High-speed imaging through a disordered medium using multi-foci compressive sensing

Abstract

The present disclosure provides a method and system which transports light through the disordered medium or multimode fiber, the light being characterized with a real-valued intensity transmission matrix. Based on this matrix, the light transmitted through the MMF is shaped into multi-foci patterns by modulating the incident light wavefront with a digital micromirror device or the like. These multi-foci patterns may be recorded with a camera. Each multi-foci pattern can theoretically have an infinite number of foci, however, most commonly the multi-foci pattern has two or three foci at different locations. Often the number of foci within a multi-foci pattern is limited by the modulation power of the spatial light modulator, namely DMD. An imaging object is placed at the MMF distal tip and illuminated by the multi-foci patterns. A measurement, or measurements, indicative of signal strength are recorded as a vector, with each illumination pattern corresponding to an individual value. These signal strength measurements could be peak-to-peak amplitude, maximum value, integration etc. With the measurement patterns and signals, the images are reconstructed which may be through any compressive sensing algorithm compatible, such as the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA).

Description

[0001] HIGH-SPEED IMAGING THROUGH A DISORDERED MEDIUM USING MULTI-FOCI COMPRESSIVE SENSING Technical Field

[0002] The present disclosure generally relates to methods and systems for use in optical image sensing. More specifically, the present disclosure relates to methods and systems for use with imaging techniques through a disordered medium which utilizes multi-foci patterns for compressive sensing.

[0003] The present disclosure seeks to improve the problem wherein conventional compressive sensing technique have low SNR, system stability and low imaging speed.

[0004] Background and Related Art

[0005] Optical endoscopy is an important tool for biomedical research and medical assessment. One of the primary advantages of optical endoscopy is its minimally invasive nature, which allows healthcare professionals to access and visualise internal structures without the need for large surgical incisions. This reduces patient discomfort, lowers the risk of complications, and promotes faster recovery times. However, the size of conventional endoscopes that are based on miniature cameras or fibre bundles have confined their utility primarily to larger spaces like the digestive tract, respiratory system, and abdominal cavity.

[0006] The advancement in multimode fibre (MMF)-based endomicroscopy imaging in the past decade enables the development of ultrathin endoscopy probes that have diameters around only 100pm, significantly expending applications of optical endoscopes in animal brain studies and needle guidance in minimally invasive surgery [1, 2, 3, 4, 5, 6, 7, 8]. Typically, a MMF requires pre-calibration before the use in imaging, due to mode dispersion that scrambles coherent light transmission through a MMF into randomly-like speckle patterns. Wavefront shaping technique is used to modulate the incident light wavefront with a spatial light modulator at the proximal tip of the MMF, to shape the speckle into a tightly focused spot at or in front of the distal tip. Then, by sequentially modulating the incident wavefront, the focused laser beam could be raster scanned across the distal fibre tip for acquiring images pixel by pixel. A series of modalities have been achieved, including fluorescence [1, 2, 3], two-photons [7], photoacoustic [8, 9], confocal

[0010] , and Raman [6] imaging. While high-resolution images of animal and human samples have been demonstrated, however, the imaging speed of MMF-based endomicroscopes has been insufficient for clinical translation. It is mainly restricted by the refresh rate of spatial light modulators. For example, the most commonly used spatial light modulator, liquid crystal ones, run at ~100 Hz, which correspondingly allows acquiring 100 image pixels in per second. In contrast, the commonly used digital micromirror devices (DMDs) have a typical rate of 23 kHz. The highest scanning speed achieved in literature is 47 kHz when using a sub-region of a micromirror array, which supported a rate of 4.7 frames per second for the acquisition of images consisting of 10,000 pixels

[0011] . However, this method leads to a trade-off in modulating power and hence the quality of light focusing. While reducing the number of scanning positions can directly improve imaging speed, it comes at the expense of image quality.

[0007] Compressive sensing has been studied as a faster alternative to raster-scan-based imaging through MMFs [12, 13, 14]. Different from raster-scan-based method that requires calibration of the MMF, compressive sensing-based imaging firstly records a set of speckles at the distal fibre tip by changing the incident light field. These speckles were used as measurement basis to illuminate the imaging object, whilst the excited fluorescence or photoacoustic signals were collected and converted into a signal vector. By making use of the sparsity as a prior-information, the images of objects could be reconstructed from the measurement basis and the signal vector. The sparse nature of the imaging object allows a smaller number of measurement speckles than the number of pixels in the resulting image. So, the rate of image acquisition could be improved by several times [13, 14]. However, the use of natural speckles through MMFs suffers from low signal-to-noise ratio (SNR) in signal excitation, leading to degraded fluorescence imaging quality than raster- scan-based imaging on tissue sample

[0015] . In photoacoustic imaging which requires a much higher excitation laser light power, more than 100 times signal averaging in photoacoustic signal measurement was required to achieve a sufficient SNR [3]. Furthermore, the use of pre-recorded speckles as measurement basis requires a high system stability, as environmental disturbance induces decorrelation between prerecorded speckles and the ones that are actually used in signal measurement. As a result, this decorrelation led to significant degradation in imaging performance.

[0008] Summary of the Invention

[0009] To address the above challenges, in this work, we developed a multi-foci compressive sensing imaging method by combining compressive sensing algorithm with wavefront shaping-based laser light focusing technique. Different from conventional MMF-based compressive sensing method, random speckles were replaced with multi-foci patterns which have multiple light foci in each pattern. These patterns were achieved through wavefront shaping using a real-valued intensity transmission matrix (RVITM) algorithm [16, 17]. Photoacoustic microscopy imaging has been demonstrated on mouse red blood cells. Laser light focusing at multiple positions in one pattern was achieved through the real-valued intensity transmission matrix wavefront shaping technique developed in [3] (PCT / GB2021 / 050099). Note that other wavefront shaping techniques such as phase conjugation, transmission matrix, iterative algorithms can also be used for generating the focal foci. By using multi-foci patterns as the measurement basis, the SNR was improved owing to higher local light fluence, whilst the multi-foci patterns showed higher resistance to environmental vibrance and thus retained higher imaging performance in practical uses. Compared with raster-scan-based imaging, the multi-foci method provided comparable image quality with 10 times enhancement in imaging speed

[0010] The present disclosure therefore differs from all prior MMF imaging techniques that rely on either raster-scanning of a focused laser beam or random speckle patterns based on compressive sensing. The present disclosure provides a method which uses a set of multifoci patterns for compressive sensing. This method addresses current limitations of conventional compressive sensing technique in terms of low SNR and system stability, and improves the imaging speed of conventional raster-scanning based approaches.

[0011] The light transport through the MMF was characterized with a real-valued intensity transmission matrix. Based on this matrix, the light transmitted through the MMF was shaped into multi-foci patterns by modulating the incident light wavefront with a DMD. These multi-foci patterns were recorded with a camera. Each pattern had two or three foci at different locations. Then, the imaging object was placed at the MMF tip and illuminated by the multi-foci patterns. In photoacoustic imaging, a fibre-optic ultrasound sensor was used to captured the excited ultrasound waves from the object. The peak-to-peak amplitudes were recorded in photoacoustic signals as a vector, with each illumination pattern corresponding to an individual value. With the measurement patterns and signals, the images were reconstructed through the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) that has been used in conventional compressive sensing technique.

[0012] The present disclosure provides the following advantages:

[0013] 1. Compared to traditional raster-scan-based imaging, the use of compressive sensing approach for image acquisition improved the image acquisition speed by more than 5 times.

[0014] 2. Compared to current compressive sensing approach that use random speckle patterns for illumination, the method in accordance with the present disclosure uses multi-foci patterns, which benefits from higher signal-to-noise ratio and higher resistance to environmental vibrance, as demonstrated in both numerical simulation and experiments.

[0015] It should be noted that the present disclosure relates to methods and systems that may be applied to many different disordered medium for imaging applications. This could include, but is not limited to, coherent fibre bundles, random localization fibre bundles, optical diffusers, or even biological tissues. The only requirement for this imaging method is a disordered medium for optical wavefront shaping. Nonetheless, throughout the application the present disclosure has largely been discussed in relation to multimode fibres, more particularly multimode optical fibres or multimode optical fibre bundles.

[0016] The present disclosure provides a method of optical fiber compressive sensing, comprising: generating a multi-foci illumination pattern for transmission along an optical fiber; projecting the multi-foci illumination pattern from a distal tip of the optical fiber onto an imaging target; measuring a signal vector S that arises in dependence on an interaction of the multi-foci illumination pattern and the imaging target; and reconstructing an image of the target in dependence on the signal vector S.

[0017] An aspect of the present disclosure provides a method of optical wavefront shaping via a disordered medium, comprising one or more of: generating a multi-foci illumination pattern for transmission along the disordered medium; projecting the multi-foci illumination pattern from a distal tip of the disordered medium onto an imaging target; measuring a signal vector S that arises in dependence on an interaction of the multi-foci illumination pattern and the imaging target; and reconstructing an image of the target in dependence on the signal vector S.

[0018] The measuring may comprise measuring a photoacoustic ultrasound signal generated in the imaging target due to the multi-foci illumination pattern, the signal vector S may be related to the amplitude of the ultrasound signal.

[0019] The measuring may comprise measuring an optical transmission signal of light from the multi-foci illumination pattern that is transmitted through the imaging target, the signal vector S may be related to the intensity of the transmitted light.

[0020] The generating step may further comprise generating, by using a wavefront shaping method, the multi-foci illumination pattern for transmission along the disordered medium.

[0021] The generating step may further comprise one or more of: characterizing the disordered medium with a real-valued intensity transmission matrix; projecting light into the disordered medium via an optical modulator, the optical modulator being controlled in dependence on the real-valued intensity transmission matrix to generate the multi-foci illumination pattern in the projected light.

[0022] The reconstructing may use a Fast Iterative Shrinkage-Thresholding Algorithm (FISTA).

[0023] The reconstructing may be performed by utilizing the following equation:

[0024] X' = argmin||TX' - S|| + A||X' 1^ wherein T = measurement matrix of a set of multi-foci patterns, X = the imaging target and S = the signal vector.

[0025] The generating step may use a real-valued intensity transmission matrix (RVITM) algorithm, the RVITM algorithm may be used for characterising the light intensity transmission through the disordered medium for generating the multi-foci illumination program for light focusing with binary amplitude modulation.

[0026] A further aspect of the present disclosure provides a system for optical fiber compressive sensing, comprising one or more of: means for generating a multi-foci illumination pattern for transmission along an optical fiber; means for projecting the multi-foci illumination pattern from a distal tip of the optical fiber onto an imaging target; means for measuring a signal vector S that arises in dependence on an interaction of the multi-foci illumination pattern and the imaging target; and means for reconstructing an image of the target in dependence on the signal vector S.

[0027] The means for measuring may comprise means for measuring a photoacoustic ultrasound signal generated in the imaging target due to the multi-foci illumination pattern, the signal vector S may be related to the amplitude of the ultrasound signal.

[0028] The means for measuring may comprise means for measuring an optical transmission signal of light from the multi-foci illumination pattern that is transmitted through the imaging target, the signal vector S may be related to the intensity of the transmitted light.

[0029] The means for generating may further comprise: means for characterizing the optical fiber with a real-valued intensity transmission matrix; means for projecting light into the optical fiber via an optical modulator, the optical modulator being controlled in dependence on the real-valued intensity transmission matrix to generate the multi-foci illumination pattern in the projected light. The means for reconstructing may use a Fast Iterative Shrinkage-Thresholding Algorithm (FISTA).

[0030] The means for reconstructing may utilize the following equation:

[0031] X' = argmin||TX' - S|| + A||X' 1^ wherein T = measurement matrix of a set of multi-foci patterns, X = the imaging target and S = the signal vector.

[0032] The means for generating may use a real-valued intensity transmission matrix (RVITM) algorithm, the RVITM algorithm may be used for characterising the light intensity transmission through the optical fiber for generating the multi-foci illumination program for light focusing with binary amplitude modulation.

[0033] A further aspect of the present disclosure provides a system for optical fiber compressive sensing, comprising one or more of: a digital micromirror device (DMD) arranged in use to generate a multi-foci illumination pattern for transmission along an optical fiber, the multi-foci illumination pattern projecting in use from a distal tip of the optical fiber onto an imaging target; means for measuring a signal vector S that arises in dependence on an interaction of the multi-foci illumination pattern and the imaging target; and a processor arranged in use to reconstruct an image of the target in dependence on the signal vector S.

[0034] The means for measuring may comprise an ultrasound sensor arranged to detect and measure a photoacoustic ultrasound signal generated in the imaging target due to the multi-foci illumination pattern, the signal vector S may be related to the amplitude of the ultrasound signal.

[0035] The means for measuring may comprise a lens and camera arranged in use to measure an optical transmission signal of light from the multi-foci illumination pattern that is transmitted through the imaging target, the signal vector S may be related to the intensity of the transmitted light.

[0036] The optical fiber may be characterized with a real-valued intensity transmission matrix, and the digital micromirror device may be controlled in dependence on the real-valued intensity transmission matrix to generate the multi-foci illumination pattern in the projected light from the distal tip of the optical fiber onto the imaging target. The reconstructing by the processor may use a Fast Iterative Shrinkage-Thresholding Algorithm (FISTA).

[0037] The reconstructing by the processor may utilize the following equation:

[0038] X' = argmin||TX' - S|| + A||X' 1^ wherein T = measurement matrix of a set of multi-foci patterns, X = the imaging target and S = the signal vector.

[0039] Further features and advantages will be apparent from the appended claims.

[0040] Brief Description of the Drawings

[0041] Further features and advantages of the present disclosure will become apparent from the following description of an embodiment thereof, presented by way of example only, and with reference to the accompanying drawings, wherein like reference numerals refer to like parts, and wherein:

[0042] Figure la shows a depiction of the principles of multi-foci compressive sensing imaging, in particular it shows the multi-foci pattern acquisition;

[0043] Figure lb shows a depiction of the signal vector acquisition for use in multi-foci compressive sensing imaging;

[0044] Figure 1c shows a depiction of the image reconstruction wherein the measurement matrix and the signal vector were fed into a compressive sensing algorithm, in accordance with the present disclosure;

[0045] Figure 2 shows a schematic diagram of the experimental configuration used to complete imaging testing, in accordance with the present disclosure;

[0046] Figures 3a-3h shows a collection of images and graphs relating to numerical simulation imaging with speckle and 2-foci measurement patterns. Figure 3a shows an example of speckle patterns at the distal fibre tip. Figure 3b and 3c show images (M = 10,000) of an object achieved through compressive sensing with 5,000 (b) and 2,000 (c) speckle measurement patterns. Figure 3d shows the object to be imaged. Figure 3e shows an example of 2-foci patterns. Figure 3f and 3g show images that have been reconstructed with 2-foci measurement patterns with 5,000 and 2,000 measurement, respectively. Figure 3h shows the evolution of imaging performance with the reduction of measurement number K; Figures 4a-4d shows a collection of graphs showing the impacts of non-ideal environments on compressive sensing imaging performance. Figure 4a shows a graph of the evolution of correlation between the original pattern and the pattern after vibration with varying fluctuation level. Figure 4b shows the evolution of imaging performance with 2-foci patterns and random speckles with varying fluctuation level. Figure 4c shows the evolution of correlation and imaging performance of 2-foci compressive sensing imaging with high fluctuation level. Figure 4d shows the evolution of imaging performance of 2-foci and random pattern compressive sensing imaging with varying noise levels;

[0047] Figures 5a-5h show a series of photoacoustic imaging of carbon fibres. Specifically, Figures 5a-5d are recorded images of multi-foci patterns and random speckle. Figures 5e-5h are reconstructed images of a carbon fibre network with corresponding patterns;

[0048] Figures 6a-6f show a series of photoacoustic images in relation to mouse red blood cells. Specifically, Figure 6a relates to an Optical microscopy image (transmission-mode) of a mouse blood smear on a cover slip. Further, Figures 6b-6f show photoacoustic images of the same sample with raster-scan mode (b), speckle compressive sensing (c) and multifoci compressive sensing with R = 1 (d), 2 (e) and 5 (f) with a scale: 5 pm;

[0049] Figure 7 is a block diagram of a system according to an embodiment of the present disclosure;

[0050] Figure 8 is a flow diagram of a method according to an embodiment of the present disclosure.

[0051] Detailed Description of the Preferred Embodiments

[0052] The present disclosure provides a method and system for use in disordered medium, disordered media or multimode imaging techniques. Specifically, the present disclosure relates to a method and system which utilizes a set of multi-foci patterns for compressive sensing. In particular, in embodiments of the present disclosure, the method and system perform steps of generating a multi-foci illumination pattern for transmission along an optical fiber; projecting the multi-foci illumination pattern from a distal tip of the optical fiber onto an imaging target; measuring a signal vector S that arises in dependence on an interaction of the multi-foci illumination pattern and the imaging target; and reconstructing an image of the target in dependence on the signal vector S. In other words, embodiments of the present disclosure provide a method and system which transports light through the disordered medium or multimode fiber, the light being characterized with a real-valued intensity transmission matrix. Based on this matrix, the light transmitted through the MMF is shaped into multi-foci patterns by modulating the incident light wavefront with a digital micromirror device or the like. These multi-foci patterns may be recorded with a camera. Each multi-foci pattern can theoretically have an infinite number of foci, however, most commonly the multi-foci pattern has two or three foci at different locations. Often the number of foci within a multi-foci pattern is limited by the modulation power of the spatial light modulator, namely DMD. An imaging object is placed at the MMF distal tip and illuminated by the multi-foci patterns. A measurement, or measurements, indicative of signal strength are recorded as a vector, with each illumination pattern corresponding to an individual value. These signal strength measurements could be peak-to-peak amplitude, maximum value, integration etc. With the measurement patterns and signals, the images are reconstructed which may be through any compressive sensing algorithm compatible, such as the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA).

[0053] The present disclosure differs from all prior disordered medium or MMF imaging techniques that rely on either raster-scanning of a focused laser beam or random speckle patterns based on compressive sensing. The present disclosure provides a method which uses a set of multi-foci patterns for compressive sensing. This method addresses current limitations of conventional compressive sensing technique in terms of low SNR and system stability and improves the imaging speed of conventional raster-scanning based approaches.

[0054] The present disclosure will now be discussed in more detail in relation to the associated Figures.

[0055] Multi-foci compressive sensing imaging

[0056] Figure la shows a depiction of the principles of multi-foci compressive sensing imaging, in particular it shows the multi-foci pattern acquisition. Further, in Figure la the multimode fibers were characterised with real-valued intensity transmission matrix to generate foci at multiple positions in each pattern by displaying optimal DMD patterns at the proximal fibre tip. These patterns were digitally recorded as the measurement matrix. However, it is worth noting that the disordered medium, namely the multimode fibers, could have been characterized by any transmission matrix characterization methods or other wavefront shaping methods that enable pattern projection, such as a genetic algorithm, a step-wide algorithm, etc. In other words, Figure la shows a breakdown of multi-foci compressive sensing imagine 1 which incorporates a series of DMD patterns 10, the DMD patterns being incident on a multimode fibre 12, and the corresponding output multi-foci patterns 14. The multi-foci patterns 14 being recorded as a measurement matrix. Fundamentally, the DMD patterns 10 are generated for single point focusing. These DMD patterns 10 are used to focus light at multiple random positions by switching on micromirrors corresponding to a value larger than 0. By displaying these DMD patterns 10, a set of multi-foci patterns 14 were recorded as the measurement basis with each pattern converted into a row in the measurement matrix T, at the output of the multimode fibre 12.

[0057] There are three steps to achieve imaging through a MMF with the multi-foci compressive sensing method. The first step is to generate multi-foci patterns via wavefront shaping (Fig. la). The RVITM algorithm, which was detailed in [16, 17], was used to characterise light transport through the MMF and generated optimal DMD patterns for single-point focusing through. To focus light at multiple random positions, optimal DMD patterns corresponding to multiple random focusing positions were summed up and then converted into binary patterns by switching on micromirrors corresponding to a value larger than 0. By displaying these DMD patterns, a set of multi-foci patterns were recorded as the measurement basis with each pattern converted into a row in the measurement matrix T.

[0058] In the second step, these patterns (T) were sequentially projected onto the object (X) to generate the signal vector (S), as shown in Fig. lb. Figure lb shows a depiction of the signal vector acquisition for use in multi-foci compressive sensing imaging. Further, in Figure lb, the multi-foci patterns were projected onto an object to generate signals and an amplitude of the raw signal was generated by each multi-foci pattern in order to form a signal vector.

[0059] In photoacoustic imaging, each element in the signal vector is the peak-to-peak amplitude of each raw ultrasound signal. Figure 1c shows a depiction of the image reconstruction wherein the measurement matrix and the signal vector were fed into a compressive sensing algorithm, in accordance with the present disclosure. Theoretically, this signal vector value corresponds to the inner product of one illumination pattern with the imaging object, which can be expressed as:

[0060] S = TX (1)

[0061] In the third step, the image of object X was computationally reconstructed by solving an optimisation problem: X = argmin||TX -S|| (2)

[0062] With the pre-knowledge that the imaging target (natural objects) has a sparse representation and nonnegative intensity distribution in image, the equation used for image reconstruction in this case was re-written as:

[0063] The second term, incorporating a Ll-norm regularization, which is commonly used to promote sparsity in the object. To achieve optimal results, the regularisation parameter A should be carefully adjusted based on factors such as the SNR and the level of sparsity exhibited by the object. The computation in this study was achieved through the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA)

[0018] for fast convergence rates.

[0064] Numerical simulation

[0065] The imaging performance achieved with random speckle and multi-foci pattern measurement basis was compared at noise-free condition in numerical simulation in MATLAB. Both random speckles and multi-foci patterns used in simulation were captured in experiments. All measurement patterns have the same number of pixels (M = 100x100). The signal generation was mimicked as the inner product of object pattern and each measurement pattern (Eq. 1). The same number (K = 10,000) of speckles and patterns were collected while various number of illumination patterns were used for image reconstruction to study the impact of size of measurement basis.

[0066] Experimental basis measurements are subject to noise arising from both fluctuations in the measurement patterns and electronic readout noise on the detector. Since it is challenging to solely study an individual factor in experiments, the resistance of speckle and multi-foci to these factors were also studied in simulation. To mimic natural fluctuation that leads to decorrelation between the pre-recorded illumination patterns and the ones used in signal generation, background noise was added onto the experimentally recorded patterns to achieve various decorrelation coefficients. The noise intensities at all patterns pixels followed a normal distribution. Fluctuation level, defined as the ratio of average of noise intensity to the mean intensity of the measurement patterns, was varied from 0 to 1.8 for both random speckles and multi-foci patterns. In addition, the average of noise intensity varying from 2 to 3.6 times of the mean intensity was investigated for 2-foci measurement basis. The original measurement patterns (without fluctuation) and the signal vectors generated with the fluctuated patterns were used in image reconstruction. The fluctuated patterns were used to measure signals while the original patterns were used in image reconstruction through compressive sensing. To study the impact of signal noise, random noise varying from 0.01 to 0.09 times of the mean value of signal was directly added onto the signal vector. Signals with noise and the original measurement patterns were used for image reconstruction.

[0067] Experimental setup

[0068] Figure 2 shows a schematic diagram of the experimental configuration used to complete imaging testing, in accordance with the present disclosure. In the schematic diagram, the laser imaging apparatus 2 comprises a laser 20, a plurality of lens 21a-d, a DMD reflector 22, a first objective magnetizer 23, a second objective magnetizer 24, a beamsplitter 25, a camera and a PC 27. The setup further comprises a multimode fiber, a needle, an object (to be detected) in a water tank, a tunable laser and a photodiode. Further details of the arrangement are discussed below.

[0069] The configuration of the imaging system is illustrated as Fig. 2. Laser light is reflected by a DMD (768 x 1080 pixels, DLP7000, Texas Instruments, Texas) onto the proximal tip of a 30 cm-long gradient index fibre (0100pm, 0.29 NA, Newport, California) via an achromatic doublet lens (f = 50 mm, AC254-050-A-ML, Thorlabs, New Jersey) and an objective (20x, 0.4 NA, RMS20x, Thorlabs, New Jersey). A sub-region of the DMD covering 128x128 micromirrors was controlled. The light patterns transmitted from the distal MMF tip were captured by a CMOS camera (C11440-22CU01, Hamamatsu, Shizuoka Pref. Japan) after magnification by an objective (20x, 0.4 NA, RMS20x, Thorlabs, New Jersey) and an achromatic doublet lens (f = 100 mm, AC254-0100-A-ML, Thorlabs, New Jersey). In photoacoustic imaging, the light source is a pulsed laser emitting at 532 nm (2 ns, SPOT-10-200-532, Elforlight, UK). The MMF was placed parallelly with a fibre-optic ultrasound sensor

[0019] and both fibres were place in the cannula of a 22-guage needle. The fibre-optic sensor is based on a plano-concave microresonator that comprised a domeshaped epoxy spacer sandwiched by two dichroic mirrors, which was interrogated by a wavelength-tuneable continuous wave laser (TSL-550, Santec, UK). The incident ultrasound waves deform the epoxy spacer leading to changes in the optical reflectivity of the microresonator [20, 19]. An optical circulator (6015-3-APC, 1525-1610 nm, Thorlabs, New Jersey) was employed to deliver the interrogation laser to the microresonator cavity and collect the reflected light using a photodiode (G9801-22, Hamamatsu, Shizuoka Pref. Japan). The output was connected to a data acquisition card (M4L4420, Spectrum Instrumentation, Grosshansdorf, Germany) after amplification with an amplifier (SPA.1411, Spectrum Instrumentation, Grosshansdorf, Germany) and then transferred to a personal computer (Intel i7, 3.2 GHz) for processing. Compared to conventional piezoelectric ultrasound transducers, the optical sensor was nearly omni-directional and had a large bandwidth and a high sensitivity with a small size (125pm in diameter) [20, 19]. After multi-foci patterns collection, carbon fibres were placed in the imaging plane and the camera module was removed. The needle tip was inserted into a custom imaging tank filled with deionised water for acoustic coupling. Excited ultrasound waves were detected by the fibre-optic sensor. Synchronisation of the DMD patterns display, laserfiring, and data acquisition was controlled by a waveform generator (33600A, Keysight, Santa Rosa, California) and a custom MATLAB program.

[0070] Numerical simulation

[0071] Figures 3a-3h shows a collection of images and graphs relating to numerical simulation imaging with speckle and 2-foci measurement patterns 3. Figure 3a shows an example of speckle patterns at the distal fibre tip. Figure 3b and 3c show images (M = 10,000) of an object achieved through compressive sensing with 5,000 (b) and 2,000 (c) speckle measurement patterns. Figure 3d shows the object to be imaged. Figure 3e shows an example of 2-foci patterns. Figure 3f and 3g show images that have been reconstructed with 2-foci measurement patterns with 5,000 and 2,000 measurement, respectively. Figure 3h shows the evolution of imaging performance with the reduction of measurement number K.

[0072] Results of compressive sensing imaging with speckles and multi-foci measurement basis on the same object were shown in Fig. 3. On the ideal condition without any fluctuation or noise, images achieved with 2-foci basis showed almost the same image fidelity as the speckle basis. As shown by Fig. 3c and 3g, compressive sensing method reconstructed the image of object with a high accuracy with the number of measurements reduce by 5 times compared to raster-scan imaging. Both basis allowed the reduction of measurement size K to M / 20 with a trade-off of image quality, which is evaluated by peak signal-to-noise ratio (PSNR) compared to the ground truth from over 27 to approximately 12 (Fig. 3h).

[0073] A further numerical simulation is shown in Figures 4a-4d which shows a collection of graphs showing the impacts of non-ideal environments on compressive sensing imaging performance 4. Figure 4a shows a graph of the evolution of correlation between the original pattern and the pattern after vibration with varying fluctuation level. Figure 4b shows the evolution of imaging performance with 2-foci patterns and random speckles with varying fluctuation level. Figure 4c shows the evolution of correlation and imaging performance of 2-foci compressive sensing imaging with high fluctuation level. Figure 4d shows the evolution of imaging performance of 2-foci and random pattern compressive sensing imaging with varying noise levels.

[0074] A total number of 2,000 measurements were used to study the impact of fluctuation in patterns and noise in signals. The 2-foci measurement basis showed stronger resistance to random fluctuation in measurement patterns than speckle measurement basis when the same level of random fluctuation was introduced in simulation, as indicated by the higher correlation coefficient between fluctuated and original patterns (Fig. 4a). Correspondingly, the 2-foci basis enabled a higher imaging performance which was evaluated by PSNR, as shown in Fig. 4b. As shown by Fig. 4c, with continuous increase of fluctuation level by enhancing the average noise intensity from 2 to 3.6, the PSNR degraded to 10, which is at the same level as the speckles patterns-based imaging when fluctuation level was at 1.8. In addition to higher resistance to source fluctuation, the 2- foci basis matrix had a 1.4 times smaller condition number than speckles (Supplementary). So, it also benefited from higher resistance to noise in signal detection. As shown in Fig. 4d, 2-foci basis had a higher PSNR than speckle basis with the same noise level.

[0075] Photoacoustic imaging

[0076] Figures 5a-5h show a series of photoacoustic images of carbon fibres 5. Specifically, Figures 5a-5d are recorded images of multi-foci patterns and random speckle. Figures 5e- 5h are reconstructed images of a carbon fibre network with corresponding patterns.

[0077] Photoacoustic imaging with multi-foci compressive sensing was experimentally demonstrated. The performance of image reconstruction using patterns with various number of foci and random speckles was compared. Each image comprises 10,000 pixels, covering an area of 50pm by 50 / mum. A number of 2,000 patterns were used for the measurement of signals. With the DMD running at 23 kHz, the rate of imaging acquisition reached 11.5 fps. As shown in Fig. 5e-h, multi-foci patterns led to higher imaging performance than random speckles. The focusing performance showed a gradual decline with the increase of number of focusing positions. Correspondingly, the image quality degraded gradually with the increase of number of foci in each pattern. The speckles compressive sensing reconstructed the general structure of carbon fibres at the central region, where distributed the highest light intensity in speckles at the tip of a graded-index MMF.

[0078] A further example of photoacoustic imaging is shown in Figures 6a-6f which show a series of photoacoustic images in relation to mouse red blood cells 6. Specifically, Figure 6a relates to an Optical microscopy image (transmission-mode) of a mouse blood smear on a cover slip. Further, Figures 6b-6f show photoacoustic images of the same sample with raster-scan mode (b), speckle compressive sensing (c) and multi-foci compressive sensing with R = 1 (d), 2 (e) and 5 (f) with a scale: 5 pm.

[0079] Biological tissue imaging was demonstrated by using 2-foci patterns to illuminate a mouse blood smear sample on a cover slip ex vivo. Mouse blood was obtained from culled mice. The procedures involving mice were ethically reviewed and carried out in accordance with the Animals (Scientific Procedures) Act 1986 (ASPA) UK Home Office regulations governing animal experimentation. The imaging performance was compared with raster-scan photoacoustic microscopy imaging and random speckle compressive sensing imaging. As shown in Fig. 6, the biconcave structures of RBCs were visualised in raster-scan and 2- foci compressive sensing imaging, while random speckle compressive sensing failed to reconstruct the structure of red blood cells (Fig. 6c). The 2-foci compressive sensing with 10,000 measurements acquired a photoacoustic image (Fig. 6d) with comparable quality to raster-scan imaging (Fig. 6b). While the reduction of measurements to 5k and 2k improved frame rate from 2.3 to 4.6 and 11.5 fps respectively, it induced the degradation of image fidelity and the loss of fine features (Fig. 6e-f). The laser power was the same as the one used in our previous study of photoacoustic endomicroscopy imaging [8]: the total energy at the single optical focus (1.2pm in diameter) was measured as ~20nJ which was 8.9% of the total output of the MMF, leading to a maximum of optical fluence of 1.7 J / cm2. The total laser power provided by the laser machine was kept the same for all imaging modes. The enhancement factor of light focusing in 2-foci pattern was measured to be 0.2 times of the single focus, leading to an optical fluence of 0.34 J / cm2at each focus.

[0080] Discussion

[0081] Multi-foci compressive sensing has been demonstrated for imaging through a MMF in both numerical simulation and experiments. To the best of our knowledge, this is the first time to combine the wavefront-shaping based foci patterns with compressive sensing algorithm for imaging through MMFs. Replacing random speckles with multi-foci patterns enables almost the same imaging performance in noise-free environment, whilst it leads to higher performance when system vibrance and signal read-out noise are inevitable. Photoacoustic endomicroscopy imaging has been demonstrated on red blood cells to visualise the biconcave cell structure. Compared to raster-scan-based imaging that was reported in study [8], the speed of image acquisition was improved by 5 times to 11.5 fps without significantly degradation of image quality. This is, to the best of our knowledge, the fastest imaging speed in photoacoustic endomicroscopy imaging. Improving SNR of the ultrasound signal has potential to optimise the imaging performance of compressive sensing imaging. It is mainly limited by the power of the laser source in this work. A laser source meeting the requirements of high repetition rate and high pulse energy is highly desired for high-quality and high-speed photoacoustic endomicroscopy imaging through a MMF. Although the experimental setup involved only photoacoustic endomicroscopy imaging by combining a MMF with a fibre-optic ultrasound sensor, the multi-foci compressive sensing algorithm can be extended to other imaging modalities such as fluorescence, two-photons, Raman, reflectance, and confocal imaging et al., while multimode fibre can be replaced by other disordered medium such as optical diffusers [21, 22] and biological tissues [23, 24].

[0082] As random speckles, 2-foci patterns, and 3-foci patterns leads to almost the same imaging performance in noise-free simulation, it is indicated that the resulting imaging performance of multi-foci compressive sensing is not dependent on the number of foci in each pattern. As such, the decline of quality of photoacoustic images is caused by the reduction in SNR of photoacoustic amplitude generated at each image pixel position. This is consistent to the image reconstruction in the central region, where the light intensity is stronger than peripheric region. So, it is suggested that concentrating more light energy into focal spots in multi-foci patterns can improve the quality of image reconstruction. The multi-foci patterns in this work are achieved via wavefront shaping using a DMD modulating the incident light wavefront. Since the DMD was used for binary amplitude modulation here, the theoretical enhancement of local light intensity is N / 2n, where N is the number of independently controlled micromirrors. The RVITM algorithm, which benefits from high energy coefficient and high system stability, was used for characterising the light intensity transmission through the MMF for generating the optimal DMD patterns for light focusing with binary amplitude modulation. A larger number of micromirrors can be employed to increase the light focusing performance but with increased characterisation time

[0025] . The DMD has also been demonstrated for phase modulation based on Lee hologram

[0026] and super-pixel

[0027] methods, with which the theoretical enhancement can increase to TTN / . However, this method suffers from low energy coefficient, which is challenging for photoacoustic imaging which requires high light fluence for ultrasound signal generation.

[0083] Conclusion

[0084] In conclusion, a multi-foci compressive sensing imaging method was developed and demonstrated on animal tissue ex vivo. It improved imaging speed by several times compared to raster-scan imaging with comparable image quality.

[0085] Figure 7 is a block diagram illustrating an arrangement of a system according to an embodiment of the present invention. Some embodiments of the present invention are designed to run on general purpose desktop or laptop computers. Therefore, according to a first embodiment, a computing apparatus 700 is provided having a central processing unit (CPU) 706, and random access memory (RAM) 704 into which data, program instructions, and the like can be stored and accessed by the CPU. The apparatus 700 is provided with a display screen 5

[0086] 720, and input peripherals in the form of a keyboard 722, and mouse 724. Keyboard 722, and mouse 724 communicate with the apparatus 700 via a peripheral input interface 708. Similarly, a display controller 702 is provided to control display 720, so as to cause it to display images under the control of CPU 706. Endoscope image 730, shape 732 and motion data 734, can be input into the apparatus and stored via shape, motion and image data input 710. In this respect, apparatus 700 comprises a computer readable storage medium 712, such as a hard disk drive, writable CD or DVD drive, zip drive, solid state drive, USB drive or the like, upon which image data 7122, motion data 7124, and shape data 7126 can be stored. Alternatively, the data 730, 732, 734 could be stored on a web-based platform, e.g. a database (e.g. XNAT), and accessed via an appropriate network. Computer readable storage medium 712 also stores various programs, which when executed by the CPU 706 cause the apparatus 700 to operate in accordance with some embodiments of the present invention.

[0087] In particular, a control interface program 716 is provided, which when executed by the CPU 706 provides overall control of the computing apparatus, and in particular provides a graphical interface on the display 720, and accepts user inputs using the keyboard 722 and mouse 724 by the peripheral interface 708. The control interface program 716 also calls, when necessary, other programs to perform specific processing actions when required. The data within the image data 7122, the motion data 7124 and the shape data 7126 provides the fundamental data from an endoscope that is used for producing multifoci patterns for compressive sensing from the produced DMD patterns.

[0088] In particular, the compressive sensing program 714 comprises a plurality of programs or algorithms that are utilized to execute the multi-foci patterns for compressive sensing. Specifically, the compressive sensing program 714 comprises a FISTA algorithm 7142, a RVITM algorithm 7144 and a MATLAB program 7146. The FISTA algorithm 7142 is used to reconstruct the images from the measurement patterns and signals. The RVITM algorithm 7144 was used to produce multi-foci patterns which have multiple light foci in each pattern, through wavefront shaping. The MATLAB program 7146 is used to synchronize the DMD patterns display, the laser firing and the data acquisition.

[0089] The detailed operation of the computing apparatus 500 has been described in more detail in relation to Figs. 1-6.

[0090] In Figure 8, an example flow diagram 8 of a method according to an embodiment of the present disclosure, is shown. The flow diagram 8 shows an example method for disordered medium compressive sensing, or more particularly optical fiber compressive sensing, or for performing high speed imaging through a multimode fibre using multi-foci compressive sensing.

[0091] In s802, a multi-foci illumination pattern for transmission along an optical fiber must be generated. In some embodiments, the generating of the multi-foci illumination pattern may comprise the following steps: characterising the optical fiber with a real-valued intensity transmission matrix; projecting light into the optical fiber via an optical modulator, the optical modulator being controlled in dependence on the real-valued intensity transmission matrix to generate the multi-foci illumination pattern in the projected light. Thus, further, in some embodiments the generating may use a real-valued intensity transmission matrix (RVITM) algorithm, the RVITM algorithm may be used for characterising the light intensity transmission through the optical fiber for generating the multi-foci illumination program for light focusing with binary amplitude modulation. Next, in s804 the multi-foci illumination pattern from s802 is projected from a distal tip of the optical fiber onto an imaging target.

[0092] Then, in s806 a signal vector S is measured S, the signal vector S being which arises in dependence on an interaction of the multi-foci illumination pattern and the imaging target. In some embodiments, the measuring may further comprise measuring a photoacoustic ultrasound signal generated in the imaging target due to the multi-foci illumination pattern, the signal vector S being related to the amplitude of the ultrasound signal. However, in some embodiments the measuring may further comprise measuring an optical transmission signal of light from the multi-foci illumination pattern that is transmitted through the imaging target, the signal vector S being related to the intensity of the transmitted light.

[0093] Finally, in s808 an image at the target is reconstructed in dependence on the signal vector S. In some embodiments, this reconstruction may be executed by a Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). Moreover, in some embodiments the reconstruction may be performed by utilizing the following equation:

[0094] X' = argmin||TX' - S|| + A||X' 1^ wherein T = measurement matrix of a set of multi-foci patterns, X = the imaging target and S = the signal vector.

[0095] Unless the context clearly requires otherwise, throughout the description and the claims, the words "comprise," "comprising," "include," "including," and the like are to be construed in an inclusive sense, as opposed to an exclusive or exhaustive sense; that is to say, in the sense of "including, but not limited to."

[0096] The words "coupled" or "connected" or "tied", as generally used herein, refer to two or more elements or nodes that may be either directly connected, or connected by way of one or more intermediate elements. Additionally, the words "herein,” "above," "below," and words of similar import, when used in this application, shall refer to this application as a whole and not to any particular portions of this application. Where the context permits, words in the Detailed Description using the singular or plural number may also include the plural or singular number, respectively. The words "or" in reference to a list of two or more items, is intended to cover all of the following interpretations of the word: any of the items in the list, all of the items in the list, and any combination of the items in the list. Various modifications, whether by addition, substitution, or deletion will be apparent to the intended reader to provide further embodiments of the present disclosure, any and all of which are intended to be encompassed by the appended claims.

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Claims

Claims1. A method of optical wavefront shaping via a disordered medium, comprising: a. generating a multi-foci illumination pattern for transmission along the disordered medium; b. projecting the multi-foci illumination pattern from a distal tip of the disordered medium onto an imaging target; c. measuring a signal vector S that arises in dependence on an interaction of the multi-foci illumination pattern and the imaging target; and d. reconstructing an image of the target in dependence on the signal vector S.

2. A method according to claim 1, wherein the measuring comprises measuring a photoacoustic ultrasound signal generated in the imaging target due to the multifoci illumination pattern, the signal vector S being related to the amplitude of the ultrasound signal.

3. A method according to claim 1, wherein the measuring comprises measuring an optical transmission signal of light from the multi-foci illumination pattern that is transmitted through the imaging target, the signal vector S being related to the intensity of the transmitted light.

4. A method according to any of the preceding claims, wherein the generating step further comprises: generating, by using a wavefront shaping method, the multi-foci illumination pattern for transmission along the disordered medium.

5. A method according to any of the preceding claims, wherein the generating step further comprises: characterizing the disordered medium with a real-valued intensity transmission matrix; projecting light into the disordered medium via an optical modulator, the optical modulator being controlled in dependence on the real-valued intensity transmission matrix to generate the multi-foci illumination pattern in the projected light.

6. A method according to any of the preceding claims, wherein the reconstructing uses a Fast Iterative Shrinkage-Thresholding Algorithm (FISTA).

7. A method according to any of the preceding claims, wherein the reconstructing is performed by utilizing the following equation:X' = argmin||TX' - S|| + A||X' 1^ wherein T = measurement matrix of a set of multi-foci patterns, X = the imaging target and S = the signal vector.

8. A method according to any of the preceding claims, wherein the generating step uses a real-valued intensity transmission matrix (RVITM) algorithm, the RVITM algorithm being used for characterising the light intensity transmission through the disordered medium for generating the multi-foci illumination program for light focusing with binary amplitude modulation.

9. A system for optical fiber compressive sensing, comprising: e. means for generating a multi-foci illumination pattern for transmission along an optical fiber; f. means for projecting the multi-foci illumination pattern from a distal tip of the optical fiber onto an imaging target; g. means for measuring a signal vector S that arises in dependence on an interaction of the multi-foci illumination pattern and the imaging target; and h. means for reconstructing an image of the target in dependence on the signal vector S.

10. A system according to claim 9, wherein the means for measuring comprises means for measuring a photoacoustic ultrasound signal generated in the imaging target due to the multi-foci illumination pattern, the signal vector S being related to the amplitude of the ultrasound signal.

11. A system according to claim 9, wherein the means for measuring comprises means for measuring an optical transmission signal of light from the multi-foci illumination pattern that is transmitted through the imaging target, the signal vector S being related to the intensity of the transmitted light.

12. A system according to any claims 9 to 11, wherein the means for generating further comprises: means for characterizing the optical fiber with a real-valued intensity transmission matrix;means for projecting light into the optical fiber via an optical modulator, the optical modulator being controlled in dependence on the real-valued intensity transmission matrix to generate the multi-foci illumination pattern in the projected light.

13. A system according to any of claims 9 to 12, wherein the means for reconstructing uses a Fast Iterative Shrinkage-Thresholding Algorithm (FISTA).

14. A system according to any of claims 9 to 13, wherein the means for reconstructing by utilizes the following equation:X' = argmin||TX' - S|| + A||X' 1^ wherein T = measurement matrix of a set of multi-foci patterns, X = the imaging target and S = the signal vector.

15. A system according to any of claims 9 to 14, wherein the means for generating uses a real-valued intensity transmission matrix (RVITM) algorithm, the RVITM algorithm being used for characterising the light intensity transmission through the optical fiber for generating the multi-foci illumination program for light focusing with binary amplitude modulation.

16. A system for optical fiber compressive sensing, comprising: i. a digital micromirror device (DMD) arranged in use to generate a multifoci illumination pattern for transmission along an optical fiber, the multifoci illumination pattern projecting in use from a distal tip of the optical fiber onto an imaging target; j. means for measuring a signal vector S that arises in dependence on an interaction of the multi-foci illumination pattern and the imaging target; and k. a processor arranged in use to reconstruct an image of the target in dependence on the signal vector S.

17. A system according to claim 16, wherein the means for measuring comprises an ultrasound sensor arranged to detect and measure a photoacoustic ultrasound signal generated in the imaging target due to the multi-foci illumination pattern, the signal vector S being related to the amplitude of the ultrasound signal.

18. A system according to claim 16, wherein the means for measuring comprises a lens and camera arranged in use to measure an optical transmission signal oflight from the multi-foci illumination pattern that is transmitted through the imaging target, the signal vector S being related to the intensity of the transmitted light.

19. A system according to any of claims 16 to 18, wherein the optical fiber is characterized with a real-valued intensity transmission matrix, and the digital micromirror device is controlled in dependence on the real-valued intensity transmission matrix to generate the multi-foci illumination pattern in the projected light from the distal tip of the optical fiber onto the imaging target.

20. A system according to any of claims 16 to 19, wherein the reconstructing by the processor uses a Fast Iterative Shrinkage-Thresholding Algorithm (FISTA).

21. A system according to any of claims 16 to 20 wherein the reconstructing by the processor utilizes the following equation:X' = argmin||TX' - S|| + A||X' 1^ wherein T = measurement matrix of a set of multi-foci patterns, X = the imaging target and S = the signal vector.

Images