arXiv subjects

Alin Achim

Publications and source records attributed to Alin Achim.

At least 55 records · Page 3Linked to original sources

arXiv2022

Optimal Transport-based Graph Matching for 3D retinal OCT image registration

Registration of longitudinal optical coherence tomography (OCT) images assists disease monitoring and is essential in image fusion applications. Mouse retinal OCT images are often collected for longitudinal study of eye disease models such as uveitis, but their quality is often poor compared with human imaging. This paper presents a novel but efficient framework involving an optimal transport based graph matching (OT-GM) method for 3D mouse OCT image registration. We first perform registration of fundus-like images obtained by projecting all b-scans of a volume on a plane orthogonal to them, hereafter referred to as the x-y plane. We introduce Adaptive Weighted Vessel Graph Descriptors (AWVGD) and 3D Cube Descriptors (CD) to identify the correspondence between nodes of graphs extracted from segmented vessels within the OCT projection images. The AWVGD comprises scaling, translation and rotation, which are computationally efficient, whereas CD exploits 3D spatial and frequency domain information. The OT-GM method subsequently performs the correct alignment in the x-y plane. Finally, registration along the direction orthogonal to the x-y plane (the z-direction) is guided by the segmentation of two important anatomical features peculiar to mouse b-scans, the Internal Limiting Membrane (ILM) and the hyaloid remnant (HR). Both subjective and objective evaluation results demonstrate that our framework outperforms other well-established methods on mouse OCT images within a reasonable execution time.

cs.CV↗

arXiv2022

Unsupervised Image Fusion Using Deep Image Priors

A significant number of researchers have applied deep learning methods to image fusion. However, most works require a large amount of training data or depend on pre-trained models or frameworks to capture features from source images. This is inevitably hampered by a shortage of training data or a mismatch between the framework and the actual problem. Deep Image Prior (DIP) has been introduced to exploit convolutional neural networks' ability to synthesize the 'prior' in the input image. However, the original design of DIP is hard to be generalized to multi-image processing problems, particularly for image fusion. Therefore, we propose a new image fusion technique that extends DIP to fusion tasks formulated as inverse problems. Additionally, we apply a multi-channel approach to enhance DIP's effect further. The evaluation is conducted with several commonly used image fusion assessment metrics. The results are compared with state-of-the-art image fusion methods. Our method outperforms these techniques for a range of metrics. In particular, it is shown to provide the best objective results for most metrics when applied to medical images.

cs.CV↗

arXiv2022

Modeling and SAR Imaging of the Sea Surface: a Review of the State-of-the-Art with Simulations

Among other remote sensing technologies, synthetic aperture radar (SAR) has become firmly established in the practice of oceanographic research. Despite solid experience in this field, comprehensive knowledge and interpretation of ocean/sea and vessel wave signatures on radar images are still very challenging. Many technical parameters and scanning conditions vary for different SAR platforms, which also imposes some restrictions on the cross-analysis of their respective images. Numerical simulation of SAR images allows the analysis of many radar imaging parameters including environmental, ship, or platform related. In this paper, we present a universal simulation framework for SAR imagery of the sea surface, which includes the superposition of sea-ship waves. This paper is the first attempt to cover exhaustively all SAR imaging effects for the sea waves and ship wakes scene. The study is based on well proven concepts: the linear theory of sea surface modeling, Michell thin-ship theory for Kelvin wake modeling, and ocean SAR imaging theory. We demonstrate the role of two main factors that affect imaging of both types of waves: (i) SAR parameters and (ii) Hydrodynamic related parameters such as wind state and Froude number. The SAR parameters include frequency, signal polarization, mean incidence angle, image resolution, variation by scanning platform (airborne or spaceborne) of the range-to-velocity (R/V) ratio, and velocity bunching with associated shifting, smearing and azimuthal cutoff effects. We perform modeling for five wave frequency spectra and four ship models. We also compare spectra in two aspects: with Cox and Munk's probability density function (PDF), and with a novel proposed evaluation of ship wake detectability. The simulation results agree well with SAR imaging theory. The study gives a fuller understanding of radar imaging mechanisms for sea waves and ship wakes.

physics.ao-ph↗

arXiv2021

Sparse regularization with a non-convex penalty for SAR imaging and autofocusing

In this paper, SAR image reconstruction with joint phase error estimation (autofocusing) is formulated as an inverse problem. An optimization model utilising a sparsity-enforcing Cauchy regularizer is proposed, and an alternating minimization framework is used to solve it, in which the desired image and the phase errors are optimized alternatively. For the image reconstruction sub-problem (f-sub-problem), two methods are presented capable of handling the problem's complex nature, and we thus present two variants of our SAR image autofocusing algorithm. Firstly, we design a complex version of the forward-backward splitting algorithm (CFBA) to solve the f-sub-problem iteratively. For the second variant, the Wirtinger alternating minimization autofocusing (WAMA) method is presented, in which techniques of Wirtinger calculus are utilized to minimize the complex-valued cost function in the f-sub-problem in a direct fashion. For both methods, the phase error estimation sub-problem is solved by simply expanding and observing its cost function. Moreover, the convergence of both algorithms is discussed in detail. By conducting experiments on both simulated scenes and real SAR images, the proposed method is demonstrated to give impressive autofocusing results compared to other state of the art methods.

eess.IV↗

arXiv2021

A Generalized Gaussian Extension to the Rician Distribution for SAR Image Modeling

In this paper, we present a novel statistical model, $\textit{the generalized-Gaussian-Rician}$ (GG-Rician) distribution, for the characterization of synthetic aperture radar (SAR) images. Since accurate statistical models lead to better results in applications such as target tracking, classification, or despeckling, characterizing SAR images of various scenes including urban, sea surface, or agricultural, is essential. The proposed statistical model is based on the Rician distribution to model the amplitude of a complex SAR signal, the in-phase and quadrature components of which are assumed to be generalized-Gaussian distributed. The proposed amplitude GG-Rician model is further extended to cover the intensity SAR signals. In the experimental analysis, the GG-Rician model is investigated for amplitude and intensity SAR images of various frequency bands and scenes in comparison to state-of-the-art statistical models that include $\mathcal{K}$, Weibull, Gamma, and Lognormal. In order to decide on the most suitable model, statistical significance analysis via Kullback-Leibler divergence and Kolmogorov-Smirnov statistics are performed. The results demonstrate the superior performance and flexibility of the proposed model for all frequency bands and scenes and its applicability on both amplitude and intensity SAR images. The Matlab package is available at https://github.com/oktaykarakus/GG-Rician-SAR-Image-Modelling.

eess.IV↗

arXiv2020

SAR Image Autofocusing using Wirtinger calculus and Cauchy regularization

In this paper, an optimization model using Cauchy regularization is proposed for simultaneous SAR image reconstruction and autofocusing. A coordinate descent framework in which the desired image and the phase errors are optimized alternatively is designed to solve the model. For the subproblem of estimating the image, we utilize the techniques of Wirtinger calculus to directly minimize the cost function which involves complex variables. We also utilise a state-of-the-art, sparsity-enforcing Cauchy regularizer. The proposed method is demonstrated to give impressive autofocusing results by conducting experiments on both simulated scene and real SAR image.

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arXiv2020

A Simulation Study to Evaluate the Performance of the Cauchy Proximal Operator in Despeckling SAR Images of the Sea Surface

The analysis of ocean surface is widely performed using synthetic aperture radar (SAR) imagery as it yields information for wide areas under challenging weather conditions, during day or night, etc. Speckle noise constitutes however the main reason for reduced performance in applications such as classification, ship detection, target tracking and so on. This paper presents an investigation into the despeckling of SAR images of the ocean that include ship wake structures, via sparse regularisation using the Cauchy proximal operator. We propose a closed-form expression for calculating the proximal operator for the Cauchy prior, which makes it applicable in generic proximal splitting algorithms. In our experiments, we simulate SAR images of moving vessels and their wakes. The performance of the proposed method is evaluated in comparison to the L1 and TV norm regularisation functions. The results show a superior performance of the proposed method for all the utilised images generated.

eess.IV↗

arXiv2020

Exploiting the Dual-Tree Complex Wavelet Transform for Ship Wake Detection in SAR Imagery

In this paper, we analyse synthetic aperture radar (SAR) images of the sea surface using an inverse problem formulation whereby Radon domain information is enhanced in order to accurately detect ship wakes. This is achieved by promoting linear features in the images. For the inverse problem-solving stage, we propose a penalty function, which combines the dual-tree complex wavelet transform (DT-CWT) with the non-convex Cauchy penalty function. The solution to this inverse problem is based on the forward-backward (FB) splitting algorithm to obtain enhanced images in the Radon domain. The proposed method achieves the best results and leads to significant improvement in terms of various performance metrics, compared to state-of-the-art ship wake detection methods. The accuracy of detecting ship wakes in SAR images with different frequency bands and spatial resolution reaches more than 90%, which clearly demonstrates an accuracy gain of 7% compared to the second-best approach.

eess.IV↗

arXiv2020

Convergence Guarantees for Non-Convex Optimisation with Cauchy-Based Penalties

In this paper, we propose a proximal splitting methodology with a non-convex penalty function based on the heavy-tailed Cauchy distribution. We first suggest a closed-form expression for calculating the proximal operator of the Cauchy prior, which then makes it applicable in generic proximal splitting algorithms. We further derive the condition required for guaranteed convergence to a solution in optimisation problems involving the Cauchy based penalty function. Setting the system parameters by satisfying the proposed condition ensures convergence even though the overall cost function is non-convex when minimisation is performed via a proximal splitting algorithm. The proposed method based on Cauchy regularisation is evaluated by solving generic signal processing examples, i.e. 1D signal denoising in the frequency domain, two image reconstruction tasks including de-blurring and denoising, and error recovery in a multiple-antenna communication system. We experimentally verify the proposed convergence conditions for various cases, and show the effectiveness of the proposed Cauchy based non-convex penalty function over state-of-the-art penalty functions such as $L_1$ and total variation ($TV$) norms.

eess.SP↗

arXiv2020

Non-convex Super-resolution of OCT images via sparse representation

We propose a non-convex variational model for the super-resolution of Optical Coherence Tomography (OCT) images of the murine eye, by enforcing sparsity with respect to suitable dictionaries learnt from high-resolution OCT data. The statistical characteristics of OCT images motivate the use of α-stable distributions for learning dictionaries, by considering the non-Gaussian case, α=1. The sparsity-promoting cost function relies on a non-convex penalty - Cauchy-based or Minimax Concave Penalty (MCP) - which makes the problem particularly challenging. We propose an efficient algorithm for minimizing the function based on the forward-backward splitting strategy which guarantees at each iteration the existence and uniqueness of the proximal point. Comparisons with standard convex L1-based reconstructions show the better performance of non-convex models, especially in view of further OCT image analysis

eess.IV↗

arXiv2020

Detection of Ship Wakes in SAR Imagery Using Cauchy Regularisation

Ship wake detection is of great importance in the characterisation of synthetic aperture radar (SAR) images of the ocean surface since wakes usually carry essential information about vessels. Most detection methods exploit the linear characteristics of the ship wakes and transform the lines in the spatial domain into bright or dark points in a transform domain, such as the Radon or Hough transforms. This paper proposes an innovative ship wake detection method based on sparse regularisation to obtain the Radon transform of the SAR image, in which the linear features are enhanced. The corresponding cost function utilizes the Cauchy prior, and on this basis, the Cauchy proximal operator is proposed. A Bayesian method, the Moreau-Yoshida unadjusted Langevin algorithm (MYULA), which is computationally efficient and robust is used to estimate the image in the transform domain by minimizing the negative log-posterior distribution. The detection accuracy of the Cauchy prior based approach is 86.7%, which is demonstrated by experiments over six COSMO-SkyMed images.

eess.SP↗

arXiv2020

Detection of Line Artefacts in Lung Ultrasound Images of COVID-19 Patients via Non-Convex Regularization

In this paper, we present a novel method for line artefacts quantification in lung ultrasound (LUS) images of COVID-19 patients. We formulate this as a non-convex regularisation problem involving a sparsity-enforcing, Cauchy-based penalty function, and the inverse Radon transform. We employ a simple local maxima detection technique in the Radon transform domain, associated with known clinical definitions of line artefacts. Despite being non-convex, the proposed technique is guaranteed to convergence through our proposed Cauchy proximal splitting (CPS) method and accurately identifies both horizontal and vertical line artefacts in LUS images. In order to reduce the number of false and missed detection, our method includes a two-stage validation mechanism, which is performed in both Radon and image domains. We evaluate the performance of the proposed method in comparison to the current state-of-the-art B-line identification method and show a considerable performance gain with 87% correctly detected B-lines in LUS images of nine COVID-19 patients. In addition, owing to its fast convergence, our proposed method is readily applicable for processing LUS image sequences.

eess.IV↗

arXiv2020

Representation Learning via Cauchy Convolutional Sparse Coding

In representation learning, Convolutional Sparse Coding (CSC) enables unsupervised learning of features by jointly optimising both an $\ell_2$-norm fidelity term and a sparsity enforcing penalty. This work investigates using a regularisation term derived from an assumed Cauchy prior for the coefficients of the feature maps of a CSC generative model. The sparsity penalty term resulting from this prior is solved via its proximal operator, which is then applied iteratively, element-wise, on the coefficients of the feature maps to optimise the CSC cost function. The performance of the proposed Iterative Cauchy Thresholding (ICT) algorithm in reconstructing natural images is compared against the common choice of $\ell_1$-norm optimised via soft and hard thresholding. ICT outperforms IHT and IST in most of these reconstruction experiments across various datasets, with an average PSNR of up to 11.30 and 7.04 above ISTA and IHT respectively.

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arXiv2020

On Solving SAR Imaging Inverse Problems Using Non-Convex Regularization with a Cauchy-based Penalty

Synthetic aperture radar (SAR) imagery can provide useful information in a multitude of applications, including climate change, environmental monitoring, meteorology, high dimensional mapping, ship monitoring, or planetary exploration. In this paper, we investigate solutions to a number of inverse problems encountered in SAR imaging. We propose a convex proximal splitting method for the optimization of a cost function that includes a non-convex Cauchy-based penalty. The convergence of the overall cost function optimization is ensured through careful selection of model parameters within a forward-backward (FB) algorithm. The performance of the proposed penalty function is evaluated by solving three standard SAR imaging inverse problems, including super-resolution, image formation, and despeckling, as well as ship wake detection for maritime applications. The proposed method is compared to several methods employing classical penalty functions such as total variation ($TV$) and $L_1$ norms, and to the generalized minimax-concave (GMC) penalty. We show that the proposed Cauchy-based penalty function leads to better image reconstruction results when compared to the reference penalty functions for all SAR imaging inverse problems in this paper.

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arXiv2020

Deep Learning Framework for Detecting Ground Deformation in the Built Environment using Satellite InSAR data

The large volumes of Sentinel-1 data produced over Europe are being used to develop pan-national ground motion services. However, simple analysis techniques like thresholding cannot detect and classify complex deformation signals reliably making providing usable information to a broad range of non-expert stakeholders a challenge. Here we explore the applicability of deep learning approaches by adapting a pre-trained convolutional neural network (CNN) to detect deformation in a national-scale velocity field. For our proof-of-concept, we focus on the UK where previously identified deformation is associated with coal-mining, ground water withdrawal, landslides and tunnelling. The sparsity of measurement points and the presence of spike noise make this a challenging application for deep learning networks, which involve calculations of the spatial convolution between images. Moreover, insufficient ground truth data exists to construct a balanced training data set, and the deformation signals are slower and more localised than in previous applications. We propose three enhancement methods to tackle these problems: i) spatial interpolation with modified matrix completion, ii) a synthetic training dataset based on the characteristics of real UK velocity map, and iii) enhanced over-wrapping techniques. Using velocity maps spanning 2015-2019, our framework detects several areas of coal mining subsidence, uplift due to dewatering, slate quarries, landslides and tunnel engineering works. The results demonstrate the potential applicability of the proposed framework to the development of automated ground motion analysis systems.

cs.CV↗

arXiv2020

Ship Wake Detection in SAR Images via Sparse Regularization

In order to analyse synthetic aperture radar (SAR) images of the sea surface, ship wake detection is essential for extracting information on the wake generating vessels. One possibility is to assume a linear model for wakes, in which case detection approaches are based on transforms such as Radon and Hough. These express the bright (dark) lines as peak (trough) points in the transform domain. In this paper, ship wake detection is posed as an inverse problem, which the associated cost function including a sparsity enforcing penalty, i.e. the generalized minimax concave (GMC) function. Despite being a non-convex regularizer, the GMC penalty enforces the overall cost function to be convex. The proposed solution is based on a Bayesian formulation, whereby the point estimates are recovered using maximum a posteriori (MAP) estimation. To quantify the performance of the proposed method, various types of SAR images are used, corresponding to TerraSAR-X, COSMO-SkyMed, Sentinel-1, and ALOS2. The performance of various priors in solving the proposed inverse problem is first studied by investigating the GMC along with the L1, Lp, nuclear and total variation (TV) norms. We show that the GMC achieves the best results and we subsequently study the merits of the corresponding method in comparison to two state-of-the-art approaches for ship wake detection. The results show that our proposed technique offers the best performance by achieving 80% success rate.

eess.SP↗

arXiv2020

Iterative Cauchy Thresholding: Regularisation with a heavy-tailed prior

In the machine learning era, sparsity continues to attract significant interest due to the benefits it provides to learning models. Algorithms aiming to optimise the $\ell_0$- and $\ell_1$-norm are the common choices to achieve sparsity. In this work, an alternative algorithm is proposed, which is derived based on the assumption of a Cauchy distribution characterising the coefficients in sparse domains. The Cauchy distribution is known to be able to capture heavy-tails in the data, which are linked to sparse processes. We begin by deriving the Cauchy proximal operator and subsequently propose an algorithm for optimising a cost function which includes a Cauchy penalty term. We have coined our contribution as Iterative Cauchy Thresholding (ICT). Results indicate that sparser solutions can be achieved using ICT in conjunction with a fixed over-complete discrete cosine transform dictionary under a sparse coding methodology.

eess.IV↗

arXiv2020

Image Fusion via Sparse Regularization with Non-Convex Penalties

The L1 norm regularized least squares method is often used for finding sparse approximate solutions and is widely used in 1-D signal restoration. Basis pursuit denoising (BPD) performs noise reduction in this way. However, the shortcoming of using L1 norm regularization is the underestimation of the true solution. Recently, a class of non-convex penalties have been proposed to improve this situation. This kind of penalty function is non-convex itself, but preserves the convexity property of the whole cost function. This approach has been confirmed to offer good performance in 1-D signal denoising. This paper demonstrates the aforementioned method to 2-D signals (images) and applies it to multisensor image fusion. The problem is posed as an inverse one and a corresponding cost function is judiciously designed to include two data attachment terms. The whole cost function is proved to be convex upon suitably choosing the non-convex penalty, so that the cost function minimization can be tackled by convex optimization approaches, which comprise simple computations. The performance of the proposed method is benchmarked against a number of state-of-the-art image fusion techniques and superior performance is demonstrated both visually and in terms of various assessment measures.

cs.CV↗