we later propose to use a data-driven approach to learn the weights by training a deep neural network on a large set of images.