Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing

Wavelets have been used extensively for several years now in astronomy for many purposes, ranging from data filtering and deconvolution, to star and galaxy detection or cosmic ray removal. More recent sparse representations such ridgelets or curvelets have also been proposed for the detection of anisotropic features such cosmic strings in the cosmic microwave background. We review in this paper a range of methods based on sparsity that have been proposed for astronomical data analysis. We also discuss what is the impact of Compressed Sensing, the new sampling theory, in astronomy for collecting the data, transferring them to the earth or reconstructing an image from incomplete measurements.Comment: Submitted. Full paper will figures available at http://jstarck.free.fr/IEEE09_SparseAstro.pd

CT Image Reconstruction by Spatial-Radon Domain Data-Driven Tight Frame Regularization

This paper proposes a spatial-Radon domain CT image reconstruction model based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model combines the idea of joint image and Radon domain inpainting model of \cite{Dong2013X} and that of the data-driven tight frames for image denoising \cite{cai2014data}. It is different from existing models in that both CT image and its corresponding high quality projection image are reconstructed simultaneously using sparsity priors by tight frames that are adaptively learned from the data to provide optimal sparse approximations. An alternative minimization algorithm is designed to solve the proposed model which is nonsmooth and nonconvex. Convergence analysis of the algorithm is provided. Numerical experiments showed that the SRD-DDTF model is superior to the model by \cite{Dong2013X} especially in recovering some subtle structures in the images

Mathematical Approaches to Digital Image Inpainting

Image inpainting process is used to restore the damaged image or missing parts of an image. This technique is used in some applications, such as removal of text in images and photo restoration. There are different types of methods used in image inpainting, such as non-inear partial differential equations(PDEs), wavelet transformation and framelet transformation. We studied the usage of the current image inpainting methods and solved the Poisson equation using a five-point stencil method. We used a modified five-point stencil method to solve the same equation. It gave better results than the standard five-point stencil method. Using modified five-point stencil method results as the initial condition, we solved the iterative linear and non-linear diffusion PDE. We considered different types of diffusion conductivity and compared their results. When compared with PSNR values, the iterative linear diffusion PDE method gave the best results where as constant diffusion conductivity PDE gave the worst result. Furthermore, inverse diffusion conductivity PDE had given better results than that of the constant diffusion PDE. However, it was worse than the Gaussian and Lorentz diffusion conductivity PDE. Gaussian and Lorentz diffusion conductivity iterative linear PDE had given a better result for image inpainting. When we use any inpainting technique, we cannot restore the original image. We studied the relationship between the error of the image inpainting and the inpainted domain. Error is proportional to the value of the Greens function. There are two types of methods to find the Greens function. The first method is solving a Poisson equation for a different shape of domain, such as a circle, ellipse, triangle and rectangle. If the inpainting domain has a different shape, then it is difficult to find the error. We used the conformal mapping method to find the error. We also developed a formula for transformation from any polygon to the unit circle. Moreover, we applied the Schwarz Christoffel transformation to transform from the upper half plane to any polygon

Image Restoration using Automatic Damaged Regions Detection and Machine Learning-Based Inpainting Technique

In this dissertation we propose two novel image restoration schemes. The first pertains to automatic detection of damaged regions in old photographs and digital images of cracked paintings. In cases when inpainting mask generation cannot be completely automatic, our detection algorithm facilitates precise mask creation, particularly useful for images containing damage that is tedious to annotate or difficult to geometrically define. The main contribution of this dissertation is the development and utilization of a new inpainting technique, region hiding, to repair a single image by training a convolutional neural network on various transformations of that image. Region hiding is also effective in object removal tasks. Lastly, we present a segmentation system for distinguishing glands, stroma, and cells in slide images, in addition to current results, as one component of an ongoing project to aid in colon cancer prognostication

Pareto Optimized Large Mask Approach for Efficient and Background Humanoid Shape Removal

The purpose of automated video object removal is to not only detect and remove the object of interest automatically, but also to utilize background context to inpaint the foreground area. Video inpainting requires to fill spatiotemporal gaps in a video with convincing material, necessitating both temporal and spatial consistency; the inpainted part must seamlessly integrate into the background in a variety of scenes, and it must maintain a consistent appearance in subsequent frames even if its surroundings change noticeably. We introduce deep learning-based methodology for removing unwanted human-like shapes in videos. The method uses Pareto-optimized Generative Adversarial Networks (GANs) technology, which is a novel contribution. The system automatically selects the Region of Interest (ROI) for each humanoid shape and uses a skeleton detection module to determine which humanoid shape to retain. The semantic masks of human like shapes are created using a semantic-aware occlusion-robust model that has four primary components: feature extraction, and local, global, and semantic branches. The global branch encodes occlusion-aware information to make the extracted features resistant to occlusion, while the local branch retrieves fine-grained local characteristics. A modified big mask inpainting approach is employed to eliminate a person from the image, leveraging Fast Fourier convolutions and utilizing polygonal chains and rectangles with unpredictable aspect ratios. The inpainter network takes the input image and the mask to create an output image excluding the background humanoid shapes. The generator uses an encoder-decoder structure with included skip connections to recover spatial information and dilated convolution and squeeze and excitation blocks to make the regions behind the humanoid shapes consistent with their surroundings. The discriminator avoids dissimilar structure at the patch scale, and the refiner network catches features around the boundaries of each background humanoid shape. The efficiency was assessed using the Structural Learned Perceptual Image Patch Similarity, Frechet Inception Distance, and Similarity Index Measure metrics and showed promising results in fully automated background person removal task. The method is evaluated on two video object segmentation datasets (DAVIS indicating respective values of 0.02, FID of 5.01 and SSIM of 0.79 and YouTube-VOS, resulting in 0.03, 6.22, 0.78 respectively) as well a database of 66 distinct video sequences of people behind a desk in an office environment (0.02, 4.01, and 0.78 respectively).publishedVersio

From Augmentation to Inpainting:Improving Visual SLAM with Signal Enhancement Techniques and GAN-based Image Inpainting

This paper undertakes a comprehensive investigation that surpasses the conventional examination of signal enhancement techniques and their effects on visual Simultaneous Localization and Mapping (vSLAM) performance across diverse scenarios. Going beyond the conventional scope, the study extends its focus towards the seamless integration of signal enhancement techniques, aiming to achieve a substantial enhancement in the overall vSLAM performance. The research not only delves into the assessment of existing methods but also actively contributes to the field by proposing innovative denoising techniques that can play a pivotal role in refining the accuracy and reliability of vSLAM systems. This multifaceted approach encompasses a thorough exploration of the intricate relationships between signal enhancement, denoising strategies, their cumulative impact on the performance of vSLAM in real-world applications and the innovative use of Generative Adversarial Networks (GANs) for image inpainting. The GANs effectively fill in missing spaces following object detection and removal, presenting a novel state-of-the-art approach that significantly enhances overall accuracy and execution speed of vSLAM. This paper aims to contribute to the advancement of vSLAM algorithms in real-world scenarios, demonstrating improved accuracy, robustness, and computational efficiency through the amalgamation of signal enhancement and advanced denoising techniques