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Quantitative Acoustic Microscopy (QAM) is an imaging technology utilising high frequency ultrasound to produce quantitative two-dimensional (2D) maps of acoustical and mechanical properties of biological tissue at microscopy scale. Increased frequency QAM allows for finer resolution at the expense of increased acquisition times and data storage cost. Compressive sampling (CS) methods have been employed to produce QAM images from a reduced sample set, with recent state of the art utilising Approximate Message Passing (AMP) methods. In this paper we investigate the use of AMP-Net, a deep unfolded model for AMP, for the CS reconstruction of QAM parametric maps. Results indicate that AMP-Net can offer superior reconstruction performance even in its stock configuration trained on natural imagery (up to 63% in terms of PSNR), while avoiding the emergence of sampling pattern related artefacts.

Managing fluid balance in dialysis patients is crucial, as improper management can lead to severe complications. In this paper, we propose a multimodal approach that integrates visual features from lung ultrasound images with clinical data to enhance the prediction of excess body fluid. Our framework employs independent encoders to extract features for each modality and combines them through a cross-domain attention mechanism to capture complementary information. By framing the prediction as a classification task, the model achieves significantly better performance than regression. The results demonstrate that multimodal models consistently outperform single-modality models, particularly when attention mechanisms prioritize tabular data. Pseudo-sample generation further contributes to mitigating the imbalanced classification problem, achieving the highest accuracy of 88.31%. This study underscores the effectiveness of multimodal learning for fluid overload management in dialysis patients, offering valuable insights for improved clinical outcomes., Comment: 5 pages, 1 figure, 1 table

We present Sparse R-CNN OBB, a novel framework for the detection of oriented objects in SAR images leveraging sparse learnable proposals. The Sparse R-CNN OBB has streamlined architecture and ease of training as it utilizes a sparse set of 300 proposals instead of training a proposals generator on hundreds of thousands of anchors. To the best of our knowledge, Sparse R-CNN OBB is the first to adopt the concept of sparse learnable proposals for the detection of oriented objects, as well as for the detection of ships in Synthetic Aperture Radar (SAR) images. The detection head of the baseline model, Sparse R-CNN, is re-designed to enable the model to capture object orientation. We also fine-tune the model on RSDD-SAR dataset and provide a performance comparison to state-of-the-art models. Experimental results shows that Sparse R-CNN OBB achieves outstanding performance, surpassing other models on both inshore and offshore scenarios. The code is available at: www.github.com/ka-mirul/Sparse-R-CNN-OBB., Comment: Submitted to 2025 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

Optical coherence tomography (OCT) and confocal microscopy are pivotal in retinal imaging, offering distinct advantages and limitations. In vivo OCT offers rapid, non-invasive imaging but can suffer from clarity issues and motion artifacts, while ex vivo confocal microscopy, providing high-resolution, cellular-detailed color images, is invasive and raises ethical concerns. To bridge the benefits of both modalities, we propose a novel framework based on unsupervised 3D CycleGAN for translating unpaired in vivo OCT to ex vivo confocal microscopy images. This marks the first attempt to exploit the inherent 3D information of OCT and translate it into the rich, detailed color domain of confocal microscopy. We also introduce a unique dataset, OCT2Confocal, comprising mouse OCT and confocal retinal images, facilitating the development of and establishing a benchmark for cross-modal image translation research. Our model has been evaluated both quantitatively and qualitatively, achieving Fr\'echet Inception Distance (FID) scores of 0.766 and Kernel Inception Distance (KID) scores as low as 0.153, and leading subjective Mean Opinion Scores (MOS). Our model demonstrated superior image fidelity and quality with limited data over existing methods. Our approach effectively synthesizes color information from 3D confocal images, closely approximating target outcomes and suggesting enhanced potential for diagnostic and monitoring applications in ophthalmology., Comment: 30 pages, 11 figures, 5 tables

In the realm of medical image fusion, integrating information from various modalities is crucial for improving diagnostics and treatment planning, especially in retinal health, where the important features exhibit differently in different imaging modalities. Existing deep learning-based approaches insufficiently focus on retinal image fusion, and thus fail to preserve enough anatomical structure and fine vessel details in retinal image fusion. To address this, we propose the Topology-Aware Graph Attention Network (TaGAT) for multi-modal retinal image fusion, leveraging a novel Topology-Aware Encoder (TAE) with Graph Attention Networks (GAT) to effectively enhance spatial features with retinal vasculature's graph topology across modalities. The TAE encodes the base and detail features, extracted via a Long-short Range (LSR) encoder from retinal images, into the graph extracted from the retinal vessel. Within the TAE, the GAT-based Graph Information Update (GIU) block dynamically refines and aggregates the node features to generate topology-aware graph features. The updated graph features with base and detail features are combined and decoded as a fused image. Our model outperforms state-of-the-art methods in Fluorescein Fundus Angiography (FFA) with Color Fundus (CF) and Optical Coherence Tomography (OCT) with confocal microscopy retinal image fusion. The source code can be accessed via https://github.com/xintian-99/TaGAT., Comment: 11 pages, 2 figures, accepted by MICCAI 2024

Microscopy images obtained from multiple camera lenses or sensors in biological experiments provide a comprehensive understanding of objects from diverse perspectives. However, using multiple microscope setups increases the risk of misalignment of identical target features across different modalities, making multimodal image registration crucial. In this work, we build upon previous successes in biological image translation (XAcGAN) and mono-modal image registration (RoTIR) to develop a deep learning model, Dual-Domain RoTIR (DD_RoTIR), specifically designed to address these challenges. While GAN-based translation models are often considered inadequate for multimodal image registration, we enhance registration accuracy by employing a feature-matching algorithm based on Transformers and rotation equivariant networks. Additionally, hierarchical feature matching is utilized to tackle the complexities of multimodal image registration. Our results demonstrate that the DD_RoTIR model exhibits strong applicability and robustness across multiple microscopy image datasets., Comment: 30 pages including supporting information; 15 figures for main context, 5 figures for supporting information; 5 tables; 5 equations in main, 12 in supporting imformation

The identification of artefacts, particularly B-lines, in lung ultrasound (LUS), is crucial for assisting clinical diagnosis, prompting the development of innovative methodologies. While the Cauchy proximal splitting (CPS) algorithm has demonstrated effective performance in B-line detection, the process is slow and has limited generalization. This paper addresses these issues with a novel unsupervised deep unfolding network structure (DUCPS). The framework utilizes deep unfolding procedures to merge traditional model-based techniques with deep learning approaches. By unfolding the CPS algorithm into a deep network, DUCPS enables the parameters in the optimization algorithm to be learnable, thus enhancing generalization performance and facilitating rapid convergence. We conducted entirely unsupervised training using the Neighbor2Neighbor (N2N) and the Structural Similarity Index Measure (SSIM) losses. When combined with an improved line identification method proposed in this paper, state-of-the-art performance is achieved, with the recall and F2 score reaching 0.70 and 0.64, respectively. Notably, DUCPS significantly improves computational efficiency eliminating the need for extensive data labeling, representing a notable advancement over both traditional algorithms and existing deep learning approaches., Comment: 16 pages, 6 figures, IEEE TMI

Driven by the filtering challenges in linear systems disturbed by non-Gaussian heavy-tailed noise, the robust Kalman filters (RKFs) leveraging diverse heavy-tailed distributions have been introduced. However, the RKFs rely on precise noise models, and large model errors can degrade their filtering performance. Also, the posterior approximation by the employed variational Bayesian (VB) method can further decrease the estimation precision. Here, we introduce an innovative RKF method, the RKFNet, which combines the heavy-tailed-distribution-based RKF framework with the deep learning (DL) technique and eliminates the need for the precise parameters of the heavy-tailed distributions. To reduce the VB approximation error, the mixing-parameter-based function and the scale matrix are estimated by the incorporated neural network structures. Also, the stable training process is achieved by our proposed unsupervised scheduled sampling (USS) method, where a loss function based on the Student's t (ST) distribution is utilised to overcome the disturbance of the noise outliers and the filtering results of the traditional RKFs are employed as reference sequences. Furthermore, the RKFNet is evaluated against various RKFs and recurrent neural networks (RNNs) under three kinds of heavy-tailed measurement noises, and the simulation results showcase its efficacy in terms of estimation accuracy and efficiency.

We present a novel ship wake simulation system for generating S-band Synthetic Aperture Radar (SAR) images, and demonstrate the use of such imagery for the classification of ships based on their wake signatures via a deep learning approach. Ship wakes are modeled through the linear superposition of wind-induced sea elevation and the Kelvin wakes model of a moving ship. Our SAR imaging simulation takes into account frequency-dependent radar parameters, i.e., the complex dielectric constant ($\varepsilon$) and the relaxation rate ($\mu$) of seawater. The former was determined through the Debye model while the latter was estimated for S-band SAR based on pre-existing values for the L, C, and X-bands. The results show good agreement between simulated and real imagery upon visual inspection. The results of implementing different training strategies are also reported, showcasing a notable improvement in accuracy of classifier achieved by integrating real and simulated SAR images during the training.

Image registration is an essential process for aligning features of interest from multiple images. With the recent development of deep learning techniques, image registration approaches have advanced to a new level. In this work, we present 'Rotation-Equivariant network and Transformers for Image Registration' (RoTIR), a deep-learning-based method for the alignment of fish scale images captured by light microscopy. This approach overcomes the challenge of arbitrary rotation and translation detection, as well as the absence of ground truth data. We employ feature-matching approaches based on Transformers and general E(2)-equivariant steerable CNNs for model creation. Besides, an artificial training dataset is employed for semi-supervised learning. Results show RoTIR successfully achieves the goal of fish scale image registration., Comment: 7 pages, 4 figures, 2 tables

Optical coherence tomography (OCT) and confocal microscopy are pivotal in retinal imaging, each presenting unique benefits and limitations. In-vivo OCT offers rapid, non-invasive imaging but can be hampered by clarity issues and motion artifacts. Ex-vivo confocal microscopy provides high-resolution, cellular detailed color images but is invasive and poses ethical concerns and potential tissue damage. To bridge these modalities, we developed a 3D CycleGAN framework for unsupervised translation of in-vivo OCT to ex-vivo confocal microscopy images. Applied to our OCT2Confocal dataset, this framework effectively translates between 3D medical data domains, capturing vascular, textural, and cellular details with precision. This marks the first attempt to exploit the inherent 3D information of OCT and translate it into the rich, detailed color domain of confocal microscopy. Assessed through quantitative and qualitative evaluations, the 3D CycleGAN framework demonstrates commendable image fidelity and quality, outperforming existing methods despite the constraints of limited data. This non-invasive generation of retinal confocal images has the potential to further enhance diagnostic and monitoring capabilities in ophthalmology. Our source code and OCT2Confocal dataset are available at https://github.com/xintian-99/OCT2Confocal., Comment: 4pages, 5 figures

In the context of lung ultrasound, the detection of B-lines, which are indicative of interstitial lung disease and pulmonary edema, plays a pivotal role in clinical diagnosis. Current methods still rely on visual inspection by experts. Vision-based automatic B-line detection methods have been developed, but their performance has yet to improve in terms of both accuracy and computational speed. This paper presents a novel approach to posing B-line detection as an inverse problem via deep unfolding of the Alternating Direction Method of Multipliers (ADMM). It tackles the challenges of data labelling and model training in lung ultrasound image analysis by harnessing the capabilities of deep neural networks and model-based methods. Our objective is to substantially enhance diagnostic accuracy while ensuring efficient real-time capabilities. The results show that the proposed method runs more than 90 times faster than the traditional model-based method and achieves an F1 score that is 10.6% higher., Comment: 4 pages, 3 figures, conference

Motivated by filtering tasks under a linear system with non-Gaussian heavy-tailed noise, various robust Kalman filters (RKFs) based on different heavy-tailed distributions have been proposed. Although the sub-Gaussian $\alpha$-stable (SG$\alpha$S) distribution captures heavy tails well and is applicable in various scenarios, its potential has not yet been explored in RKFs. The main hindrance is that there is no closed-form expression of its mixing density. This paper proposes a novel RKF framework, RKF-SG$\alpha$S, where the signal noise is assumed to be Gaussian and the heavy-tailed measurement noise is modelled by the SG$\alpha$S distribution. The corresponding joint posterior distribution of the state vector and auxiliary random variables is approximated by the Variational Bayesian (VB) approach. Also, four different minimum mean square error (MMSE) estimators of the scale function are presented. The first two methods are based on the Importance Sampling (IS) and Gauss-Laguerre quadrature (GLQ), respectively. In contrast, the last two estimators combine a proposed Gamma series (GS) based method with the IS and GLQ estimators and hence are called GSIS and GSGL. Besides, the RKF-SG$\alpha$S is compared with the state-of-the-art RKFs under three kinds of heavy-tailed measurement noises, and the simulation results demonstrate its estimation accuracy and efficiency. All the code needed to reproduce the results presented in this work are available at: https://github.com/PengchengH/Robust-Kalman-Filters-Based-on-the-Sub-Gaussian-alpha-stable-Distribution.

Studies have proved that the number of B-lines in lung ultrasound images has a strong statistical link to the amount of extravascular lung water, which is significant for hemodialysis treatment. Manual inspection of B-lines requires experts and is time-consuming, whilst modelling automation methods is currently problematic because of a lack of ground truth. Therefore, in this paper, we propose a novel semi-supervised learning method for the B-line detection task based on contrastive learning. Through multi-level unsupervised learning on unlabelled lung ultrasound images, the features of the artefacts are learnt. In the downstream task, we introduce a fine-tuning process on a small number of labelled images using the EIoU-based loss function. Apart from reducing the data labelling workload, the proposed method shows a superior performance to model-based algorithm with the recall of 91.43%, the accuracy of 84.21% and the F1 score of 91.43%., Comment: 5 pages, 3 figures, conference

Manual examination of faecal smear samples to identify the existence of parasitic eggs is very time-consuming and can only be done by specialists. Therefore, an automated system is required to tackle this problem since it can relate to serious intestinal parasitic infections. This paper reviews the ICIP 2022 Challenge on parasitic egg detection and classification in microscopic images. We describe a new dataset for this application, which is the largest dataset of its kind. The methods used by participants in the challenge are summarised and discussed along with their results., Comment: The 29th IEEE International Conference on Image Processing

Automatic detection of parasitic eggs in microscopy images has the potential to increase the efficiency of human experts whilst also providing an objective assessment. The time saved by such a process would both help ensure a prompt treatment to patients, and off-load excessive work from experts' shoulders. Advances in deep learning inspired us to exploit successful architectures for detection, adapting them to tackle a different domain. We propose a framework that exploits two such state-of-the-art models. Specifically, we demonstrate results produced by both a Generative Adversarial Network (GAN) and Faster-RCNN, for image enhancement and object detection respectively, on microscopy images of varying quality. The use of these techniques yields encouraging results, though further improvements are still needed for certain egg types whose detection still proves challenging. As a result, a new dataset has been created and made publicly available, providing an even wider range of classes and variability., Comment: 7 pages, 3 figures, 1 table

High accuracy coastline/shoreline extraction from SAR imagery is a crucial step in a number of maritime and coastal monitoring applications. We present a method based on image segmentation using the Generalised Gamma Mixture Model superpixel algorithm (MISP-GGD). MISP-GGD produces superpixels adhering with great accuracy to object edges in the image, such as the coastline. Unsupervised clustering of the generated superpixels according to textural and radiometric features allows for generation of a land/water mask from which a highly accurate coastline can be extracted. We present results of our proposed method on a number of SAR images of varying characteristics., Comment: To appear in proceedings CIE RADAR 2021

Monitoring of ground movement close to the rail corridor, such as that associated with landslips caused by ground subsidence and/or uplift, is of great interest for the detection and prevention of possible railway faults. Interferometric synthetic-aperture radar (InSAR) data can be used to measure ground deformation, but its use poses distinct challenges, as the data is highly sparse and can be particularly noisy. Here we present a scheme for processing and interpolating noisy, sparse InSAR data into a dense spatio-temporal stack, helping suppress noise and opening up the possibility for treatment with deep learning and other image processing methods., Comment: in submission to ICIP 2022

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.

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.

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.

In the field of biomedical imaging, ultrasonography has become increasingly widespread, and an important auxiliary diagnostic tool with unique advantages, such as being non-ionising and often portable. This article reviews the state-of-the-art in medical ultrasound image computing and in particular its application in the examination of the lungs. First, we review the current developments in medical ultrasound technology. We then focus on the characteristics of lung ultrasonography and on its ability to diagnose a variety of diseases through the identification of various artefacts. We review medical ultrasound image processing methods by splitting them into two categories: (1) traditional model-based methods, and (2) data driven methods. For the former, we consider inverse problem based methods by focusing in particular on ultrasound image despeckling, deconvolution, and line artefacts detection. Among the data-driven approaches, we discuss various works based on deep/machine learning, which include various effective network architectures implementing supervised, weakly supervised and unsupervised learning., Comment: 14 pages, 12 figures

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.

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.

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., Comment: 9 pages, 3 figures

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., Comment: 6 pages, 2 Figures. This work has been presented in IGARSS 2020

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 {\alpha}-stable distributions for learning dictionaries, by considering the non-Gaussian case, {\alpha}=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, Comment: 4 pages, 2 figures, 1 table, 1 algorithm, submitted to ISBI2021

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., Comment: 19 pages, 9 figures, journal draft

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., Comment: 20 Pages, 11 figures, 5 tables

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.

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., Comment: 16 pages, 9 figures

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., Comment: 18 pages, 7 figures

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., Comment: 7 pages, 4 figures, 2 tables

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., Comment: 16 pages, 9 figures

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., Comment: 9 pages, 2 Figures and 2 Tables

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.

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., Comment: 18 pages

In this paper, we consider the problem of recovering compressively sensed ultrasound images. We build on prior work, and consider a number of existing approaches that we consider to be the state-of-the-art. The methods we consider take advantage of a number of assumptions on the signals including those of temporal and spatial correlation, block structure, prior knowledge of the support, and non-Gaussianity. We conduct a series of intensive tests to quantify the performance of these methods. We find that by altering the parameters of the structured Sparse Bayesian Learning approaches considered, we can significantly improve the objective quality of the reconstructed images. The results we achieve are a significant improvement upon previously proposed reconstruction techniques. In addition, we further show that by careful choice of parameters, we can obtain near-optimal results whilst requiring only a small fraction of the computational time needed for the best reconstruction quality., Comment: 12 pages

This paper describes a new method for mitigating the effects of atmospheric distortion on observed sequences that include large moving objects. In order to provide accurate detail from objects behind the distorting layer, we solve the space-variant distortion problem using recursive image fusion based on the Dual Tree Complex Wavelet Transform (DT-CWT). The moving objects are detected and tracked using the improved Gaussian mixture models (GMM) and Kalman filtering. New fusion rules are introduced which work on the magnitudes and angles of the DT-CWT coefficients independently to achieve a sharp image and to reduce atmospheric distortion, respectively. The subjective results show that the proposed method achieves better video quality than other existing methods with competitive speed., Comment: IEEE International Conference on Image Processing 2018