3. Sparse And Low Rank Decomposition Based Batch Image Alignment For Speckle Reduction Of Retinal Oct Images

Introduction

Optical Coherence Tomography (OCT) is a vital non-invasive imaging system for obtaining high-resolution 3D images of tissues, particularly in ophthalmology. Speckle noise poses a challenge in OCT images, and various techniques, including compounding methods and post-processing approaches, are employed for noise reduction.

Speckle is a fundamental property of the signals and images acquired by narrow-band detection systems like Synthetic-Aperture Radar (SAR), ultrasound and OCT. Not only the optical properties of the system, but also the motion of the subject to be imaged, size and temporal coherence of the light source, multiple scattering, phase deviation of the beam and aperture of the detector can affect the speckle.

This project introduces a novel registration-based speckle reduction technique using sparse and low-rank decomposition. The method iteratively aligns B-scans, separating image features and noise components, achieving sub-pixel accuracy for improved Signal-to-Noise Ratio (SNR) and Contrast-to-Noise Ratio (CNR). Comparative results with translation and rigid registration methods demonstrate the effectiveness of the proposed technique. The paper advocates for further exploration of this approach in future investigations.

Methodology (Robust Alignment by Sparse and Low-Rank Decomposition “RASL”)

Assuming a set of n B-scans, the data matrix D can be created by stacking the vectorized images as columns of the matrix. Additional optimization is needed in order to compensate the misalignment. This is done by assuming a set of parametric transformations, τ, applied to the images. In this formulation we have:

This is a non-convex and NP-hard problem to solve due to the need for minimizing the rank and the 1 norm. Convex relaxation of the problem  results in:

Starting from an initial set of transformation, here the identity transformation, and setting rigid transformation as the desired transformation, at each iteration this linearized convex optimization problem is solved until reaching convergence. Algorithm 1 summarizes the process.
Solving the third step, linearized convex optimization problem, is done by Augmented Lagrange Multiplier (ALM) method which has been proven to have reliable results for such optimization problems. The final result of the algorithm is the well-aligned stack of images, decomposed into low-rank data set containing image information and sparse component consisting of speckle noise. The final image is created by pixel-wise median filtering of the final low-rank component of the data.

Results and discussion

Considering 6 regions of interest (ROl) in the final results, one only containing background noise and the rest containing image features. the metrics can be defined as follows:

As for other registration based methods, translation and rigid registration techniques available in “ImageJ” software package are considered for comparison. the figure shown in introduction represents final results using 50 misaligned noisy retinal OCT images. However figure below shows the improvement in the average SNR of the final image for different methods used.

meanwhile the improvement of the CNR can be shown in figure below

Conclusions:

This project presents a novel application of sparse and low-rank decomposition for batch image alignment to reduce noise in Optical Coherence Tomography (OCT) images. The alignment process addresses misalignments caused by eye movements in stacks of noisy retinal OCT images. The method decomposes vectorized image data into low-rank and sparse components at each iteration, enhancing final alignment and separating noise from the signal. The performance is evaluated using Signal-to-Noise Ratio (SNR) and Contrast-to-Noise Ratio (CNR) metrics, comparing favorably with other registration-based techniques for speckle noise reduction. Although the approach outperforms alternative methods in terms of SNR and CNR, it involves higher computational costs. Future research should explore GPU implementations to expedite the process. Additionally, newer techniques in sparse and low-rank decomposition proposed in the literature will be considered for further improvement.