Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography

Compressed intracellular motility via non-uniform temporal sampling in dynamic optical coherence tomography

Significance

Optical coherence tomography has great utility for capturing dynamic processes, but such applications are particularly data-intensive. Samples such as biological tissues exhibit temporal features at varying time scales, which makes data reduction challenging.

Aim

We propose a method for capturing short- and long-term correlations of a sample in a compressed way using non-uniform temporal sampling to reduce scan time and memory overhead.

Approach

The proposed method separates the relative contributions of white noise, fluctuating features, and stationary features. The method is demonstrated on mammary epithelial cell spheroids in three-dimensional culture for capturing intracellular motility without loss of signal integrity.

Results

Results show that the spatial patterns of motility are preserved and that hypothesis tests of spheroids treated with blebbistatin, a motor protein inhibitor, are unchanged with up to eightfold compression.

Conclusions

The ability to measure short- and long-term correlations compressively will enable new applications in (3+1)D imaging and high-throughput screening.

On the Determination of Lagrange Multipliers for a Weighted LASSO Problem Using Geometric and Convex Analysis Techniques

Compressed Sensing (CS) encompasses a broad array of theoretical and applied techniques for recovering signals, given partial knowledge of their coefficients, cf. Candés (C. R. Acad. Sci. Paris, Ser. I 346, 589-592 (2008)), Candés et al. (IEEE Trans. Inf. Theo (2006)), Donoho (IEEE Trans. Inf. Theo. 52(4), (2006)), Donoho et al. (IEEE Trans. Inf. Theo. 52(1), (2006)). Its applications span various fields, including mathematics, physics, engineering, and several medical sciences, cf. Adcock and Hansen (Compressive Imaging: Structure, Sampling, Learning, p. 2021), Berk et al. (2019 13th International conference on Sampling Theory and Applications (SampTA) pp. 1-5. IEEE (2019)), Brady et al. (Opt. Express 17(15), 13040-13049 (2009)), Chan (Terahertz imaging with compressive sensing. Rice University, USA (2010)), Correa et al. (2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 7789-7793 (2014, May) IEEE), Gao et al. (Nature 516(7529), 74-77 (2014)), Liu and Kang (Opt. Express 18(21), 22010-22019 (2010)), McEwen and Wiaux (Mon. Notices Royal Astron. Soc. 413(2), 1318-1332 (2011)), Marim et al. (Opt. Lett. 35(6), 871-873 (2010)), Yu and Wang (Phys. Med. Biol. 54(9), 2791 (2009)), Yu and Wang (Phys. Med. Biol. 54(9), 2791 (2009)). Motivated by our interest in the mathematics behind Magnetic Resonance Imaging (MRI) and CS, we employ convex analysis techniques to analytically determine equivalents of Lagrange multipliers for optimization problems with inequality constraints, specifically a weighted LASSO with voxel-wise weighting. We investigate this problem under assumptions on the fidelity term A x - b 2 2 , either concerning the sign of its gradient or orthogonality-like conditions of its matrix. To be more precise, we either require the sign of each coordinate of 2 ( A x - b ) T A to be fixed within a rectangular neighborhood of the origin, with the side lengths of the rectangle dependent on the constraints, or we assume A T A to be diagonal. The objective of this work is to explore the relationship between Lagrange multipliers and the constraints of a weighted variant of LASSO, specifically in the mentioned cases where this relationship can be computed explicitly. As they scale the regularization terms of the weighted LASSO, Lagrange multipliers serve as tuning parameters for the weighted LASSO, prompting the question of their potential effective use as tuning parameters in applications like MR image reconstruction and denoising. This work represents an initial step in this direction.

Deep learning empowered highly compressive SS-OCT via learnable spectral-spatial sub-sampling

With the rapid advances of light source technology, the A-line imaging rate of swept-source optical coherence tomography (SS-OCT) has experienced a great increase in the past three decades. The bandwidths of data acquisition, data transfer, and data storage, which can easily reach several hundred megabytes per second, have now been considered major bottlenecks for modern SS-OCT system design. To address these issues, various compression schemes have been previously proposed. However, most of the current methods focus on enhancing the capability of the reconstruction algorithm and can only provide a data compression ratio (DCR) up to 4 without impairing the image quality. In this Letter, we proposed a novel design paradigm, in which the sub-sampling pattern for interferogram acquisition is jointly optimized with the reconstruction algorithm in an end-to-end manner. To validate the idea, we retrospectively apply the proposed method on an ex vivo human coronary optical coherence tomography (OCT) dataset. The proposed method could reach a maximum DCR of ∼62.5 with peak signal-to-noise ratio (PSNR) of 24.2 dB, while a DCR of ∼27.78 could yield a visually pleasant image with a PSNR of ∼24.6 dB. We believe the proposed system could be a viable remedy for the ever-growing data issue in SS-OCT.

GPU-accelerated iterative method for FD-OCT image reconstruction with an image-level cross-domain regularizer

The image reconstruction for Fourier-domain optical coherence tomography (FD-OCT) could be achieved by iterative methods, which offer a more accurate estimation than the traditional inverse discrete Fourier transform (IDFT) reconstruction. However, the existing iterative methods are mostly A-line-based and are developed on CPU, which causes slow reconstruction. Besides, A-line-based reconstruction makes the iterative methods incompatible with most existing image-level image processing techniques. In this paper, we proposed an iterative method that enables B-scan-based OCT image reconstruction, which has three major advantages: (1) Large-scale parallelism of the OCT dataset is achieved by using GPU acceleration. (2) A novel image-level cross-domain regularizer was developed, such that the image processing could be performed simultaneously during the image reconstruction; an enhanced image could be directly generated from the OCT interferogram. (3) The scalability of the proposed method was demonstrated for 3D OCT image reconstruction. Compared with the state-of-the-art (SOTA) iterative approaches, the proposed method achieves higher image quality with reduced computational time by orders of magnitude. To further show the image enhancement ability, a comparison was conducted between the proposed method and the conventional workflow, in which an IDFT reconstructed OCT image is later processed by a total variation-regularized denoising algorithm. The proposed method can achieve a better performance evaluated by metrics such as signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR), while the speed is improved by more than 30 times. Real-time image reconstruction at more than 20 B-scans per second was realized with a frame size of 4096 (axial) × 1000 (lateral), which showcases the great potential of the proposed method in real-world applications.

Compressive-sensing swept-source optical coherence tomography angiography with reduced noise

Optical coherence tomography angiography (OCTA), as a functional extension of optical coherence tomography (OCT), has exhibited a great potential to aid in clinical diagnostics. Currently, OCTA still suffers from motion artifact and noise. Therefore, in this article, we propose to implement compressive sensing (CS) on B-scans to reduce motion artifact by increasing B-scan rate. Meanwhile, a noise reduction filter is specially designed by combining CS, Gaussian filter and median filter. Specially, CS filtering is realized by averaging multiple CS repetitions on en-face OCTA images with varied sampling functions. The method is evaluated on in vivo OCTA images of human skin. The results show that vasculature structures can be reconstructed well through CS on B-scans with a sampling rate of 70%. Moreover, the noise can be significantly eliminated by the developed filter. This implies that our method has a good potential to expedite OCTA imaging and improve the image quality.

De-aliased depth-range-extended optical coherence tomography based on dual under-sampling

We demonstrate a dual under-sampling (DUS) method to achieve de-aliased and depth-range-extended optical coherence tomography (OCT) imaging. The spectral under-sampling can significantly reduce the data size but causes well-known aliasing artifacts. A change in the sampling frequency used to acquire the interference spectrum alters the aliasing period within the output window except for the true image; this feature is utilized to distinguish the true image from the aliasing artifacts. We demonstrate that with DUS, the data size is reduced to 37% at an extended depth range of 24 mm, over which the true depth can be precisely measured without ambiguity. This reduction in data size and precise measuring capability would be beneficial for reducing the acquisition time for OCT imaging in various biomedical and industrial applications.

Bio-Inspired In-Sensor Compression and Computing Based on Phototransistors

The biological nervous system possesses a powerful information processing capability, and only needs a partial signal stimulation to perceive the entire signal. Likewise, the hardware implementation of an information processing system with similar capabilities is of great significance, for reducing the dimensions of data from sensors and improving the processing efficiency. Here, it is reported that indium-gallium-zinc-oxide thin film phototransistors exhibit the optoelectronic switching and light-tunable synaptic characteristics for in-sensor compression and computing. Phototransistor arrays can compress the signal while sensing, to realize in-sensor compression. Additionally, a reservoir computing network can also be implemented via phototransistors for in-sensor computing. By integrating these two systems, a neuromorphic system for high-efficiency in-sensor compression and computing is demonstrated. The results reveal that even for cases where the signal is compressed by 50%, the recognition accuracy of reconstructed signal still reaches ≈96%. The work paves the way for efficient information processing of human-computer interactions and the Internet of Things.

Convolutional dictionary learning for blind deconvolution of optical coherence tomography images

In this study, we demonstrate a sparsity-regularized, complex, blind deconvolution method for removing sidelobe artefacts and stochastic noise from optical coherence tomography (OCT) images. Our method estimates the complex scattering amplitude of tissue on a line-by-line basis by estimating and deconvolving the complex, one-dimensional axial point spread function (PSF) from measured OCT A-line data. We also present a strategy for employing a sparsity weighting mask to mitigate the loss of speckle brightness within tissue-containing regions caused by the sparse deconvolution. Qualitative and quantitative analyses show that this approach suppresses sidelobe artefacts and background noise better than traditional spectral reshaping techniques, with negligible loss of tissue structure. The technique is particularly useful for emerging OCT applications where OCT images contain strong specular reflections at air-tissue boundaries that create large sidelobe artefacts.

Compressive sensing for polarization sensitive optical coherence tomography

In this report, we report on the implementation of compressive sensing (CS) and sparse sampling in polarization sensitive optical coherence tomography (PS-OCT) to reduce the number of B-scans (frames consisting of an array of A-scans, where each represents a single depth profile of reflections) required for effective volumetric (3D dataset composed of an array of B-scans) PS-OCT measurements (i.e. OCT intensity, and phase retardation) reconstruction. Sparse sampling of PS-OCT is achieved through randomization of step sizes along the slow-axis of PS-OCT imaging, covering the same spatial ranges as those with equal slow-axis step sizes, but with a reduced number of B-scans. Tested on missing B-scan rates of 25%, 50% and 75%, we found CS could reconstruct reasonably good (as evidenced by a correlation coefficient >0.6) PS-OCT measurements with a maximum reduced B-scan rate of 50%, thereby accelerating and doubling the rate of volumetric PS-OCT measurements.

3-D compressed sensing optical coherence tomography using predictive coding

We present a compressed sensing (CS) algorithm and sampling strategy for reconstructing 3-D Optical Coherence Tomography (OCT) image volumes from as little as 10% of the original data. Reconstruction using the proposed method, Denoising Predictive Coding (DN-PC), is demonstrated for five clinically relevant tissue types including human heart, retina, uterus, breast, and bovine ligament. DN-PC reconstructs the difference between adjacent b-scans in a volume and iteratively applies Gaussian filtering to improve image sparsity. An a-line sampling strategy was developed that can be easily implemented in existing Spectral-Domain OCT systems and reduce scan time by up to 90%.

Reconstruction of Optical Coherence Tomography Images Using Mixed Low Rank Approximation and Second Order Tensor Based Total Variation Method

This paper proposes a mixed low-rank approximation and second-order tensor-based total variation (LRSOTTV) approach for the super-resolution and denoising of retinal optical coherence tomography (OCT) images through effective utilization of nonlocal spatial correlations and local smoothness properties. OCT imaging relies on interferometry, which explains why OCT images suffer from a high level of noise. In addition, data subsampling is conducted during OCT A-scan and B-scan acquisition. Therefore, using effective super-resolution algorithms is necessary for reconstructing high-resolution clean OCT images. In this paper, a low-rank regularization approach is proposed for exploiting nonlocal self-similarity prior to OCT image reconstruction. To benefit from the advantages of the redundancy of multi-slice OCT data, we construct a third-order tensor by extracting the nonlocal similar three-dimensional blocks and grouping them by applying the k-nearest-neighbor method. Next, the nuclear norm is used as a regularization term to shrink the singular values of the constructed tensor in the non-local correlation direction. Further, the regularization approaches of the first-order tensor-based total variation (FOTTV) and SOTTV are proposed for better preservation of retinal layers and suppression of artifacts in OCT images. The alternative direction method of multipliers (ADMM) technique is then used to solve the resulting optimization problem. Our experiments show that integrating SOTTV instead of FOTTV into a low-rank approximation model can achieve noticeably improved results. Our experimental results on the denoising and super-resolution of OCT images demonstrate that the proposed model can provide images whose numerical and visual qualities are higher than those obtained by using state-of-the-art methods.

High signal-to-noise ratio reconstruction of low bit-depth optical coherence tomography using deep learning

SIGNIFICANCE

Reducing the bit depth is an effective approach to lower the cost of an optical coherence tomography (OCT) imaging device and increase the transmission efficiency in data acquisition and telemedicine. However, a low bit depth will lead to the degradation of the detection sensitivity, thus reducing the signal-to-noise ratio (SNR) of OCT images.

AIM

We propose using deep learning to reconstruct high SNR OCT images from low bit-depth acquisition.

APPROACH

The feasibility of our approach is evaluated by applying this approach to the quantized 3- to 8-bit data from native 12-bit interference fringes. We employ a pixel-to-pixel generative adversarial network (pix2pixGAN) architecture in the low-to-high bit-depth OCT image transition.

RESULTS

Extensively, qualitative and quantitative results show our method could significantly improve the SNR of the low bit-depth OCT images. The adopted pix2pixGAN is superior to other possible deep learning and compressed sensing solutions.

CONCLUSIONS

Our work demonstrates that the proper integration of OCT and deep learning could benefit the development of healthcare in low-resource settings.

Super-resolution technology to simultaneously improve optical & digital resolution of optical coherence tomography via deep learning

Optical coherence tomography (OCT) has stimulated a wide range of medical image-based diagnosis and treatment. In cardiac imaging, OCT has been used in assessing plaques before and after stenting. While needed in many scenarios, high resolution comes at the costs of demanding optical design and data storage/transmission. In OCT, there are two types of resolutions to characterize image quality: optical and digital resolutions. Although multiple existing works have heavily emphasized on improving the digital resolution, the studies on improving optical resolution or both resolutions remain scarce. In this paper, we focus on improving both resolutions. In particular, we investigate a deep learning method to address the problem of generating a high-resolution (HR) OCT image from a low optical and low digital resolution (L2R) image. To this end, we have modified the existing super-resolution generative adversarial network (SR-GAN) for OCT image reconstruction. Experimental results from the human coronary OCT images have demonstrated that the reconstructed images from highly compressed data could achieve high structural similarity and accuracy in comparison with the HR images. Besides, our method has obtained better denoising performance than the block-matching and 3D filtering (BM3D) and Denoising Convolutional Neural Networks (DnCNN) denoising method.

Super-Resolution of Optical Coherence Tomography Images by Scale Mixture Models

In this paper, a new statistical model is proposed for the single image super-resolution of retinal Optical Coherence Tomography (OCT) images. OCT imaging relies on interfero-metry, which explains why OCT images suffer from a high level of noise. Moreover, data subsampling is carried out during the acquisition of OCT A-scans and B-scans. So, it is necessary to utilize effective super-resolution algorithms to reconstruct high-resolution clean OCT images. In this paper, a nonlocal sparse model-based Bayesian framework is proposed for OCT restoration. For this reason, by characterizing nonlocal patches with similar structures, known as a group, the sparse coefficients of each group of OCT images are modeled by the scale mixture models. In this base, the coefficient vector is decomposed into the point-wise product of a random vector and a positive scaling variable. Estimation of the sparse coefficients depends on the proposed distribution for the random vector and scaling variable where the Laplacian random vector and Generalized Extreme-Value (GEV) scale parameter (Laplacian+GEV model) show the best goodness of fit for each group of OCT images. Finally, a new OCT super-resolution method based on this new scale mixture model is introduced, where the maximum a posterior estimation of both sparse coefficients and scaling variables are calculated efficiently by applying an alternating minimization method. Our experimental results prove that the proposed OCT super-resolution method based on the Laplacian+GEV model outperforms other competing methods in terms of both subjective and objective visual qualities.

Blur resolved OCT: full-range interferometric synthetic aperture microscopy through dispersion encoding

We present a computational method for full-range interferometric synthetic aperture microscopy (ISAM) under dispersion encoding. With this, one can effectively double the depth range of optical coherence tomography (OCT), whilst dramatically enhancing the spatial resolution away from the focal plane. To this end, we propose a model-based iterative reconstruction (MBIR) method, where ISAM is directly considered in an optimization approach, and we make the discovery that sparsity promoting regularization effectively recovers the full-range signal. Within this work, we adopt an optimal nonuniform discrete fast Fourier transform (NUFFT) implementation of ISAM, which is both fast and numerically stable throughout iterations. We validate our method with several complex samples, scanned with a commercial SD-OCT system with no hardware modification. With this, we both demonstrate full-range ISAM imaging and significantly outperform combinations of existing methods.

Optical coherence tomography using physical domain data compression to achieve MHz A-scan rates

The three-dimensional volumetric imaging capability of optical coherence tomography (OCT) leads to the generation of large amounts of data, which necessitates high speed acquisition followed by high dimensional image processing and visualization. This signal acquisition and processing pipeline demands high A-scan rates on the front end, which has driven researchers to push A-scan acquisition rates into the MHz regime. To this end, the optical time-stretch approach uses a mode locked laser (MLL) source, dispersion in optical fiber, and a single analog-to-digital converter (ADC) to achieve multi-MHz A-scan rates. While enabling impressive performance this Nyquist sampling approach is ultimately constrained by the sampling rate and bandwidth of the ADC. Additionally such an approach generates massive amounts of data. Here we present a compressed sensing (CS) OCT system that uses a MLL, electro-optic modulation, and optical dispersion to implement data compression in the physical domain and rapidly acquire real-time compressed measurements of the OCT signals. Compression in the analog domain prior to digitization allows for the use of lower bandwidth ADCs, which reduces cost and decreases the required data capacity of the sampling interface. By leveraging a compressive A-scan optical sampling approach and the joint sparsity of C-scan data we demonstrate 14.4-MHz to 144-MHz A-scan acquisition speeds using a sub-Nyquist 1.44 Gsample/sec ADC sampling rate. Furthermore we evaluate the impact of data compression and resulting imaging speed on image quality.

Structural and Functional Sensing of Bio-Tissues Based on Compressive Sensing Spectral Domain Optical Coherence Tomography

In this paper, a full depth 2D CS-SDOCT approach is proposed, which combines two-dimensional (2D) compressive sensing spectral-domain optical coherence tomography (CS-SDOCT) and dispersion encoding (ED) technologies, and its applications in structural imaging and functional sensing of bio-tissues are studied. Specifically, by introducing a large dispersion mismatch between the reference arm and sample arm in SD-OCT system, the reconstruction of the under-sampled A-scan data and the removal of the conjugated images can be achieved simultaneously by only two iterations. The under-sampled B-scan data is then reconstructed using the classic CS reconstruction algorithm. For a 5 mm × 3.2 mm fish-eye image, the conjugated image was reduced by 31.4 dB using 50% × 50% sampled data (250 depth scans and 480 spectral sampling points per depth scan), and all A-scan data was reconstructed in only 1.2 s. In addition, we analyze the application performance of the CS-SDOCT in functional sensing of locally homogeneous tissue. Simulation and experimental results show that this method can correctly reconstruct the extinction coefficient spectrum under reasonable iteration times. When 8 iterations were used to reconstruct the A-scan data in the imaging experiment of fisheye, the extinction coefficient spectrum calculated using 50% × 50% data was approximately consistent with that obtained with 100% data.

Dual-Channel Spectral Domain Optical Coherence Tomography Based on a Single Spectrometer Using Compressive Sensing

Dual-channel spectral domain optical coherence tomography (SD-OCT) is one of the effective methods for improving imaging depth and imaging speed. In this paper, we design a dual-channel SD-OCT system based on a single spectrometer that can operate in two modes: (1) Increasing imaging speed and (2) expanding imaging depth. An optical path offset is preintroduced between the two channels to separate the two-channel data. However, this offset increases the requirement for the spectral resolution of the spectrometer in mode (1), so compressive sensing (CS) technology is used herein to overcome this problem. Consequently, in mode (1), when the spectral resolution of the spectrometer is the same as that used in the single-channel system, we use a dual-channel SD-OCT system combined with CS technology to double the imaging speed. In mode (2), when the spectral resolution of the spectrometer is only half of that used in a single-channel system, the imaging depth can be nearly doubled. We demonstrate the feasibility and effectiveness of the method proposed in this work by imaging a mirror, a fish fin, a fish eye, and an onion.

Compressed sensing spectral domain optical coherence tomography with a hardware sparse-sampled camera

We present a sparse-sampled camera for compressed sensing spectral domain optical coherence tomography (CS SD-OCT), which is mainly composed of a novel mask with specially designed coating and a commercially available CCD camera. The sparse-sampled camera under-samples the SD-OCT spectrum in hardware, thus reduces the acquired image data and can achieve faster A-scan speed than conventional CCD camera with the same pixel number. Compared with a conventional SD-OCT system, the CS SD-OCT system equipped with the sparse-sampled camera has better fall-off and SNR performance. CS-OCT imaging of bio-tissue is also demonstrated.

Compressed sensing-enabled phase-sensitive swept-source optical coherence tomography

Here we present a novel phase-sensitive swept-source optical coherence tomography (PhS-SS-OCT) system. The simultaneously recorded calibration signal, which is commonly used in SS-OCT to stabilize the phase, is randomly sub-sampled during the acquisition, and it is later reconstructed based on the Compressed Sensing (CS) theory. We first mathematically investigated the method, and verified it through computer simulations. We then conducted a vibrational frequency test and a flow velocity measurement in phantoms to demonstrate the system's capability of handling phase-sensitive tasks. The proposed scheme shows excellent phase stability with greatly discounted data bandwidth compared with conventional procedures. We further showcased the usefulness of the system in biological samples by detecting the blood flow in ex vivo swine left marginal artery. The proposed system is compatible with most of the existing SS-OCT systems and could be a preferred solution for future high-speed phase-sensitive applications.

Three-dimensional endoscopic OCT using sparse sampling with a miniature magnetic-driven scanning probe

We propose to apply sparse sampling and compressive sensing (CS) reconstruction in three-dimensional (3D) endoscopic optical coherence tomography (OCT) to reduce the amount of data required in the imaging process. We used a homemade miniature side-imaging magnetic-driven scanning probe with an outer diameter of 1.4 mm in a 1310 nm swept-source OCT system to acquire two-dimensional (2D) circumferential cross-sectional images of an ex vivo pigeon trachea sample. 3D imaging is then achieved by reconstruction from the multiple 2D images acquired while pulling the sample with a translation stage. Given a total translation distance, we achieved sparse sampling by randomizing the step sizes of the translation stage such that the total number of the acquired 2D frames was reduced compared with conventional 3D imaging with equally spaced step positions. We tested the CS reconstruction with reduced 2D frame numbers of 40%, 60%, and 80% compared with the case of equally spaced step positions. The results show that it is possible to recover reasonable OCT images using sparse sampling with CS reconstruction. Compared with the conventional equally spaced sampling method, our method provides a novel way for image acquisition and reconstruction that could significantly reduce the amount of 3D OCT imaging data, and thus the acquisition time.

Full-depth compressive sensing spectral-domain optical coherence tomography based on a compressive dispersion encoding method

By combining the advantages of compressive sensing optical coherence tomography (OCT) and full-depth OCT in terms of imaging time and imaging depth, we demonstrate how compressive sampling and dispersion encoding can be simultaneously used to reconstruct a full-depth OCT image. Moreover, by considering the image processing speed, we propose a two-step compressive dispersion encoding (TCDE) method, in which a large dispersion imbalance is introduced between the reference arm and the sample arm and two iterations are performed. The first iteration selects the signals with higher intensity and then removes their conjugate items and incoherent aliasing artifacts caused by undersampling based on the least squares method. The second iteration selects the signals with lower intensity. Experimental results show that nearly the same conjugate inhibition ratio can be obtained with 50% sampled data and 100% sampled data using the TCDE method. Full-depth images of a glass slide, an onion, and a live fish eye are obtained from 50% and 100% sampled data using the TCDE method. For a 1.4  mm×3.6  mm fish eye image, the conjugate items are reduced by 33.2 and 31.7 dB using 50% sampled data and 100% sampled data, respectively.

Optical coherence tomography retinal image reconstruction via nonlocal weighted sparse representation

We present a nonlocal weighted sparse representation (NWSR) method for reconstruction of retinal optical coherence tomography (OCT) images. To reconstruct a high signal-to-noise ratio and high-resolution OCT images, utilization of efficient denoising and interpolation algorithms are necessary, especially when the original data were subsampled during acquisition. However, the OCT images suffer from the presence of a high level of noise, which makes the estimation of sparse representations a difficult task. Thus, the proposed NWSR method merges sparse representations of multiple similar noisy and denoised patches to better estimate a sparse representation for each patch. First, the sparse representation of each patch is independently computed over an overcomplete dictionary, and then a nonlocal weighted sparse coefficient is computed by averaging representations of similar patches. Since the sparsity can reveal relevant information from noisy patches, combining noisy and denoised patches' representations is beneficial to obtain a more robust estimate of the unknown sparse representation. The denoised patches are obtained by applying an off-the-shelf image denoising method and our method provides an efficient way to exploit information from noisy and denoised patches' representations. The experimental results on denoising and interpolation of spectral domain OCT images demonstrated the effectiveness of the proposed NWSR method over existing state-of-the-art methods.

Segmentation Based Sparse Reconstruction of Optical Coherence Tomography Images

We demonstrate the usefulness of utilizing a segmentation step for improving the performance of sparsity based image reconstruction algorithms. In specific, we will focus on retinal optical coherence tomography (OCT) reconstruction and propose a novel segmentation based reconstruction framework with sparse representation, termed segmentation based sparse reconstruction (SSR). The SSR method uses automatically segmented retinal layer information to construct layer-specific structural dictionaries. In addition, the SSR method efficiently exploits patch similarities within each segmented layer to enhance the reconstruction performance. Our experimental results on clinical-grade retinal OCT images demonstrate the effectiveness and efficiency of the proposed SSR method for both denoising and interpolation of OCT images.

Unconventional methods of imaging: computational microscopy and compact implementations

In the past two decades or so, there has been a renaissance of optical microscopy research and development. Much work has been done in an effort to improve the resolution and sensitivity of microscopes, while at the same time to introduce new imaging modalities, and make existing imaging systems more efficient and more accessible. In this review, we look at two particular aspects of this renaissance: computational imaging techniques and compact imaging platforms. In many cases, these aspects go hand-in-hand because the use of computational techniques can simplify the demands placed on optical hardware in obtaining a desired imaging performance. In the first main section, we cover lens-based computational imaging, in particular, light-field microscopy, structured illumination, synthetic aperture, Fourier ptychography, and compressive imaging. In the second main section, we review lensfree holographic on-chip imaging, including how images are reconstructed, phase recovery techniques, and integration with smart substrates for more advanced imaging tasks. In the third main section we describe how these and other microscopy modalities have been implemented in compact and field-portable devices, often based around smartphones. Finally, we conclude with some comments about opportunities and demand for better results, and where we believe the field is heading.

Iterative l(1)-min algorithm for fixed pattern noise removal in fiber-bundle-based endoscopic imaging

In this study, we developed a signal processing method for fixed pattern noise removal in fiber-bundle-based endoscopic imaging. We physically acquired the fixed pattern of the fiber bundle and used it as a prior image in an l₁ norm minimization (l₁-min) algorithm. We chose an iterative shrinkage thresholding algorithm for l₁ norm minimization. In addition to fixed pattern noise removal, this method also improved image contrast while preserving spatial resolution. The effectiveness of this method was demonstrated on images obtained from a dark-field illuminated reflectance fiber-optic microscope (DRFM). The iterative l₁-min algorithm presented in this paper, in combination with the DRFM system that we previously developed, enables high-resolution, high-sensitivity, intrinsic-contrast, and in situ cellular imaging which has great potential in clinical diagnosis and biomedical research.

Iterative re-weighted approach to high-resolution optical coherence tomography with narrow-band sources

Optical coherence tomography (OCT) is a non-invasive optical imaging modality capable of high resolution imaging of internal tissue structures. It is widely believed that the high axial resolution in OCT systems requires a wide-bandwidth light source. As a result, often the potential advantages of narrow-bandwidth sources (in terms of cost and/or imaging speed) are understood to come at the cost of significant reduction in imaging resolution. In this paper, we argue that this trade-off between resolution and speed is a shortcoming imposed by the-state-of-the-art A-scan reconstruction algorithm, Fast Fourier Transform, and can be circumvented through use of alternative processing methods. In particular, we investigate the shortcomings of the FFT as well as previously proposed alternatives and demonstrate the first application of an iterative regularized re-weighted l(2) norm method to improve the axial resolution of fast scan rate OCT systems in the narrow-bandwidth imaging conditions. We validate our claims via experimental results generated from a home-built OCT system used to image layered phantom and in vivo data. Our results rely on new, sophisticated signal processing algorithms to generate higher precision (i.e., higher resolution) OCT images at correspondingly fast scan rates. In other words, our work demonstrates the feasibility of simultaneously more reliable and more comfortable medical imaging systems for patients by reducing the overall scan time, without sacrificing image quality.

Volumetric (3D) compressive sensing spectral domain optical coherence tomography

In this work, we proposed a novel three-dimensional compressive sensing (CS) approach for spectral domain optical coherence tomography (SD OCT) volumetric image acquisition and reconstruction. Instead of taking a spectral volume whose size is the same as that of the volumetric image, our method uses a sub set of the original spectral volume that is under-sampled in all three dimensions, which reduces the amount of spectral measurements to less than 20% of that required by the Shan-non/Nyquist theory. The 3D image is recovered from the under-sampled spectral data dimension-by-dimension using the proposed three-step CS reconstruction strategy. Experimental results show that our method can significantly reduce the sampling rate required for a volumetric SD OCT image while preserving the image quality.

Real-time dispersion-compensated image reconstruction for compressive sensing spectral domain optical coherence tomography

In this work, we propose a novel dispersion compensation method that enables real-time compressive sensing (CS) spectral domain optical coherence tomography (SD OCT) image reconstruction. We show that dispersion compensation can be incorporated into CS SD OCT by multiplying the dispersion-correcting terms by the undersampled spectral data before CS reconstruction. High-quality SD OCT imaging with dispersion compensation was demonstrated at a speed in excess of 70 frames per s using 40% of the spectral measurements required by the well-known Shannon/Nyquist theory. The data processing and image display were performed on a conventional workstation having three graphics processing units.

GPU-accelerated non-uniform fast Fourier transform-based compressive sensing spectral domain optical coherence tomography

We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial) × 1,000(lateral).

Real-time compressive sensing spectral domain optical coherence tomography

We developed and demonstrated real-time compressive sensing (CS) spectral domain optical coherence tomography (SD-OCT) B-mode imaging at excess of 70 fps. The system was implemented using a conventional desktop computer architecture having three graphics processing units. This result shows speed gain of 459 and 112 times compared to the best CS implementations based on the MATLAB and C++, respectively, and that real-time CS SD-OCT imaging can finally be realized.

Fast acquisition and reconstruction of optical coherence tomography images via sparse representation

In this paper, we present a novel technique, based on compressive sensing principles, for reconstruction and enhancement of multi-dimensional image data. Our method is a major improvement and generalization of the multi-scale sparsity based tomographic denoising (MSBTD) algorithm we recently introduced for reducing speckle noise. Our new technique exhibits several advantages over MSBTD, including its capability to simultaneously reduce noise and interpolate missing data. Unlike MSBTD, our new method does not require an a priori high-quality image from the target imaging subject and thus offers the potential to shorten clinical imaging sessions. This novel image restoration method, which we termed sparsity based simultaneous denoising and interpolation (SBSDI), utilizes sparse representation dictionaries constructed from previously collected datasets. We tested the SBSDI algorithm on retinal spectral domain optical coherence tomography images captured in the clinic. Experiments showed that the SBSDI algorithm qualitatively and quantitatively outperforms other state-of-the-art methods.

Energy-guided learning approach to compressive FD-OCT

High quality, large size volumetric imaging of biological tissue with optical coherence tomography (OCT) requires large number and high density of scans, which results in large data acquisition volume. This may lead to corruption of the data with motion artifacts related to natural motion of biological tissue, and could potentially cause conflicts with the maximum permissible exposure of biological tissue to optical radiation. Therefore, OCT can benefit greatly from different approaches to sparse or compressive sampling of the data where the signal is recovered from its sub-Nyquist measurements. In this paper, a new energy-guided compressive sensing approach is proposed for improving the quality of images acquired with Fourier domain OCT (FD-OCT) and reconstructed from sparse data sets. The proposed algorithm learns an optimized sampling probability density function based on the energy distribution of the training data set, which is then used for sparse sampling instead of the commonly used uniformly random sampling. It was demonstrated that the proposed energy-guided learning approach to compressive FD-OCT of retina images requires 45% fewer samples in comparison with the conventional uniform compressive sensing (CS) approach while achieving similar reconstruction performance. This novel approach to sparse sampling has the potential to significantly reduce data acquisition while maintaining image quality.

Compressive sensing with dispersion compensation on non-linear wavenumber sampled spectral domain optical coherence tomography

We propose a novel compressive sensing (CS) method on spectral domain optical coherence tomography (SDOCT). By replacing the widely used uniform discrete Fourier transform (UDFT) matrix with a new sensing matrix which is a modification of the non-uniform discrete Fourier transform (NUDFT) matrix, it is shown that undersampled non-linear wavenumber spectral data can be used directly in the CS reconstruction. Thus k-space grid filling and k-linear mask calibration which were proposed to obtain linear wavenumber sampling from the non-linear wavenumber interferometric spectra in previous studies of CS in SDOCT (CS-SDOCT) are no longer needed. The NUDFT matrix is modified to promote the sparsity of reconstructed A-scans by making them symmetric while preserving the value of the desired half. In addition, we show that dispersion compensation can be implemented by multiplying the frequency-dependent correcting phase directly to the real spectra, eliminating the need for constructing complex component of the real spectra. This enables the incorporation of dispersion compensation into the CS reconstruction by adding the correcting term to the modified NUDFT matrix. With this new sensing matrix, A-scan with dispersion compensation can be reconstructed from undersampled non-linear wavenumber spectral data by CS reconstruction. Experimental results show that proposed method can achieve high quality imaging with dispersion compensation.

Modified compressive sensing optical coherence tomography with noise reduction

We study noise reduction using modified compressive sensing optical coherence tomography. We show that averaged modified compressed sensing (CS) reconstruction achieves better image quality in terms of signal-to-noise ratio, local contrast, and contrast-to-noise ratio, compared to the classical averaging method while reducing the total amount of data required to reconstruct the images. The same is also true when compared with standard CS-based averaging method with the same amount of undersampled data.

Compressed sensing with linear-in-wavenumber sampling in spectral-domain optical coherence tomography

We propose a novel method called compressed sensing with linear-in-wavenumber sampling (k-linear CS) to retrieve an image for spectral-domain optical coherence tomography (SD-OCT). An array of points that is evenly spaced in wavenumber domain is sampled from an original interferogram by a preset k-linear mask. Then the compressed sensing based on l1 norm minimization is applied on these points to reconstruct an A-scan data. To get an OCT image, this method uses less than 20% of the total data as required in the typical process and gets rid of the spectral calibration with numerical interpolation in traditional CS-OCT. Therefore k-linear CS is favorable for high speed imaging. It is demonstrated that the k-linear CS has the same axial resolution performance with ~30 dB higher signal-to-noise ratio (SNR) as compared with the numerical interpolation. Imaging of bio-tissue by SD-OCT with k-linear CS is also demonstrated.

Sparsity based denoising of spectral domain optical coherence tomography images

In this paper, we make contact with the field of compressive sensing and present a development and generalization of tools and results for reconstructing irregularly sampled tomographic data. In particular, we focus on denoising Spectral-Domain Optical Coherence Tomography (SDOCT) volumetric data. We take advantage of customized scanning patterns, in which, a selected number of B-scans are imaged at higher signal-to-noise ratio (SNR). We learn a sparse representation dictionary for each of these high-SNR images, and utilize such dictionaries to denoise the low-SNR B-scans. We name this method multiscale sparsity based tomographic denoising (MSBTD). We show the qualitative and quantitative superiority of the MSBTD algorithm compared to popular denoising algorithms on images from normal and age-related macular degeneration eyes of a multi-center clinical trial. We have made the corresponding data set and software freely available online.

Homotopic, non-local sparse reconstruction of optical coherence tomography imagery

The resolution in optical coherence tomography imaging is an important parameter which determines the size of the smallest features that can be visualized. Sparse sampling approaches have shown considerable promise in producing high resolution OCT images with fewer camera pixels, reducing both the cost and the complexity of an imaging system. In this paper, we propose a non-local approach to the reconstruction of high resolution OCT images from sparsely sampled measurements. An iterative strategy is introduced for minimizing a homotopic, non-local regularized functional in the spatial domain, subject to data fidelity constraints in the k-space domain. The novel algorithm was tested on human retinal, corneal, and limbus images, acquired in-vivo, demonstrating the effectiveness of the proposed approach in generating high resolution reconstructions from a limited number of camera pixels.

Broadband superluminescent diode-based ultrahigh resolution optical coherence tomography for ophthalmic imaging

Spectral domain optical coherence tomography (SD-OCT) with ultrahigh resolution can be used to measure precise structures in the context of ophthalmic imaging. We designed an ultrahigh resolution SD-OCT system based on broadband superluminescent diode (SLD) as the light source. An axial resolution of 2.2 μm in tissue, a scan depth of 1.48 mm, and a high sensitivity of 93 dB were achieved by the spectrometer designed. The ultrahigh-resolution SD-OCT system was employed to image the human cornea and retina with a cross-section image of 2048 × 2048 pixels. Our research demonstrated that ultrahigh -resolution SD-OCT can be achieved using broadband SLD in a simple way.