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Transform image processing methods are methods that work in domains of image transforms, such as Discrete Fourier, Discrete Cosine, Wavelet and alike. They are the basic tool in image compression, in image restoration, in image re-sampling…
The recent impressive results of deep learning-based methods on computer vision applications brought fresh air to the research and industrial community. This success is mainly due to the process that allows those methods to learn…
Image subtraction in astronomy is a tool for transient object discovery such as asteroids, extra-solar planets and supernovae. To match point spread functions (PSFs) between images of the same field taken at different times a convolution…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
Discrete trigonometric transformations, such as the discrete Fourier and cosine/sine transforms, are important in a variety of applications due to their useful properties. For example, one well-known property is the convolution theorem for…
Mathematical morphology (MM) helps to describe and analyze shapes using set theory. MM can be effectively applied to binary images which are treated as sets. Basic morphological operators defined can be used as an effective tool in image…
Convolution is an essential operation in signal and image processing and consumes most of the computing power in convolutional neural networks. Photonic convolution has the promise of addressing computational bottlenecks and outperforming…
Image decomposition is a crucial subject in the field of image processing. It can extract salient features from the source image. We propose a new image decomposition method based on convolutional neural network. This method can be applied…
Efficient and high-fidelity polarization demosaicking is critical for industrial applications of the division of focal plane (DoFP) polarization imaging systems. However, existing methods have an unsatisfactory balance of speed, accuracy,…
Feature extraction is a key step in image processing for pattern recognition and machine learning processes. Its purpose lies in reducing the dimensionality of the input data through the computing of features which accurately describe the…
Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…
The decomposition of an image into a linear combination of digitised basis functions is an everyday task in astronomy. A general method is presented for performing such a decomposition optimally into an arbitrary set of digitised basis…
We propose a new fast algorithm for solving one of the standard formulations of frame-based image deconvolution: an unconstrained optimization problem, involving an $\ell_2$ data-fidelity term and a non-smooth regularizer. Our approach is…
Although much research has been devoted to the problem of restoring Poissonian images, namely in the fields of medical and astronomical imaging, applying the state of the art regularizers (such as those based on wavelets or total variation)…
The prevalence of digital sensors, such as digital cameras and mobile phones, simplifies the acquisition of photos. Digital sensors, however, suffer from producing Moire when photographing objects having complex textures, which deteriorates…
This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
Interferometric closure invariants encode calibration-independent details of an object's morphology. Excepting simple cases, a direct backward transformation from closure invariants to morphologies is not well established. We demonstrate…
A simple, yet general, formalism for the optimized linear combination of astrophysical images is constructed and demonstrated. The formalism allows the user to combine multiple undersampled images to provide oversampled output at high…