WO2006041127A1 - 劣化情報復元方法と復元装置 - Google Patents
劣化情報復元方法と復元装置 Download PDFInfo
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- G06T5/00—Image enhancement or restoration
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Definitions
- the present invention relates to restoration of degradation information. Specifically, the present invention relates to a method and apparatus for restoring original information from information deteriorated by transmission.
- the image formation of light in an image is regarded as one event, and the original image is restored by using the technique used in the technical field of probability statistics.
- Richardson The method using the Lucy algorithm
- the distribution is normalized and regarded as a probability density function distribution of the phenomenon of light image formation in the original image.
- the distribution of illuminance in the degraded image the distribution is normalized and regarded as the distribution of light in the degraded image and the probability density function of the event.
- PSF Point Spread Function
- the Richardson-Lucy algorithm uses the degraded image distribution and PSF distribution respectively, and based on Bayes's theory, it is the most likely distribution of the original image distribution that realizes the distribution of degraded images. Is estimated by iterative calculation.
- the distribution of PSF can be calculated, for example, by calculating the parameter force of the optical system, or the distribution of the image when the point image is actually transmitted can be obtained by experiment.
- Non-Patent Document 1 WH Richardson, "Baesian— based iterative method of image restoration", Journal of Optical Society of America , (USA), 1972, 62 ⁇ , P55-59
- Non-Patent Document 2 LB Lucy. B. Lucy), "Iterative technique for the rectification of observed distributions", Astronomical Journal, (USA) ), 1974, 79 ⁇ , p745-7 54
- the transfer characteristics of the optical system are calculated based on parameters such as lens numerical aperture, illumination wavelength, aberration, and defocus. If some of these parameters are unknown or some are inaccurate, the calculated transfer characteristics of the optical system will be inaccurate. Thus, when the transfer characteristic of the optical system is inaccurate, the original image cannot be accurately restored using the conventional image restoration method as described above. Prior to restoration of the original image, it is necessary to accurately evaluate the transfer characteristics of the optical system.
- the present invention solves the above problems.
- the present invention provides a technique capable of accurately estimating transfer characteristics of a transmission system by performing iterative calculation based on the distribution of deterioration information and the distribution of original information.
- the present invention provides a technique capable of accurately estimating both the transfer characteristic of the transmission system and the distribution of the original information by performing iterative calculation based only on the distribution of deterioration information. .
- One method of the present invention is a method for estimating a frequency response distribution of a transmission system from original information and degradation information.
- This method comprises the steps of identifying a distribution of deterioration information, identifying a spectral distribution of the original information distribution, and identifying an initial estimated distribution of the impulse response of the transmission system. And (1) Fourier transforming the estimated distribution of the impulse response to obtain a first function, and (2) a spectrum of the original information distribution in the first function. Multiplying the distribution to obtain a second function; (3) obtaining a third function by performing an inverse Fourier transform on the second function; and (4) determining the distribution of the deterioration information as the third function.
- impulse response refers to the distribution of deterioration information when the distribution of original information is given by a unit impulse function.
- impulse response refers to the PSF distribution.
- the frequency response indicates the ratio of the spectrum distribution of the degradation information distribution to the spectrum distribution of the original information distribution.
- the frequency response refers to the distribution of the optical transfer function (OTF).
- the information handled by the method of the present invention is not limited to an image, but can be applied to a time history of an electric signal.
- the present invention will be described by taking the case of handling an image as information. The principle of this method will be described.
- the original image is a black and white image and the original image is transmitted via a certain optical system to form a black and white deteriorated image
- the original image and the deteriorated image have the same size, and the position of the point in the image can be expressed by coordinates (X, y), and the illuminance distribution of the original image is f (x , Y), and the illumination distribution of the degraded image is expressed as g (x, y).
- the OTF of the above optical system is the distribution of the original image; ⁇ (x, y) spatial spectrum F ⁇ (s, t), and the degraded image distribution g (x, y) spatial spectrum G (s, For t), it is a complex function H (s, t) that satisfies the following relationship.
- H (s, t) which is an OTF determined by the optical system and imaging conditions, is used for any original image distribution f (x, y). It is possible to obtain a degraded image g (x, y).
- OTF which is a complex function, consists of an amplitude transfer function (MTF) that expresses the magnitude of complex amplitude (MTF) M (s, t) and a phase transfer function (PTF) that expresses phase shift (PTF). ) Using P (s, t),
- the phase-related characteristics of the optical system can be accurately evaluated.
- the above OTF can calculate the characteristic parameter force of the optical system. it can.
- the distribution of the original image and the distribution of the deteriorated image are treated as a probability density function, and the original image is estimated based on Bayes' theory.
- the original image distribution; ⁇ (x, y) and degraded image distribution g (x, y) set above can be handled as a probability density function by performing the following normality.
- the optical transfer function H (S, t) is also normalized.
- H (s, t) is normalized using the value at the point where the spatial frequency is zero.
- the normalized distribution f (x, y) of the original image and the distribution g (x, y) of the degraded image are non-negative functions, and the integral value in the defined region is 1. Can be treated as a probability density function.
- f (x, y) is the probability density function of the event of imaging at the coordinates (x, y) of the original image.
- g (x, y) is the probability density function of the image and the phenomenon at the coordinates (x, y) of the degraded image.
- the distribution of the original image and the deteriorated image is calculated from the distribution of the deteriorated image based on Bayes's theory. Can be estimated.
- V ( Xi , ⁇ ) is an event where a point light source exists at the coordinates (x, y) of the original image
- a (X, y) is an event where a point image is formed at the coordinates (X, y) of the degraded image.
- the original point image is formed at the point (x, y) in the degraded image.
- the image distribution P (V (x, y) I A (x, y)) is estimated as follows.
- the left side of the above expression represents the distribution of the estimated original image when a point image is formed in the degraded image.
- the distribution f (x, y) satisfying the above relationship is defined as f (x, y) (x, y) on the right side of equation (14). 14) The f (x, y) on the left side of f) is assumed to be f (x, y), and f (x, y) is iterated, f (x k + 1 kk
- the convergence value of (x, y) corresponds to the estimated distribution of the original image based on Bayes' theory.
- the first estimated distribution f (x, y) of the original image is set before performing the iterative calculation.
- the first estimated distribution f (x, y) set an arbitrary distribution.
- the degraded image distribution g (x, y) is not significantly different from the original image distribution f (x, y), so the first estimated distribution f ( ⁇ , y)
- Equation (14) includes a convolution integral using PS (h (x, y)).
- PS h (x, y)
- Whether or not k has converged may be determined, for example, by setting the number of iterations in advance and determining the number of iterations.
- Judgment may be made based on whether or not the sum of the absolute values of the calculated differences falls below a certain threshold value.
- k is treated as a complex function in order to accurately evaluate the phase characteristics during the restoration process.
- H (s, t), which is an OTF, is specified based on the characteristics of the transmission system.
- f (x, y) is the first estimated distribution of the original image
- FT " 1 () represents the two-dimensional inverse Fourier transform.
- the real part of k corresponds to the restored image f (x, y) of the original image.
- an original image can be estimated using Fourier transform without using convolution integral, inverse Fourier transform, and four arithmetic operations. For this reason, it is possible to significantly reduce the processing time compared to the case of using the Richardson-Lu Cy algorithm.
- the OTF distribution H (s, t) is estimated by performing Fourier transform on the calculated h (x, y). can do.
- h (x, y) on the right side of equation (14) is set to h (x, y), and the left side k of equation (24)
- H (x, y) is set to h (x, y), and the iterative calculation for h (x, y) is performed to obtain the k + 1 k k bundle value of h (x, y).
- the Fourier transform of the convergence value of h (x, y) obtained by the above iteration is k
- k is treated as a complex function in order to accurately evaluate the phase characteristics during the iterative calculation.
- the distribution g (x, y) of the degraded image and the distribution f ( ⁇ , y) of the original image are specified.
- the real part of g (x, y) is set as the illuminance distribution in the degraded image
- the imaginary part of g (x, y) is set to 0.
- the real part of f (x, y) is the illuminance distribution in the original image
- the imaginary part of f (x, y) is 0, and then the original image distribution f (x, y) is Fourier transformed. Calculate the spectral distribution F (s, t) of the original image distribution.
- Y may be any distribution.
- the first estimated distribution h (x, y) of PSF is real
- the part is 1 and the imaginary part is 0.
- F # (s, t) is an inversion function of F (s, t)
- F (s, t) F (—s, —t).
- the OTF of the transmission system can be suitably estimated.
- OTFs for all frequency bands can be estimated even when the original image distribution does not include a specific frequency band!
- the original image can be restored, and if the degraded image and the original image are known, the OTF can be estimated.
- Another method of the present invention is a method for restoring original information from deterioration information.
- the method includes a step of identifying a distribution of degradation information, a step of identifying an initial estimated distribution of original information, a step of identifying an initial estimated distribution of an impulse response of a transmission system, and (A) said degradation Updating the estimated distribution of the impulse response based on the distribution of information, the estimated distribution of the original information, and the estimated distribution of the impulse response; and (B) the distribution of the deterioration information and the estimated distribution of the original information
- the step (A) of updating the estimated distribution of the impulse response includes: (A1) Fourier transforming the estimated distribution of the original information to obtain the spectral distribution of the estimated distribution of the original information. And (A2) obtaining a first function by Fourier transforming the estimated distribution of the impulse response, and (A3) multiplying the first function by the spectral distribution of the estimated distribution of the original information to obtain a second function. (A4) obtaining a third function by performing inverse Fourier transform on the second function, and (A5) dividing the distribution of the degradation information by the third function to obtain a fourth function.
- the step (B) of updating the estimated distribution of the original information includes (B1) Fourier transforming the estimated distribution of the impulse response to obtain an estimated distribution of the frequency response of the transmission system; (B2) obtaining a first function by Fourier transforming the estimated distribution of the original information; (B3) obtaining a second function by multiplying the first function by the estimated distribution of the frequency response; (B4) a step of obtaining a third function by performing inverse Fourier transform on the second function, and (B5) a step of obtaining a fourth function by dividing the distribution of the deterioration information by the third function.
- OTF it is possible to obtain a more improved estimated distribution by calculation based on Bayes's theory using the distribution of the degraded image and the estimated distribution of the original image.
- a more improved estimated distribution can be obtained by calculation based on Bayes's theory using the distribution of the degraded image and the estimated distribution of OTF.
- Estimated distribution force of OTF used to estimate the original image The closer to the true OTF distribution, the closer the estimated distribution to the true original image can be obtained.
- the estimated distribution of the original image approaches the distribution of the true original image
- the estimated distribution of OTF is It approaches the true OTF distribution and results in both a well-reconstructed original image and a well-estimated OTF.
- the original image can be restored from only the deteriorated image by sequentially performing the following steps.
- the first estimated distribution of the original image and the first estimated distribution of PSF are set. Any initial distribution of the original image may be used. In general, since the distribution of the degraded image does not greatly vary the distribution power of the original image, it is preferable to use the distribution of the degraded image as the initial estimated distribution of the original image. Any distribution may be used for the initial estimated distribution of PSF.
- Equations (27) to (29) is performed to improve the estimated PSF distribution h (s, t)
- the estimated original image distribution approaches the true original image distribution!
- the OTF distribution approaches the true OTF distribution. Therefore, the original image can be restored by performing the above iterative calculation.
- the step of updating the estimated distribution of the impulse response of (A) repeats the steps of (A2) to (A10), and In the step (B) of updating the estimated distribution of the original information, the steps (B2) to (B10) are preferably repeatedly executed.
- the frequency response estimation method or the degradation information restoration method described above can be embodied as a program that causes a computer to execute each step.
- Figure 12 shows an example of the computer hardware configuration.
- FIG. 8 illustrates a functional block diagram of the apparatus 1000 of the present invention.
- the device 1000 of the present invention is a device that estimates the distribution of the frequency response of the transmission system from the original information and the degradation information.
- the device 1000 includes a means 1002 for identifying the distribution of deterioration information, a means 1004 for identifying the spectral distribution of the original information distribution, a means 1006 for identifying the initial estimated distribution of the impulse response of the transmission system, and (1) Means 1008 for obtaining a first function by Fourier transforming the estimated distribution of impulse responses; and (2) means 1010 for obtaining a second function by multiplying the first function by the spectral distribution of the distribution of the original information.
- FIG. 9, FIG. 10 and FIG. 11 illustrate functional block diagrams of the apparatus 1100 of the present invention.
- the apparatus 1100 of the present invention is an apparatus that restores original information from deterioration information.
- the apparatus 1100 includes means 1102 for identifying the distribution of deterioration information, means 1104 for identifying the initial estimated distribution of the original information, means 1106 for identifying the first estimated distribution of the impulse response of the transmission system, and (A ) Means 1108 for updating the estimated distribution of the impulse response based on the distribution of the deterioration information, the estimated distribution of the original information, and the estimated distribution of the impulse response; and (B) the distribution of the deterioration information and the original information Based on the estimated distribution and the estimated distribution of the impulse response, a means 1110 for updating the estimated distribution of the original information, a means 1112 for causing the above means (A) and (B) to alternately perform processing, and an original information A means 1114 for outputting original information based on the estimated distribution is provided.
- FIG. 10 shows a functional block diagram of the means 1108 for updating the estimated distribution of the impulse response (A).
- the means 1108 for updating the estimated distribution of the impulse response (A) is (A1) means 1116 for obtaining a spectral distribution of the estimated distribution of the original information by Fourier transforming the estimated distribution of the original information, and (A2) the impulse response.
- FIG. 11 shows an example of a functional block diagram of the means 1110 for updating the estimated distribution of the original information (B).
- the means 1110 for updating the estimated distribution of the original information in (B) includes (B1) means 1134 for obtaining an estimated distribution of the frequency response of the transmission system by performing a Fourier transform on the estimated distribution of the impulse response.
- the means 1108 for updating the estimated distribution of the impulse response (A) described above includes the above (A2) to (A10).
- a means 1152 for causing the means to perform an iterative process, and a means 1110 for updating the estimated distribution of the original information of (B) includes a means 1154 for causing the means of (B2) to (B10) to perform an iterative process.
- the frequency response of the transmission system can be estimated based on the distribution of the deterioration information and the distribution of the original information.
- frequency responses for all frequencies can be obtained even if the distribution of the original information does not have a specific frequency band.
- the method, program or device described above can be applied to visualization of the dynamics of nano-level structures of biological macromolecules such as peptides and proteins, and image analysis in the field of astronomy. Is possible.
- FIG. 1 is a diagram showing a flowchart of a method according to a first embodiment of the present invention.
- FIG. 2 is a view showing a flowchart of a method according to a second embodiment of the present invention.
- FIG. 3 is a diagram showing a flowchart of a PSF estimation process in the method according to the second embodiment of the present invention.
- FIG. 4 is a view showing a flowchart of an original image estimation process in the method according to the second embodiment of the present invention.
- FIG. 5 is a diagram showing an outline of a method according to the first embodiment of the present invention.
- FIG. 6 is a diagram showing an outline of a method according to a second embodiment of the present invention.
- FIG. 7 is a diagram schematically showing transmission through an optical system to an original image force deteriorated image.
- FIG. 8 is a functional block diagram of a frequency response distribution estimation apparatus 1000 according to the present invention.
- FIG. 9 is a functional block diagram of a degradation information restoration apparatus 1100 according to the present invention.
- FIG. 10 is a functional block diagram of (A) means 1108 for updating an estimated distribution of impulse responses of restoration apparatus 1100.
- FIG. 11 is a functional block diagram of (B) means 1110 for updating the estimated distribution of original information of restoration apparatus 1100.
- FIG. 12 is a diagram illustrating a hardware configuration example of a computer.
- FIG. 1 is a flowchart for explaining the method of this embodiment.
- the black and white original image 10 when transmitted through the optical system 12 and becomes the black and white deteriorated image 14, the original image 10 and the deteriorated image 14 It deals with the method of estimating the OTF of optical system 12.
- the method of this embodiment performs iterative calculation using the black and white original image 10 and the black and white deteriorated image 14 to estimate the OTF of the optical system 12.
- the original image 10 and the deteriorated image 14 have the same size, and the position of a point on the image can be expressed by (x, y).
- the real part of the distribution g (x, y) is the illuminance distribution in the degraded image
- the real part of the distribution f (x, y) is the illuminance distribution in the original image.
- step 502 the distribution g (x, y) of the deteriorated image is specified.
- the phase characteristic of g (x, y) is unknown, so the real part of g (x, y) is the illuminance distribution in the degraded image, and g
- step 504 the distribution f (x, y) of the original image is specified.
- the phase characteristics of f (x, y) are unknown, so the real part of f (x, y) is the illuminance distribution in the original image, and the imaginary part of f (x, y) is all 0.
- Step 506 the first estimated distribution h (x, y) of the PSF of the optical system 12 is set.
- h (x, y) 1 is set for all (x, y). Also step
- the number k of iterations is set to zero.
- step 508 the distribution f (x, y) of the original image is Fourier transformed, and the result is set to F (s, t).
- s is the spatial frequency in the X direction
- t is the spatial frequency in the y direction.
- the above Fourier transform is related to the spatial frequency in the two-dimensional plane and is defined by the following equation.
- FT () in the above equation and FIG. 1 represents a two-dimensional Fourier transform.
- the above-described Fourier transform can be suitably implemented by using a fast Fourier transform.
- the function F (s, t) calculated by the above represents the spatial spectrum of the original image distribution f (x, y).
- step 510 the estimated PSF distribution h (x, y) is Fourier transformed, and the result is obtained.
- the function 1 ⁇ (3, t) corresponds to the first function.
- k is a non-negative integer and increases in a later step 526 depending on the number of iterations.
- step 512 the function K (s, t) calculated in step 510 is multiplied by the spectral distribution F (s, t) of the original image calculated in step 508 to obtain the function (s, t). calculate.
- step 514 the function K (s, t) calculated in step 512 is subjected to inverse Fourier transform
- the inverse Fourier transform described above calculates the real space distribution from the spectrum related to the spatial frequency in the two-dimensional plane, and is defined by the following equation.
- FT- 1 () in the above equation and FIG. 1 represents a two-dimensional inverse Fourier transform.
- step 516 the degraded image distribution g (x, y) specified in step 502 is divided by the function L (x, y) calculated in step 514 to obtain a function (x, y). Is calculated. Function (x, y) is
- step 518 the function L (x, y) calculated in step 516 is Fourier-transformed to obtain the result.
- the function K (s, t) corresponds to the fifth function.
- step 520 the function K (s, t) calculated in step 518 is multiplied by F # (s, t).
- step 522 the function K (s, t) calculated in step 520 is subjected to inverse Fourier transform, and the result is obtained.
- the function L (x, y) corresponds to the seventh function.
- step 524 the function L calculated in step 522 is added to the estimated PS distribution h (x, y). Multiply (x, y) to calculate an improved PSF estimated distribution h (x, y).
- the function L7 is
- the estimated distribution of PSF including the phase characteristics can be improved by the above method.
- step 526 the improved estimated PSF distribution h (x, y) and the estimated PSF distribution h (x, x,
- step 528 If it is determined that the convergence has not been reached, the process proceeds to step 528. If the absolute value of the difference is below the threshold ⁇ for all ( x , y) (YES in step 526), the improved PSF estimated distribution h (x, y) has converged The process is step 5
- step 528 the number k of iterations is increased by one.
- the process proceeds to step 510, and the processes from step 510 to step 524 are performed again.
- step 530 the estimated distribution h (x, y) of the PSF obtained as a result of the iterative calculation is Fourier transformed.
- the H (s, t) calculated by the above method may be displayed on a display, printed on paper using a printing device, or stored in a storage device such as a hard disk. Alternatively, it may be transmitted to another computer via a communication line.
- Figure 5 shows how the OTF distribution of the optical system is estimated from the degraded image 14 and the original image 10 by the method described above.
- Figure 5 shows the real part of the PSF distribution corresponding to the estimated OTF distribution.
- PSF estimated distribution 52 shows the result when the above iterative calculation is repeated twice
- PSF estimated distribution 54 shows the result when the above iterative calculation is repeated 50 times
- PSF estimated distribution 56 is This shows the case where the above iterative calculation is repeated 250 times.
- a monochrome original image 10 is transmitted via the optical system 12.
- the deteriorated image 14 is black and white
- the original image 10 is restored and the OTF of the optical system 12 is estimated based only on the deteriorated image 14.
- the method of this embodiment assumes an appropriate distribution for each of the original image distribution and the OTF distribution.
- the improved OTF distribution of the optical system 12 is estimated by iterative calculation using the assumed distribution of the original image and the distribution of the degraded image.
- the improved distribution of the original image is estimated by iterative calculation using the estimated OTF distribution and the distribution of the degraded image.
- the original image 10 and the degraded image 14 have the same size, and the position of a point on the image can be expressed by (x, y).
- the distribution g (x, y) describing the degraded image 14 and the distributions f (x, y) and f n (x, y) describing the original image 10 estimated during the iterative calculation are Estimated in the process of iterative calculation, kk
- PSF distributions h (x, y) and h m (s, y) are all treated as complex functions.
- the real part of the distribution g (x, y) is the illuminance distribution in the degraded image
- FIG. 2 shows a flowchart of the image restoration method of the present embodiment.
- step 602 the degraded image distribution g (x, y) is specified.
- the real part of g (x, y) is the illuminance distribution in the degraded image
- the imaginary part of g (x, y) is all zero.
- Step 604 the initial estimated distribution f (x, y) of the original image is set.
- the degraded image distribution g (x, y) is used as the initial estimated distribution f (x, y) of the original image.
- the distribution of the original image and the distribution of the degraded image are considered not to differ greatly, so the original image can be restored by setting the original estimated distribution f (x, y) of the original image as described above.
- step 604 the first estimated distribution h (x, y) of PSF is set.
- First of PSF An arbitrary distribution can be set as the estimated distribution h (x, y). Method of this example
- step 604 the number of iterations k is set to zero.
- step 606 the number k of iterations is increased by one.
- step 608 the PSF estimated distribution h (x, y) is calculated. K for this calculation
- step 610 the estimated distribution h (x, y) of the PSF is Fourier transformed to obtain the estimated OTF k.
- step 612 an estimated distribution f (x, y) of the original image is calculated. K for this calculation
- step 614 the difference between the estimated distribution f (x, y) of the original image updated in step 612 and the estimated distribution f of the original image before being updated is calculated, and the difference is calculated for all ( x, y) versus k— 1
- step 606 If it is determined that the convergence has not been reached, the process proceeds to step 606, and the processes from step 606 to step 612 are repeated again. If the difference is less than the threshold ⁇ for all (x, y) (YES in step 614), the estimated distribution f (x, y) of the original image reaches convergence and k
- step 616 the estimated distribution f (x, y) of the original image obtained as a result of the iterative calculation is restored to k.
- the distribution f (x, y) of the original image is generally a complex function.
- the real part of the restored original image distribution f (x, y ) represents the illuminance distribution in the original image.
- the f (x, y) calculated by the above method may be displayed on a display, printed on paper using a printing device, or stored in a storage device such as a hard disk. Alternatively, it may be transmitted to another computer via a communication line.
- h (x, y) is estimated using steps 702 to 726 shown in the flowchart of FIG.
- step 702 the first estimated distribution h ° (x, y) of h (x, y) is set. K k of this example
- step 702 the number of iterations m for estimating h (x, y) is set to 0.
- step 704 an estimated distribution F (s, t) of the spectrum of the original image is set.
- step 706 the estimated distribution h m (x, y) of h (x, y) is Fourier transformed and the result is kk
- the function K (s, t) corresponds to the first function.
- step 708 the function K (s, t) calculated in step 706 is multiplied by the estimated distribution F (s, t) of the spectrum of the original image calculated in step 704 to obtain the function K (s, t) is calculated.
- the function K (s, t) corresponds to the second function.
- step 710 the function K (s, t) calculated in step 708 is inverse Fourier transformed
- the function L (x, y) corresponds to the third function.
- step 712 the degraded image distribution g (x, y) specified in step 604 in FIG. 2 is divided by the function L (x, y) calculated in step 710 in FIG. Calculate (x, y).
- the number (x, y) corresponds to the fourth function.
- step 714 the function L (x, y) calculated in step 712 is Fourier-transformed to obtain the result.
- the function K (s, t) corresponds to the fifth function.
- step 716 the function K (s, t) calculated in step 714 is multiplied by F # (s, t).
- step 718 the function K (s, t) calculated in step 716 is subjected to inverse Fourier transform.
- the function L (x, y) corresponds to the seventh function.
- step 720 the function set in step 718 is added to the estimated distribution h m (x, y) of h (x, y). Multiply the number L (x, y) and set the result to the improved estimated distribution h m + 1 (x, y) of h (x, y).
- step 722 the number m of iterations for estimating h (x, y) is increased by 1 k.
- step 724 the number of iterations for estimating h (x, y)
- the number of recalculations is 5 times. If the number of repetitions m is less than 5 (NO in step 724), the process proceeds to step 706, and the processes from step 706 to step 722 are performed again. If the number of repetitions m is 5 or more (YES in step 724), the process proceeds to step 726.
- step 726 the distribution h 5 (x, y) obtained as a result of the above iterative calculation is set as the kk estimated distribution of h (x, y).
- the above iterative calculation is based on the degraded image distribution g (x, y) and the original image distribution f (x, y).
- the original image distribution f (x, y) is the true original image component k k— 1
- f (x, y) is estimated using steps 802-8 k shown in the flowchart of FIG.
- step 802 the first estimated distribution f ° (x, y) of f (x, y) is set. K k of this example
- f (x, y) that has already been obtained is set as k ⁇ 1 k k with the first estimated distribution f ° (x, y) of f (x, y). Also, in step 802, iterative calculation iteration k for estimating f (x, y) k
- step 804 the estimated distribution f n (x, y) of f (x, y) is Fourier transformed, and the result is kk
- the function K (s, t) corresponds to the first function.
- step 806 the function K (s, t) calculated in step 804 is multiplied by the estimated OTF distribution H (s, t) calculated in step 610 in Fig. 2 to obtain the function (s, t ) Is calculated.
- step 808 the function K (s, t) calculated in step 806 is subjected to inverse Fourier transform.
- the function L (x, y) corresponds to the third function.
- step 810 the degraded image distribution g (x, y) identified in step 602 in FIG. 2 is divided by the function L (x, y) calculated in step 808 in FIG. Calculate (x, y).
- step 812 the function L (x, y) calculated in step 810 is subjected to Fourier transform, and the result is obtained.
- the function K (s, t) corresponds to the fifth function.
- step 814 the function K (s, t) calculated in step 812 is multiplied by H # (s, t).
- H # (s, t) is the OTF calculated in step 610 of Figure 2.
- step 816 the function K (s, t) calculated in step 814 is inverse Fourier transformed.
- the function L (x, y) corresponds to the seventh function.
- step 818 the function kk calculated in step 816 is added to the estimated distribution f n (x, y) of f (x, y).
- step 820 the number n of iterations for estimating f (x, y) is incremented by one.
- step 822 the number n of iterations for estimating f (x, y) is equal to or less than the threshold value k.
- the number of recalculations is 5 times. If the number of repetitions n is less than 5 (NO in step 822), the process proceeds to step 804, and the processes up to step 804 and step 820 are performed again. If the number of repetitions n is 5 or more (YES in step 822), the process proceeds to step 824.
- step 824 the distribution f 5 (x, y) obtained as a result of the above iterative calculation is set as the estimated kk distribution of f (x, y).
- the above iterative calculation is based on the degraded image distribution g (x, y) and the OTF distribution H (s, t).
- FIG. 6 using the above method, an iterative calculation is performed based only on the degraded image 14, The result of restoring the original image 62 is shown. Characters that are almost unrecognizable in the degraded image 14 due to blurred outlines can be clearly recognized as characters in the restored original image 62.
- Figure 6 shows the distribution 64 of the PSF real part corresponding to the OTF of the optical system 12 estimated in parallel with the restoration of the original image 62.
- the illuminance distribution fr (x, y) of the R color component in the original image can be estimated by iterative calculation using the illuminance distribution gr (x, y) of the R color component in the degraded image. .
- the original image can be restored from the illuminance distribution of each RGB of the original image estimated by the above.
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US20090013020A1 (en) | 2009-01-08 |
EP1801753B1 (en) | 2016-12-07 |
US8019803B2 (en) | 2011-09-13 |
EP1801753A1 (en) | 2007-06-27 |
JP4568730B2 (ja) | 2010-10-27 |
EP1801753A4 (en) | 2010-03-10 |
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