Implicit method for nonlinear complex diffusion with applications to image denoising

In this paper we focus on the development and implementation of an implicit finite difference method for solving a complex diffusion differential equation with applications to noise filtering in images. We give a complete characterization of the implementation of the fully implicit method, including the characterization of the derivatives for Newton's method at each step. In order to show the feasibility of the method, we compare the implicit method with the semi-implicit and apply it to both in vivo images of the human retina by optical coherence tomography (OCT) and standard images (Lena and the Cameraman). We compute noise removal performance metrics to show the effect of several parameters in the performance of the method.info:eu-repo/semantics/publishedVersio

QuaSI: Quantile Sparse Image Prior for Spatio-Temporal Denoising of Retinal OCT Data

Optical coherence tomography (OCT) enables high-resolution and non-invasive 3D imaging of the human retina but is inherently impaired by speckle noise. This paper introduces a spatio-temporal denoising algorithm for OCT data on a B-scan level using a novel quantile sparse image (QuaSI) prior. To remove speckle noise while preserving image structures of diagnostic relevance, we implement our QuaSI prior via median filter regularization coupled with a Huber data fidelity model in a variational approach. For efficient energy minimization, we develop an alternating direction method of multipliers (ADMM) scheme using a linearization of median filtering. Our spatio-temporal method can handle both, denoising of single B-scans and temporally consecutive B-scans, to gain volumetric OCT data with enhanced signal-to-noise ratio. Our algorithm based on 4 B-scans only achieved comparable performance to averaging 13 B-scans and outperformed other current denoising methods.Comment: submitted to MICCAI'1

A Splitting Algorithm for Medical Image Denoising

In this work we consider a stable algorithm for integrating a mathematical model based on mean curvature motion equation proposed in (Alvarez, Lions, Morel 1992) for image denoising. The scheme is constructed using a finite difference space discretisation and semi-implicit time discretisation and is considered with a splitting algorithm that can be implemented in parallel. We apply this algorithm to the problem of denoising optical coherence tomograms from the human retina while preserving image features

Sparse And Low Rank Decomposition Based Batch Image Alignment for Speckle Reduction of retinal OCT Images

Optical Coherence Tomography (OCT) is an emerging technique in the field of biomedical imaging, with applications in ophthalmology, dermatology, coronary imaging etc. Due to the underlying physics, OCT images usually suffer from a granular pattern, called speckle noise, which restricts the process of interpretation. Here, a sparse and low rank decomposition based method is used for speckle reduction in retinal OCT images. This technique works on input data that consists of several B-scans of the same location. The next step is the batch alignment of the images using a sparse and low-rank decomposition based technique. Finally the denoised image is created by median filtering of the low-rank component of the processed data. Simultaneous decomposition and alignment of the images result in better performance in comparison to simple registration-based methods that are used in the literature for noise reduction of OCT images.Comment: Accepted for presentation at ISBI'1

Semantic denoising autoencoders for retinal optical coherence tomography

Noise in speckle-prone optical coherence tomography tends to obfuscate important details necessary for medical diagnosis. In this paper, a denoising approach that preserves disease characteristics on retinal optical coherence tomography images in ophthalmology is presented. We propose semantic denoising autoencoders, which combine a convolutional denoising autoencoder with a priorly trained ResNet image classifier as regularizer during training. This promotes the perceptibility of delicate details in the denoised images that are important for diagnosis and filters out only informationless background noise. With our approach, higher peak signal-to-noise ratios with PSNR = 31.0 dB and higher classification performance of F1 = 0.92 can be achieved for denoised images compared to state-of-the-art denoising. It is shown that semantically regularized autoencoders are capable of denoising retinal OCT images without blurring details of diseases

Ocular fundus Imaging: from structure to function

Imaging the ocular fundus, namely the retina, to detect and/or monitor changes over time from the healthy condition is of fundamental importance to assess onset and disease progression and is a valuable tool to understand the basic mechanisms of ocular diseases. Current trends point to the need for less or non-invasive approaches, to the need for detailed (higher spatial and temporal resolution) imaging systems and to the quantification as opposed to qualitative classification of any findings. In this work we present a snapshot of our research by presenting two examples of technical development aiming to obtain structural and function information from the human retina, in vivo, using non-invasive techniques, namely optical coherence tomography imaging. Based on our experience and developed work, we are now starting to bridge the gap to brain imaging as the eye is only the starting point of vision.FCTFEDERProgram COMPET

Stability of finite difference schemes for complex diffusion processes

In this paper we present a rigorous proof for the stability of a class of finite difference schemes applied to nonlinear complex diffusion equations. Complex diffusion is a common and broadly used denoising procedure in image processing. To illustrate the theoretical results we present some numerical examples based on an explicit scheme applied to a nonlinear equation in the context of image denoising.FCT PTDC/SAU-ENB/111139/200

Improved adaptive complex diffusion despeckling filter

Despeckling optical coherence tomograms from the human retina is a fundamental step to a better diagnosis or as a preprocessing stage for retinal layer segmentation. Both of these applications are particularly important in monitoring the progression of retinal disorders. In this study we propose a new formulation for a well-known nonlinear complex diffusion filter. A regularization factor is now made to be dependent on data, and the process itself is now an adaptive one. Experimental results making use of synthetic data show the good performance of the proposed formulation by achieving better quantitative results and increasing computation speed.Fundação para a Ciência e TecnologiaFEDERPrograma COMPET