Image processing apparatus, image processing method, image processing program, and recording medium

Abstract

In the present invention, in a noise estimation step S2, a noise image included in a subject image that includes linear noise extending along a first direction is estimated. In this instance, an evaluation function that includes a first term, which represents the difference between the result of having performed second-direction differential processing and first-direction low-frequency-component extraction processing on the subject image and the result of having performed second-direction differential processing and first-direction low-frequency-component extraction processing on a noise image, is used to derive a noise image for which the value of the evaluation function is minimal. In a noise reduction step S3, an image in which noise is reduced from the subject image is generated on the basis of the subject image and the noise image. Thus, there are realized an image processing method, etc., with which it is possible to process a subject image that includes linear noise extending along one direction and to generate a post-noise-reduction-processing image that maintains the quantitative properties of the subject image.

Description

Technical Field

[0001] The present disclosure relates to an image processing apparatus, an image processing method, an image processing program, and a recording medium.

Background Art

[0002] There are several known techniques for creating a phase differential image based on one or more interference images obtained by an apparatus applying a differential interference microscope, and further obtaining a phase image based on the phase differential image. In these techniques, a phase image can be created by performing an integration process or a deconvolution process on the phase differential image. These techniques are suitably used, for example, when obtaining a phase image of cells.

[0003] The phase image created in this way may include linear noise (linear artifacts) extending along one direction, and in that case, it often includes a plurality of linear noises parallel to each other. Images including linear noise extending along one direction include not only phase images obtained using an apparatus applying a differential interference microscope, but also other types of images.

[0004] Non-Patent Document 1 describes a technique capable of processing a target image including linear noise extending along one direction to generate an image with reduced noise.

Prior Art Documents

Non-Patent Documents

[0005]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0006] However, in the technique described in Non-Patent Document 1, although an image with reduced noise can be generated from the target image, even if the target image has quantitativeness, the quantitativeness is lost in the image after the noise reduction process.

[0007] An embodiment aims to provide an image processing apparatus, an image processing method, an image processing program, and a recording medium that can process a target image including linear noise extending along one direction and generate an image after noise reduction that maintains the quantitativeness of the target image.

Means for Solving the Problems

[0008] An embodiment is an image processing apparatus. The image processing apparatus is an apparatus that processes a target image including linear noise extending along a first direction to generate an image with reduced noise, and includes a noise estimation unit that estimates a noise image included in the target image, and a noise reduction unit that generates an image with reduced noise from the target image based on the target image and the noise image. The noise estimation unit uses an evaluation function including a first term representing the difference between the result of performing differential processing in a second direction orthogonal to the first direction and low-frequency component extraction processing in the first direction on the target image, and the result of performing differential processing in the second direction and low-frequency component extraction processing in the first direction on the noise image, to obtain a noise image that minimizes the value of the evaluation function.

[0009] An embodiment is an image processing method. The image processing method is a method for processing a target image including linear noise extending along a first direction to generate an image with reduced noise, including a noise estimation step of estimating a noise image included in the target image, and a noise reduction step of generating an image with reduced noise from the target image based on the target image and the noise image. In the noise estimation step, an evaluation function including a first term representing the difference between the result of performing differential processing in a second direction orthogonal to the first direction and low-frequency component extraction processing in the first direction on the target image and the result of performing differential processing in the second direction and low-frequency component extraction processing in the first direction on the noise image is used to obtain a noise image that minimizes the value of the evaluation function.

[0010] An embodiment is an image processing program. The image processing program is a program for causing a computer to execute each step of the above image processing method.

[0011] An embodiment is a recording medium. The recording medium is a computer-readable medium on which the above image processing program is recorded.

Advantages of the Invention

[0012] According to the image processing apparatus, image processing method, image processing program, and recording medium of the embodiment, it is possible to process a target image including linear noise extending along one direction and generate an image after noise reduction processing that maintains the quantitative nature that the target image had.

Brief Description of the Drawings

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[0014] Hereinafter, embodiments of an image processing apparatus, an image processing method, an image processing program, and a recording medium will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same reference numerals are assigned to the same elements, and redundant descriptions are omitted. The present invention is not limited to these examples.

[0015] FIG. 1 is a diagram showing the configuration of an image processing apparatus 1 according to the present embodiment. The image processing apparatus 1 includes a control unit 10, a target image creation unit 11, a noise estimation unit 12, a noise reduction unit 13, an input unit 14, a storage unit 15, and a display unit 16. The image processing apparatus 1 may be a computer. The control unit 10 controls the operations of the target image creation unit 11, the noise estimation unit 12, the noise reduction unit 13, the input unit 14, the storage unit 15, and the display unit 16, and includes a CPU.

[0016] The target image creation unit 11, the noise estimation unit 12, and the noise reduction unit 13 perform image processing and include a processing device such as a CPU, a DSP, or an FPGA. The input unit 14 inputs data of an image to be processed and inputs image processing conditions using a keyboard or a mouse.

[0017] The storage unit 15 stores data of various images and includes a hard disk drive, a flash memory, a RAM, a ROM, and the like. Note that the target image creation unit 11, the noise estimation unit 12, the noise reduction unit 13, and the storage unit 15 may be configured by cloud computing. The display unit 16 displays an image to be processed, an image during processing, and an image after processing, and includes, for example, a liquid crystal display.

[0018] The storage unit 15 stores a program for causing the target image creation unit 11, the noise estimation unit 12, and the noise reduction unit 13 to execute each step of the image processing. This image processing program may be stored in the storage unit 15 at the time of manufacturing or shipping of the image processing apparatus 1, or may be stored in the storage unit 15 after shipping, having been acquired via a communication line, or may be stored in the storage unit 15 having been recorded on a computer-readable recording medium 2. The recording medium 2 may be arbitrarily selected, such as a flexible disk, CD-ROM, DVD-ROM, BD-ROM, USB memory, etc.

[0019] FIG. 2 is a flowchart for explaining the image processing method of the present embodiment. The image processing method of the present embodiment includes a target image creation step S1, a noise estimation step S2, and a noise reduction step S3.

[0020] The target image creation step S1 is a process performed by the target image creation unit 11. The noise estimation step S2 is a process performed by the noise estimation unit 12. The noise reduction step S3 is a process performed by the noise reduction unit 13. As an example, the case of creating a phase image from a phase differential image in the target image creation step S1 will be described.

[0021] In the target image creation step S1, the target image creation unit 11 creates a phase image by performing integration processing or deconvolution processing on the phase differential image. The phase image created here is the target image to be subjected to the noise reduction process.

[0022] In the noise estimation step S2, the noise estimation unit 12 estimates the noise image included in the target image (phase image). In the noise reduction step S3, the noise reduction unit 13 generates an image with reduced noise (post-noise reduction processed image) from the target image based on the target image and the noise image. Specifically, the post-noise reduction processed image can be generated by subtracting the noise image from the target image. Hereinafter, each step will be described in detail with specific image examples.

[0023] Fig. 3(a) is a diagram showing a phase differential image. This phase differential image is created from an interference image obtained by an apparatus applying a differential interference microscope. The shear direction in the differential interference microscope is the horizontal direction in this figure. This phase differential image shows, in addition to several cells as the observation target, a background region around them where the phase is substantially uniform (i.e., the phase differential is substantially 0).

[0024] Fig. 3(b) is a diagram showing a phase image. This phase image is created by the target image creation unit 11 in the target image creation step S1 by performing an integration process on the phase differential image in Fig. 3(a). Specifically, assuming the phase image to be obtained is x, the differential process in the first direction (the horizontal direction, the shear direction in the figure) for the phase image x is A, the phase differential image is b, and a positive constant is λ, the phase image x can be obtained by solving the optimization problem represented by the following equation (1).

Equation

[0025] In the above, λ is set to a value in the range of, for example, 10 -5 ~10 -2 . The phase image x can be obtained such that, under the constraint condition that the phase value is 0 or more, the difference between Ax, which is the result of performing the differential process A in the first direction on the phase image x, and the phase differential image b is minimized. As shown in this figure, the phase image x includes linear noise (linear artifacts) extending along the first direction (the horizontal direction in the figure).

[0026] Fig. 4(a) is a diagram showing a noise image. This noise image is estimated by the noise estimation unit 12 in the noise estimation step S2 as being included in the phase image in Fig. 3(b) (the target image to be subjected to noise reduction processing). Details of the estimation process of the noise image in the noise estimation step S2 will be described later.

[0027] FIG. 4(b) is a diagram showing the image after the noise reduction process. This image after the noise reduction process is generated by subtracting the noise image in FIG. 4(a) from the target image (phase image) in FIG. 3(b) by the noise reduction unit 13 in the noise reduction step S3. As shown in this figure, the image after the noise reduction process has had the noise contained in the target image reduced and has maintained the quantitative property that the target image had.

[0028] Next, the process of estimating the noise image included in the target image in the noise estimation step S2 will be described in detail. Let the target image be x and the noise image included in the target image x be y.

[0029] Let the low-pass component extraction process in the first direction (the left-right direction in the figure) for the image be L 1 and the high-pass component extraction process in the first direction for the image be L 2 Let the differential process in the second direction (the up-down direction orthogonal to the first direction in the figure) for the image be D, and the process of extracting the background region in the image be M. Also, let the positive constants be λ and μ.

[0030] In the above, for example, λ is set to a value in the range of 10 -3 ~10 -1 and μ is set to a value in the range of 10 -2 ~1. The noise image y is estimated by solving the optimization problem represented by the following equation (2) for the evaluation function E(x, y) represented by the following equation (3).

Equation

Equation

[0031] The first term of the evaluation function E(x, y) represented by the above equation (3) is the result L 1 Dx obtained by performing the differential process D in the second direction and the low-pass component extraction process L 1 in the first direction on the target image x, and the differential process D in the second direction and the low-pass component extraction process L on the noise image y1 As a result of performing 1 represents the difference between Dy and. Differentiation processing D and low-frequency component extraction processing L for each image 1 The order of is arbitrary. Also, differentiation processing D and low-frequency component extraction processing L are performed on the difference between the target image x and the noise image y 1 may be performed.

[0032] Since the linear noise (linear artifact) contained in the target image extends along the first direction (left-right direction) of the target image, the change in noise is large along the second direction, and the spatial frequency of the noise is low along the first direction. Therefore, the noise image y can be obtained as the one that minimizes the first term of the evaluation function E(x, y).

[0033] FIGS. 5 and 6 are diagrams showing image examples for explaining the first term of the evaluation function E(x, y). FIG. 5(a) is a diagram showing the target image x. FIG. 5(b) is a diagram showing the image Dx which is the result of performing the differentiation processing D in the second direction on the target image x of FIG. 5(a). In this image Dx, the noise is clear, but the information (high-frequency component) of the observation target also exists.

[0034] FIG. 5(c) is the image L 1 which is the result of performing the low-frequency component extraction processing L in the first direction on the image Dx of FIG. 5(b) 1 showing Dx. In this image L 1 Dx, the low-frequency components are extracted.

[0035] FIG. 6(a) is a diagram showing the noise image y during the estimation process. FIG. 6(b) is a diagram showing the image Dy which is the result of performing the differentiation processing D in the second direction on the noise image y of FIG. 6(a). Ideally, the information (high-frequency component) of the observation target does not exist in the noise image at the end of the estimation process, but the information (high-frequency component) of the observation target exists in the image Dy during the estimation process.

[0036] FIG. 6(c) is the image L 1 which is the result of performing the low-frequency component extraction processing L in the first direction on the image Dy of FIG. 6(b) 1This is a diagram showing Dy. Since there should ideally be no information (high-frequency components) of the object to be observed in the noise image at the end of the estimation process, this image L 1 Dy is approximately the same as the image Dy.

[0037] The first term of the evaluation function E(x, y) is the image L in Fig. 5(c) 1 Dx and the image L in Fig. 6(c) 1 represents the difference from Dy. A noise image y is obtained such that this difference is minimized.

[0038] The second term of the evaluation function E(x, y) represented by the above equation (3) represents the difference between the result Mx of performing the background region extraction process M on the target image x and the result My of performing the background region extraction process M on the noise image y. The background region extraction process M may be performed on the difference between the target image x and the noise image y. In both the target image x and the noise image y, there is no information of the object to be observed in the background region, and only noise exists. Therefore, the noise image y can be obtained such that the second term of the evaluation function E(x, y) is minimized.

[0039] The third term of the evaluation function E(x, y) represented by the above equation (3) is the result L 2 of performing the high-frequency component extraction process L 2 in the first direction on the noise image y. Along the first direction, the spatial frequency of the noise is lower than the spatial frequency of the information of the object to be observed and does not have high components. Therefore, the noise image y can be obtained such that the third term of the evaluation function E(x, y) is minimized. Fig. 7 is a diagram showing the image L 2 which is the result of performing the high-frequency component extraction process L 2 in the first direction on the noise image y during the estimation process in Fig. 6(a).

[0040] Generally, it is impossible to obtain a noisy image y that can simultaneously minimize all of the first, second, and third terms of the evaluation function E(x, y) expressed by the above equation (3). Therefore, by solving the optimization problem expressed by the above equation (2) such that the evaluation function E(x, y) expressed as a linear sum of the first, second, and third terms using constants λ and μ as in the above equation (3) is minimized, the noisy image y is estimated.

[0041] Note that the evaluation function E(x, y) needs to include the first term in the above equation (3), but it does not necessarily need to include both or either of the second and third terms in the above equation (3).

[0042] That is, the evaluation function E(x, y) may be expressed by any of the following equations (4), (5), and (6) by setting the value of the constant λ or μ to 0 in the above equation (3).

Equation

Equation

Equation

[0043] Next, the noisy image and the image after noise reduction processing obtained when using the evaluation function E(x, y) of each of the above equations (3) to (6) will be described. In any case, the phase image shown in Fig. 3(b) is used as the target image x to be subjected to noise reduction processing.

[0044] When using the evaluation function E(x, y) of the above equation (3), in the noise estimation step S2, the noisy image y shown in Fig. 4(a) is obtained, and in the noise reduction step S3, the image after noise reduction processing shown in Fig. 4(b) is obtained. Here, λ = 1×10 -2 and μ = 1×10 -1 The image after noise reduction processing has sufficiently reduced the noise contained in the target image and sufficiently maintains the quantitative nature of the target image.

[0045] When using the evaluation function E(x, y) of the above formula (4), in the noise estimation step S2, the noise image y shown in Fig. 8(a) is obtained, and in the noise reduction step S3, the image after the noise reduction process shown in Fig. 8(b) is obtained. Here, μ = 1×10 -1 is. The noise image y obtained in this case contains the information of the observation target. Therefore, although the image after the noise reduction process has the noise reduced and some of the information of the observation target is lost, it still relatively well maintains the quantitative property that the target image had.

[0046] When using the evaluation function E(x, y) of the above formula (5), in the noise estimation step S2, the noise image y shown in Fig. 9(a) is obtained, and in the noise reduction step S3, the image after the noise reduction process shown in Fig. 9(b) is obtained. Here, λ = 1×10 -2 is. In the noise image y obtained in this case, a calculation error occurs in the part indicated by the arrow in the figure. Therefore, although the reduction of the noise in the image after the noise reduction process is incomplete, it still relatively well maintains the quantitative property that the target image had.

[0047] When using the evaluation function E(x, y) of the above formula (6), in the noise estimation step S2, the noise image y shown in Fig. 10(a) is obtained, and in the noise reduction step S3, the image after the noise reduction process shown in Fig. 10(b) is obtained. The noise image y obtained in this case contains the information of the observation target. Therefore, although the image after the noise reduction process has the noise reduced and some of the information of the observation target is lost, it still relatively well maintains the quantitative property that the target image had.

[0048] As a comparative example, when using the evaluation function E(x, y) of the following formula (7) that does not include the first term in the above formula (3), in the noise estimation step S2, the noise image y shown in Fig. 11(a) is obtained, and in the noise reduction step S3, the image after the noise reduction process shown in Fig. 11(b) is obtained. Here, λ = 1×10 -1and μ = 1. In this case, the noise image y obtained cannot estimate the noise in the region where the observation target exists. Therefore, the image after the noise reduction process has not had the noise reduced in the region where the observation target exists. [Number]

[0049] In this way, by solving the optimization problem represented by the above equation (2) so that any one of the evaluation functions E(x, y) in the above equations (3) to (6) becomes the minimum, the noise image y can be estimated with high accuracy. And the image after the noise reduction process obtained based on the target image x and the noise image y has had the noise contained in the target image reduced and maintains the quantitative property that the target image had. Note that most preferably, it is the case of using the evaluation function E(x, y) of the above equation (3).

[0050] FIG. 12 and FIG. 13 are diagrams showing images after the noise reduction process obtained by the image processing method of the present embodiment when the refractive index of the solution in which the cells to be observed are immersed is each value. The refractive index of the solution was adjusted by adjusting the concentration of BSA (bovine serum albumin) contained in the solution. The refractive index of the solution was measured using an Abbe refractometer manufactured by ATAGO Co., Ltd. The evaluation function E(x, y) of the above equation (3) was used. Here, λ = 1 × 10 -2 and μ = 1 × 10 -1 is.

[0051] FIG. 12(a) is a diagram showing an image after the noise reduction process obtained when the refractive index of the solution is about 1.335. FIG. 12(b) is a diagram showing an image after the noise reduction process obtained when the refractive index of the solution is about 1.342. FIG. 13(a) is a diagram showing an image after the noise reduction process obtained when the refractive index of the solution is about 1.349. FIG. 13(b) is a diagram showing an image after the noise reduction process obtained when the refractive index of the solution is about 1.362.

[0052] As shown in these figures, regardless of the refractive index value of the solution, the obtained image after noise reduction processing has reduced the noise contained in the target image and maintained the quantitativeness of the target image. As the refractive index of the solution increases, the phase difference between the cell and the solution decreases.

[0053] As shown in Fig. 13(b), even when the phase difference between the cell and the solution is small, the obtained image after noise reduction processing has sufficiently reduced the noise contained in the target image. The refractive index of the solution when the phase difference between the cell and the solution becomes 0 can be determined with high precision as the refractive index of the cell.

[0054] The image processing apparatus, the image processing method, the image processing program, and the recording medium are not limited to the above-described embodiments and configuration examples, and various other modifications are possible.

[0055] The image processing apparatus according to the above embodiment is an apparatus that processes a target image including linear noise extending along a first direction to generate an image with reduced noise, and includes a noise estimation unit that estimates a noise image included in the target image, and a noise reduction unit that generates an image with reduced noise from the target image based on the target image and the noise image. The noise estimation unit uses an evaluation function including a first term representing the difference between the result of performing differential processing in a second direction orthogonal to the first direction and low-frequency component extraction processing in the first direction on the target image and the result of performing differential processing in the second direction and low-frequency component extraction processing in the first direction on the noise image, and obtains a noise image that minimizes the value of the evaluation function.

[0056] In the above image processing apparatus, the noise estimation unit may be configured to use an evaluation function further including a second term representing the difference between the background region in the target image and the background region in the noise image, and obtain a noise image that minimizes the value of the evaluation function.

[0057] In the above-described image processing apparatus, the noise estimation unit may be configured to obtain a noise image that minimizes the value of an evaluation function using an evaluation function that further includes a third term representing the result of performing high-frequency component extraction processing in the first direction on the noise image.

[0058] The above-described image processing apparatus may further include a target image creation unit that creates a target image by performing integration processing or deconvolution processing in the first direction on the differential image.

[0059] The above-described image processing apparatus may be configured to use, as the target image, a phase image created by performing integration processing or deconvolution processing in the first direction on the phase differential image.

[0060] The image processing method according to the above-described embodiment is a method for processing a target image including linear noise extending along a first direction to generate an image with reduced noise, the method including a noise estimation step of estimating a noise image included in the target image, and a noise reduction step of generating, based on the target image and the noise image, an image with reduced noise from the target image. In the noise estimation step, an evaluation function including a first term representing the difference between the result of performing differential processing in a second direction orthogonal to the first direction and low-frequency component extraction processing in the first direction on the target image and the result of performing differential processing in the second direction and low-frequency component extraction processing in the first direction on the noise image is used to obtain a noise image that minimizes the value of the evaluation function.

[0061] In the noise estimation step of the above-described image processing method, an evaluation function that further includes a second term representing the difference between the background region in the target image and the background region in the noise image may be used to obtain a noise image that minimizes the value of the evaluation function.

[0062] In the noise estimation step of the above-described image processing method, an evaluation function that further includes a third term representing the result of performing high-frequency component extraction processing in the first direction on the noise image may be used to obtain a noise image that minimizes the value of the evaluation function.

[0063] The above image processing method may further include a target image creation step of creating a target image by performing an integration process or a deconvolution process in a first direction on a differential image.

[0064] The above image processing method may be configured such that a phase image created by performing an integration process or a deconvolution process in a first direction on a phase differential image is used as the target image.

[0065] The image processing program according to the above embodiment is a program for causing a computer to execute each step of the above image processing method.

[0066] The recording medium according to the above embodiment is a computer-readable medium on which the above image processing program is recorded.

Industrial Applicability

[0067] The embodiment can be used as an image processing apparatus, an image processing method, an image processing program, and a recording medium that can process a target image including linear noise extending along one direction and generate an image after noise reduction processing that maintains the quantitative properties of the target image.

Description of Reference Numerals

[0068] 1... Image processing apparatus, 2... Recording medium, 10... Control unit, 11... Target image creation unit, 12... Noise estimation unit, 13... Noise reduction unit, 14... Input unit, 15... Storage unit, 16... Display unit.

Claims

1. An apparatus for processing a target image including linear noise extending along a first direction to generate an image with the noise reduced, comprising: a target image creation unit that creates the target image by performing integration processing or deconvolution processing in the first direction on a differential image; a noise estimation unit that estimates a noise image included in the target image; a noise reduction unit that generates an image with the noise reduced from the target image based on the target image and the noise image; wherein the noise estimation unit uses an evaluation function including a first term representing a difference between a result of performing differential processing in a second direction orthogonal to the first direction and low-frequency component extraction processing in the first direction on the target image and a result of performing differential processing in the second direction and low-frequency component extraction processing in the first direction on the noise image, and obtains the noise image that minimizes the value of the evaluation function; an image processing apparatus.

2. An apparatus for processing a target image including linear noise extending along a first direction to generate an image with the noise reduced, comprising: a noise estimation unit that uses, as the target image, a phase image created by performing integration processing or deconvolution processing in the first direction on a phase differential image, and estimates a noise image included in the target image; a noise reduction unit that generates an image with the noise reduced from the target image based on the target image and the noise image; wherein the noise estimation unit uses an evaluation function including a first term representing a difference between a result of performing differential processing in a second direction orthogonal to the first direction and low-frequency component extraction processing in the first direction on the target image and a result of performing differential processing in the second direction and low-frequency component extraction processing in the first direction on the noise image, and obtains the noise image that minimizes the value of the evaluation function; an image processing apparatus.

3. The noise estimation unit uses the evaluation function further including a second term representing a difference between a background region in the target image and a background region in the noise image, and obtains the noise image that minimizes the value of the evaluation function. The image processing apparatus according to Claim 1 or 2.

4. The noise estimation unit uses the evaluation function further including a third term representing a result of performing high-frequency component extraction processing in the first direction on the noise image, and obtains the noise image that minimizes the value of the evaluation function. The image processing apparatus according to any one of Claims 1 to 3.

5. The image processing apparatus according to claim 1, wherein a phase image created by performing integral processing or deconvolution processing in the first direction on a phase differential image is used as the target image.

6. A method for processing a target image including linear noise extending along a first direction to generate an image with reduced noise, comprising: A target image creation step of creating the target image by performing integral processing or deconvolution processing in the first direction on a differential image; A noise estimation step of estimating a noise image included in the target image; A noise reduction step of generating an image with reduced noise from the target image based on the target image and the noise image; characterized in that: In the noise estimation step, using an evaluation function including a first term representing a difference between a result of performing differential processing in a second direction orthogonal to the first direction and low-frequency component extraction processing in the first direction on the target image and a result of performing differential processing in the second direction and low-frequency component extraction processing in the first direction on the noise image, a noise image that minimizes the value of the evaluation function is obtained. Image processing method.

7. A method for processing a target image including linear noise extending along a first direction to generate an image with reduced noise, comprising: A noise estimation step of using, as the target image, a phase image created by performing integral processing or deconvolution processing in the first direction on a phase differential image and estimating a noise image included in the target image; A noise reduction step of generating an image with reduced noise from the target image based on the target image and the noise image; characterized in that: In the noise estimation step, using an evaluation function including a first term representing a difference between a result of performing differential processing in a second direction orthogonal to the first direction and low-frequency component extraction processing in the first direction on the target image and a result of performing differential processing in the second direction and low-frequency component extraction processing in the first direction on the noise image, a noise image that minimizes the value of the evaluation function is obtained. Image processing method.

8. In the noise estimation step, using the evaluation function further including a second term representing a difference between a background region in the target image and a background region in the noise image, a noise image that minimizes the value of the evaluation function is obtained. The image processing method according to claim 6 or 7.

9. In the noise estimation step, the noise image that minimizes the value of the evaluation function is obtained by using the evaluation function further including a third term representing the result of performing the high-frequency component extraction process in the first direction on the noise image. The image processing method according to any one of claims 6 to 8.

10. The image processing method according to claim 6, wherein a phase image created by performing the integration process or the deconvolution process in the first direction on the phase differential image is used as the target image.

11. An image processing program for causing a computer to execute each step of the image processing method according to any one of claims 6 to 10.

12. A computer-readable recording medium recording the image processing program according to claim 11.

Images