Computational adaptive optical microscopic imaging method based on sparse blind deconvolution

Abstract

The invention discloses a computational adaptive optical microscopic imaging method based on sparse blind deconvolution. The method comprises the following steps: firstly, carrying out multi-frequency fusion filtering preprocessing on an acquired fluorescence image, inhibiting low-frequency noise and enhancing medium-high frequency details; then, based on image gradient sparse prior, the image and a point spread function are updated through blind deconvolution alternate iteration; then utilizing a Zernike polynomial to fit aberration to obtain an aberration-containing point spread function; and finally, performing deconvolution to realize image deblurring and aberration correction. According to the method, extra hardware and precise point spread function calibration are not needed, and high noise robustness and system universality are achieved; compared with traditional Richardson-Lucy deconvolution, the method has the advantages that the point spread function and the sample information can be reconstructed from a single blurred image at the same time, the requirement for accurate point spread function calibration is avoided, the image resolution and contrast of a wide-field and confocal fluorescence microscope system are improved, and the method is suitable for being applied to the fields of dynamic life science research, medical imaging and the like.

Description

Technical Field

[0001] This invention relates to the field of optical microscopy imaging technology, and more specifically to a computational adaptive optical microscopy imaging method based on sparse blind deconvolution. Background Technology

[0002] In the life sciences, optical microscopes are widely recognized as an indispensable tool for probing the complexity of the microscopic world, playing a crucial role in subcellular dynamics, neuroscience research, tumor diagnosis, and many other areas of exploration. The historical evolution of microscopes is characterized by a continuous pursuit of enhanced imaging capabilities and reliance on sophisticated optical systems. This advancement has helped reveal minute details within cellular structures and capture the complex dynamics of life processes. However, the presence of optical aberrations poses a significant challenge to achieving perfect imaging. The performance of optical microscopes is fundamentally limited by the design parameters of the optical system, and the presence of aberrations reduces the microscope's resolution and contrast. Therefore, a deeper understanding of these aberrations and the development of effective correction methods are essential for advancing high-resolution imaging.

[0003] To address these issues, adaptive optics is integrated into microscopes to correct aberrations caused by sample refractive index inhomogeneities, component defects, and microscope misalignment. Active optics (AO) typically employs deformable mirror arrays or spatial light modulators to actively correct wavefront aberrations, achieving high-resolution imaging by guiding light from a single light source at different angles to a common focal point on the sensor. However, the need for integration with various microscope optical paths limits its universal applicability. To overcome this, techniques such as Fourier transform microscopy and differential phase-contrast microscopy do not rely on additional compensation hardware. They use phase retrieval algorithms for aberration correction, leveraging inherent data redundancy to simultaneously recover the complex field of the specimen and the spatially varying aberrations of the system, reconstructing high-quality images. However, these methods usually require acquiring multiple images for aberration correction.

[0004] While traditional adaptive optics methods perform well in aberration correction, they typically require complex optical components and are cumbersome to operate. Furthermore, they may be limited in practical applications by factors such as the need to acquire multiple images or additional hardware.

[0005] In summary, there is currently a lack of a fast, high-resolution, and high-contrast computational adaptive optics microscopy imaging method that can achieve high-quality aberration correction. Summary of the Invention

[0006] To achieve high-quality aberration-corrected computational adaptive optics microscopy imaging, this invention provides a computational adaptive optics microscopy imaging method based on sparse blind deconvolution.

[0007] The technical solution adopted in this invention is as follows: A computational adaptive optics microscopy imaging method based on sparse blind deconvolution, comprising the following steps: Step 1. Use the fluorescence incoherent microscopy mode of the imaging system to capture fluorescence images; Step 2. Before initializing the point spread function, perform multi-frequency fusion filtering on the fluorescence image obtained in Step 1 to suppress low-frequency components in the frequency domain and enhance mid-frequency and high-frequency components respectively, to obtain a preprocessed image with enhanced spectrum. Step 3. Initialize the point spread function; Step 4. Based on sparse priors, combine the preprocessed image with the current point spread function to iteratively update the image; Step 5. Iteratively update the point spread function based on the current image; Step 6. Repeat steps 4 and 5 until the change in the point spread function is less than the set threshold to obtain an initial estimate of the point spread function. Use Zernike polynomials to fit the estimated point spread function to the aberrations to obtain the point spread function containing the aberrations. Step 7. Using the aberration-containing spread function obtained in Step 6, perform deconvolution iteration on the preprocessed image obtained in Step 2 to achieve image deblurring; Steps 3 to 6 can be repeated multiple times as needed to further optimize the point spread function and image reconstruction results.

[0008] Preferably, in step 1, the imaging system includes an incoherent illumination source, an excitation / emission filter assembly matching the sample wavelength, an objective lens imaging optical path, and a camera; the sample is excited by spatially incoherent light generated by the incoherent illumination source, and the fluorescence signal is separated by the excitation / emission filter assembly and transmitted to the camera by the objective lens imaging optical path to achieve low-noise wide-field fluorescence imaging.

[0009] Preferably, in step 2, the multi-frequency fusion filtering process includes: transforming the fluorescence image to the frequency domain to obtain a frequency domain representation; constructing a low-frequency suppression function to suppress the background and slowly changing low-frequency components; constructing intermediate-frequency and high-frequency enhancement window functions respectively to enhance the intermediate-frequency and high-frequency bands; weightedly fusing the enhanced intermediate-frequency and high-frequency spectral components to obtain a fused spectrum; and performing an inverse Fourier transform on the fused spectrum to obtain a preprocessed image.

[0010] Preferably, in step 2, the mathematical expression of the multi-frequency fusion filtering process is as follows: ① Let the fluorescence image acquired in step 1 be represented as

[0011] ② Perform a Fourier transform on the fluorescence image to obtain its frequency domain representation.

[0012] To describe different frequency bands, a frequency radius is introduced.

[0013] ③ To suppress background noise and slowly changing low-frequency components, a low-frequency suppression function based on a Gaussian function is constructed.

[0014] The spectrum after low-frequency suppression is expressed as follows:

[0015] ④ To enhance the mid-frequency and high-frequency detail information of the image, Gaussian window functions for mid-frequency and high-frequency enhancement are constructed respectively. The first window function for mid-frequency enhancement and the second window function for high-frequency enhancement are expressed as follows:

[0016]

[0017]

[0018] To achieve spectrum enhancement, a window function with enhanced weights is introduced.

[0019] This yields the enhanced mid-frequency and high-frequency spectra.

[0020]

[0021] ⑤ Weighted fusion of the enhanced spectral components of the intermediate frequency and high frequency frequencies is performed to obtain the fused spectrum.

[0022] ⑥ Perform an inverse Fourier transform on the fused spectrum to obtain the preprocessed image with enhanced spectrum.

[0023] It serves as the input for subsequent point spread function initialization, sparse blind deconvolution, and aberration-containing deconvolution iterations; in, Represents the spatial coordinates of the image. Represents spatial frequency coordinates. Indicates the location of the center of the spectrum. This is the bandwidth parameter of the low-frequency suppression function. and These are the bandwidth parameters for the intermediate frequency and high frequency windows, respectively. and These are the enhancement coefficients for intermediate and high frequencies, respectively. and For fusion weighting coefficients.

[0024] Preferably, the first window function and the second window function in step 2 are a smooth window function, a bandpass window function, a weighted frequency response function, or any combination thereof.

[0025] Preferably, in step 3, the initial point spread function is: Point spread function Initialize to an ideal point spread function, let

[0026] in, Let the pupil plane coordinates be... The circular aperture of the imaging system Indicates Fourier transform, This indicates the relevant operations.

[0027] Preferably, in step 4, the process of iteratively updating the image based on sparse prior estimation and the current point spread function is as follows: ① Assuming an ideal image probability density of each pixel value If it satisfies a Gaussian distribution, that is, let

[0028] ② Assume the noise follows a normal distribution, and the noise probability density is:

[0029] ③ Maximize the spread function at known points and real-life images Image in case The probability density, that is, maximizing the probability density of the following expression.

[0030] When the above expression is maximized, the corresponding iteratively updated image for

[0031]

[0032]

[0033] in, For the number of iterations, The standard deviation of the gradient image is represented by... For the first A gradient filter, express The gradient image, where Π represents the cumulative multiplication operation. The standard deviation of the noise. These are real-shot fluorescence images taken in step 1. Point spread function The corresponding Toplitz matrix, For the first The Topplitz matrix corresponding to each derivative filter.

[0034] Preferably, in step 5, the mathematical expression for iteratively updating the point spread function based on the current image is:

[0035]

[0036]

[0037] in, for The corresponding Toplitz matrix.

[0038] Preferably, in step 6, the process of using Zernike polynomials to fit the estimated point spread function to an aberration, thereby obtaining the point spread function containing aberrations, is as follows: ① Determine the pupil function

[0039] ② The coefficient matrix is ​​obtained by performing the least squares method on the estimated point spread function hN.

[0040] ③ Solve for the point spread function containing aberrations.

[0041] in, For spatial frequency, Let be the highest order of the Zernik polynomial. For each orthogonal Zernike polynomial coefficient, For containing A matrix with such coefficients, Indicates Fourier transform, This indicates the relevant operations.

[0042] Preferably, in step 7, RL deconvolution is used to recover the fluorescence image to achieve image deblurring, and the iterative formula is:

[0043] in, Represents image coordinates, For the deblurred image, the first estimate, For the first This estimate These are real-world fluorescence images acquired in step 1. This is the point spread function obtained in step 6.

[0044] The present invention has the following beneficial effects: 1. No need for precise point spread function calibration: The sparse blind deconvolution method is adopted, which does not rely on prior system calibration or precise point spread function measurement. The point spread function can be estimated and the original image can be restored simultaneously from a single blurred fluorescence image, which simplifies the imaging process and reduces operational complexity. 2. Improve noise robustness: By introducing the gradient sparsity of fluorescence images as a prior constraint and combining it with Zernike polynomials to perform structured modeling of the point spread function, low-frequency noise is suppressed and mid-to-high frequency signals are enhanced in frequency domain preprocessing, so that high-quality image details can still be stably recovered under low signal-to-noise ratio conditions. 3. High-quality aberration correction: By integrating sparse priors and the Zernike aberration model, the system aberrations can be estimated more accurately and the point spread function can be reconstructed, effectively improving image resolution and contrast and achieving imaging effects close to the diffraction limit. 4. System versatility: It does not depend on specific hardware configurations and is applicable to a variety of optical imaging systems such as wide-field fluorescence microscopes and confocal laser scanning microscopes, possessing strong portability and broad application potential. Attached Figure Description

[0045] Figure 1 This is a flowchart of the adaptive optics microscopy imaging method based on sparse blind deconvolution in an embodiment of the present invention.

[0046] Figure 2 This is an example of the observation results of mitochondria in COS-7 cells labeled with the mitochondrial red fluorescent probe (MitoTracker™ Red CMXRos) under wide-field fluorescence in an embodiment of the present invention.

[0047] Figure 3 This is a comparison of the image reconstruction effect of mitochondria in COS-7 cells labeled with the mitochondrial red fluorescent probe (MitoTracker™ Red CMXRos) under wide-field fluorescence in an embodiment of the present invention.

[0048] Figures (a)-(c) show a magnified comparison of the details of the marked areas in the figures, demonstrating the reconstruction results of the original wide-field fluorescence image, the traditional RL deconvolution method, and the blind deconvolution method proposed in the embodiments of the present invention. Detailed Implementation

[0049] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0050] This embodiment presents a computational adaptive optics microscopy imaging method based on sparse blind deconvolution, comprising: estimating the blind point spread function under sparse priors and performing aberration modeling on the estimated point spread function based on Zernike polynomials to attempt to reconstruct the original image without any systematic knowledge. A regularizer is used to address this approximation problem, leveraging prior knowledge of natural image statistics, particularly the sparsity of the derivative distribution in fluorescence imaging, to identify the point spread function kernel that maximizes the posterior probability. The obtained point spread function is further refined through aberration estimation. To achieve single-image aberration correction, this embodiment introduces common aberration prior knowledge into the reconstruction process, using Zernike polynomials as basis functions to describe pupil distortion, simplifying the solution space degrees of freedom from a two-dimensional matrix to a minimum set of coefficients for the dominant Zernike modes, thereby optimizing the reconstruction of finite original images.

[0051] In the embodiments, such as Figure 1 The diagram shows the flowchart of a computational adaptive optics microscopy imaging method based on sparse blind deconvolution. The following is a detailed explanation with simulation results.

[0052] Step 1. Use the fluorescence incoherent microscopy mode of the imaging system to capture fluorescence images.

[0053] The imaging system includes an incoherent illumination source, an excitation / emission filter assembly that matches the sample wavelength, an objective lens imaging optical path, and a camera. The sample is excited by spatially incoherent light generated by the incoherent illumination source. The fluorescence signal is separated by the excitation / emission filter assembly and then transmitted to the camera through the objective lens imaging optical path, thereby achieving low-noise wide-field fluorescence imaging.

[0054] Step 2. Multi-frequency fusion filtering preprocessing.

[0055] Before initializing the point spread function, the fluorescence image acquired in step 1 is converted to the frequency domain, and its spectrum is segmented. First, the background and slowly changing low-frequency components are weakened by low-frequency suppression. Then, two different window functions are used to enhance the mid-frequency and high-frequency bands respectively. The enhanced mid-frequency and high-frequency spectral components are then weighted and fused, and the pre-processed image with enhanced spectrum is obtained by inverse transformation.

[0056] Let the fluorescence image acquired in step 1 be represented as

[0057] First, a Fourier transform is performed on the fluorescence image to obtain its frequency domain representation.

[0058] in, These are spatial frequency coordinates.

[0059] To describe different frequency bands, a frequency radius is introduced.

[0060] in, Indicates the location of the center of the spectrum.

[0061] To suppress background noise and slowly varying low-frequency components, a low-frequency suppression function based on a Gaussian function is constructed. Used to reduce background and slowly changing components.

[0062] The spectrum after low-frequency suppression is expressed as follows:

[0063] Based on this, Gaussian window functions for the mid-frequency and high-frequency frequencies are constructed to enhance the mid-frequency and high-frequency detail information of the image, respectively.

[0064] The first window function used for intermediate frequency enhancement is expressed as follows:

[0065] The second window function for high-frequency enhancement is expressed as follows:

[0066] in, , and These are the bandwidth parameters for the mid-frequency and high-frequency windows, respectively.

[0067] To achieve spectrum enhancement, a window function with enhanced weights is introduced.

[0068] in, and These are the enhancement coefficients for the intermediate frequency and high frequency, respectively.

[0069] This yields the enhanced mid-frequency and high-frequency spectra.

[0070]

[0071] Subsequently, the enhanced spectral components of the intermediate frequency and high frequency are weighted and fused to obtain the fused spectrum.

[0072] in, and For fusion weighting coefficients.

[0073] Finally, an inverse Fourier transform is performed on the fused spectrum to obtain the preprocessed image with enhanced spectrum.

[0074] Preprocessed images The preprocessed image serves as input for subsequent point spread function initialization, sparse blind deconvolution, and aberration-containing deconvolution iterations, improving the image's spectral distribution, enhancing mid-to-high frequency details, and increasing the stability of the reconstruction process.

[0075] Step 3. Initialize the point spread function.

[0076] Point spread function Initialize it to an ideal point spread function, that is, let:

[0077] here, Let the pupil plane coordinates be... The circular aperture of the imaging system This indicates that a Fourier transform is being performed. This indicates the relevant operations.

[0078] Step 4. Based on sparse prior estimation and current point spread function Iteratively update the ideal image .

[0079] Since the fluorescence intensity of a sample in fluorescence imaging is mainly concentrated in a few pixels, the probability of brighter pixels appearing in its gradient image is low. Therefore, we can assume an ideal image. probability density of each pixel value If the distribution satisfies a Gaussian distribution, then let:

[0080] In the formula, This represents the number of iterations, starting from 1. The standard deviation of the gradient image is represented by... For the first A gradient filter, express gradient image, This indicates a cumulative multiplication operation.

[0081] Assuming the noise follows a normal distribution, its probability density... for:

[0082] In the formula, The standard deviation of the noise. The image shown is a real-world fluorescence image captured in step 1.

[0083] Maximize the spread function at known points and real-life images Image in case The probability density is equivalent to maximizing the following probability density:

[0084] When the above expression is maximized, the corresponding ideal image is... for:

[0085] In the formula, , ,and Point spread function The corresponding Toplitz matrix, For the first The Topplitz matrix corresponding to each derivative filter.

[0086] Step 5. Based on the current ideal image Iterative update point spread function .

[0087] Optimal point spread function kernel It can be represented as:

[0088] In the formula , ,and for The corresponding Toplitz matrix.

[0089] Step 6. Repeat steps 3 and 4 until the point spread function is obtained. If the change is less than a set threshold, the estimated point spread function is fitted with an aberration using Zernike polynomials to obtain the aberration-inclusive point spread function. .

[0090] Here, considering that Zernike polynomials are often used to express pupillary aberration, simplifying aberration modeling to solving for the coefficients corresponding to a set of Zernike moduli reduces the dimensionality of the solution space, making aberration correction possible from a single original image. Based on this, the pupil function can be expressed as:

[0091] In the formula For spatial frequency, Let be the highest order of the Zernik polynomial. For each orthogonal Zernike polynomial coefficient, For containing A matrix with such coefficients. For The coefficient matrix obtained by performing the least squares method is:

[0092] Thus, the point spread function containing aberrations can be solved. : .

[0093] Step 7. Use the point spread function obtained in Step 5. Deconvolution iteration is performed on the fluorescence image to achieve image deblurring.

[0094] The fluorescence image is recovered using RL deconvolution, with the following iterative formula:

[0095] in, Represents image coordinates, For the deblurred image, the first k estimate, For the first k +1 estimate, These are real-world fluorescence images acquired in step 1. This is the point spread function obtained in step 5.

[0096] Furthermore, the method described in this embodiment was used to image stained mitochondria under a wide-field fluorescence microscope at an oil immersion depth of 100 × 1.45 NA. The results were compared with those of blurred images and traditional RL deconvolution. Figure 2 and Figure 3 As shown. Compared to traditional methods, this embodiment can provide higher resolution.

[0097] Obviously, the above embodiments of the present invention are merely illustrative examples to illustrate the invention and are not intended to limit the implementation of the invention. Other obvious variations or modifications derived from the essential spirit of the invention still fall within the protection scope of the invention.

Claims

1. A computational adaptive optics microscopy imaging method based on sparse blind deconvolution, characterized in that, Includes the following steps: Step 1. Use the fluorescence incoherent microscopy mode of the imaging system to capture fluorescence images; Step 2. Before initializing the point spread function, perform multi-frequency fusion filtering on the fluorescence image obtained in Step 1 to suppress low-frequency components in the frequency domain and enhance mid-frequency and high-frequency components respectively, to obtain a preprocessed image with enhanced spectrum. Step 3. Initialize the point spread function; Step 4. Based on sparse priors, combine the preprocessed image with the current point spread function to iteratively update the image; Step 5. Iteratively update the point spread function based on the current image; Step 6. Repeat steps 4 and 5 until the change in the point spread function is less than the set threshold to obtain an initial estimate of the point spread function. Use Zernike polynomials to fit the estimated point spread function to the aberrations to obtain the point spread function containing the aberrations. Step 7. Using the aberration-containing spread function obtained in Step 6, perform deconvolution iteration on the preprocessed image obtained in Step 2 to achieve image deblurring; Steps 3 to 6 can be repeated multiple times as needed to further optimize the point spread function and image reconstruction results.

2. The computational adaptive optics microscopy imaging method based on sparse blind deconvolution according to claim 1, characterized in that, In step 1, the imaging system includes an incoherent illumination source, an excitation / emission filter assembly that matches the sample wavelength, an objective lens imaging optical path, and a camera. The sample is excited by spatially incoherent light generated by the incoherent illumination source. The fluorescence signal is separated by the excitation / emission filter assembly and then transmitted to the camera through the objective lens imaging optical path, thereby achieving low-noise wide-field fluorescence imaging.

3. The computational adaptive optics microscopy imaging method based on sparse blind deconvolution according to claim 1, characterized in that, Step 2, the multi-frequency fusion filtering process includes: The fluorescence image is transformed to the frequency domain to obtain its frequency domain representation; Construct a low-frequency suppression function to suppress background and slowly changing low-frequency components; Construct intermediate frequency (IF) and high frequency (HF) enhancement window functions respectively to enhance the IF and HF bands; The enhanced intermediate frequency and high frequency spectral components are weighted and fused to obtain the fused spectrum; The fused spectrum is subjected to inverse Fourier transform to obtain the preprocessed image.

4. The computational adaptive optics microscopy imaging method based on sparse blind deconvolution according to claim 3, characterized in that, In step 2, the mathematical expression of the multi-frequency fusion filtering process is as follows: ① Let the fluorescence image acquired in step 1 be represented as ② Perform a Fourier transform on the fluorescence image to obtain its frequency domain representation. To describe different frequency bands, a frequency radius is introduced. ③ To suppress background noise and slowly changing low-frequency components, a low-frequency suppression function based on a Gaussian function is constructed. The spectrum after low-frequency suppression is expressed as follows: ④ To enhance the mid-frequency and high-frequency detail information of the image, Gaussian window functions for mid-frequency and high-frequency enhancement are constructed respectively. The first window function for mid-frequency enhancement and the second window function for high-frequency enhancement are expressed as follows: To achieve spectrum enhancement, a window function with enhanced weights is introduced. This yields the enhanced mid-frequency and high-frequency spectra. ⑤ Weighted fusion of the enhanced spectral components of the intermediate frequency and high frequency frequencies is performed to obtain the fused spectrum. ⑥ Perform an inverse Fourier transform on the fused spectrum to obtain the preprocessed image with enhanced spectrum. It serves as the input for subsequent point spread function initialization, sparse blind deconvolution, and aberration-containing deconvolution iterations; in, Represents the spatial coordinates of the image. Represents spatial frequency coordinates. Indicates the location of the center of the spectrum. This is the bandwidth parameter of the low-frequency suppression function. and These are the bandwidth parameters for the intermediate frequency and high frequency windows, respectively. and These are the enhancement coefficients for intermediate and high frequencies, respectively. and For fusion weighting coefficients.

5. The computational adaptive optics microscopy imaging method based on sparse blind deconvolution according to claim 4, characterized in that, The first window function and the second window function in step 2 are smooth window functions, bandpass window functions, weighted frequency response functions, or any combination thereof.

6. The computational adaptive optics microscopy imaging method based on sparse blind deconvolution according to claim 1, characterized in that, In step 3, the point spread function is initialized as follows: Point spread function Initialize to an ideal point spread function, let in, Let the pupil plane coordinates be... The circular aperture of the imaging system Indicates Fourier transform, This indicates the relevant operations.

7. The computational adaptive optics microscopy imaging method based on sparse blind deconvolution according to claim 1, characterized in that, In step 4, the process of iteratively updating the image based on sparse prior estimation and the current point spread function is as follows: ① Assuming an ideal image probability density of each pixel value If it satisfies a Gaussian distribution, that is, let ② Assume the noise follows a normal distribution, and the noise probability density is: ③ Maximize the spread function at known points and real-life images Image in case The probability density, that is, maximizing the probability density of the following expression. When the above expression is maximized, the corresponding iteratively updated image for in, For the number of iterations, The standard deviation of the gradient image is represented by... For the first A gradient filter, express gradient image, Π represents cumulative multiplication. The standard deviation of the noise. These are real-shot fluorescence images taken in step 1. Point spread function The corresponding Toplitz matrix, For the first The Topplitz matrix corresponding to each derivative filter.

8. The computational adaptive optics microscopy imaging method based on sparse blind deconvolution according to claim 1, characterized in that, In step 5, the mathematical expression for iteratively updating the point spread function based on the current image is: in, for The corresponding Toplitz matrix.

9. The computational adaptive optics microscopy imaging method based on sparse blind deconvolution according to claim 1, characterized in that, In step 6, the process of using Zernike polynomials to fit the estimated point spread function to an aberration, thereby obtaining the point spread function containing aberrations, is as follows: ① Determine the pupil function ② The coefficient matrix is ​​obtained by performing the least squares method on the estimated point spread function hN. ③ Solve for the point spread function containing aberrations. in, For spatial frequency, Let be the highest order of the Zernik polynomial. For each orthogonal Zernike polynomial coefficient, For containing A matrix with such coefficients, Indicates Fourier transform, This indicates the relevant operations.

10. The computational adaptive optics microscopy imaging method based on sparse blind deconvolution according to claim 1, characterized in that, In step 7, RL deconvolution is used to recover the fluorescence image, thereby achieving image deblurring. The iterative formula is: in, Represents image coordinates, For the deblurred image, the first estimate, For the first time estimate, These are real-world fluorescence images acquired in step 1. This is the point spread function obtained in step 6.

Images