A method for eliminating ringing artifacts in single-pixel imaging

Abstract

The present invention provides a method for eliminating ringing artifacts in single-pixel imaging, belonging to the field of image filtering technology. The present invention uses a Butterworth low-pass filter to automatically eliminate the ringing artifacts from a single-pixel imaging spectrum graph containing ringing artifacts and reconstruct a higher-quality image. The present invention solves the problem that ringing artifacts exist in the reconstructed target scene of SPI at low sampling rates. The present invention can automatically eliminate ringing artifacts using only a Butterworth low-pass filter, which is more efficient than existing methods and provides a method for achieving high-quality SPI at low sampling rates.

Description

Technical Field

[0001] The present invention belongs to the technical field of image filtering, and in particular relates to a method for eliminating ringing artifacts in single-pixel imaging. Background Art

[0002] In single-pixel imaging (SPI) methods, such as Fourier SPI, Hadamard SPI, and discrete cosine transform SPI, undersampling is often used to shorten imaging time. This method reconstructs the target scene by obtaining a truncated spectrum, which only captures low-frequency information and discards high-frequency information. However, this truncated spectrum can cause ringing artifacts to appear in the reconstructed image. Ringing artifacts are oscillations caused by sharp changes in grayscale in the output image, similar to the vibrations in the air caused by the striking of a bell. Ringing artifacts produce false edges in the reconstructed image, reducing image contrast and resulting in poor reconstruction quality. Finding a method that can effectively remove ringing artifacts among the various SPI methods is highly desirable.

[0003] Existing techniques use contextual learning from Fourier transform SPI images to remove ringing artifacts and restore details in 256×256 images. Compared to deep learning-based ringing artifact removal methods, this method eliminates the need for extensive training and utilizes only a Butterworth low-pass filter, making the overall process more efficient. Existing techniques also use image fusion to preserve image details to remove ringing artifacts. This method involves sub-pixel shifting and image fusion, increasing the computational effort and algorithmic complexity. Summary of the Invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for eliminating ringing artifacts in single-pixel imaging, which solves the current phenomenon that ringing artifacts exist in the reconstructed target scene at a low sampling rate of SPI.

[0005] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0006] This solution provides a method for eliminating ringing artifacts in single-pixel imaging, comprising the following steps:

[0007] S1, obtain the spectrum of the target scene at a low sampling rate;

[0008] S2. Obtain a new spectrum of the target scene through a first-order Butterworth low-pass filter according to the frequency of the target scene;

[0009] S3. Reconstructing the new spectrum of the target scene by using inverse transformation to eliminate ringing artifacts appearing in single-pixel imaging, thereby obtaining a restored target scene.

[0010] Furthermore, the step S1 includes the following steps:

[0011] S101, using the SPI optical system to collect a light intensity signal reflected when the target scene is illuminated by the modulated pattern, and saving the reflected light intensity signal to a computer via a data acquisition card;

[0012] S102: Convert the stored light intensity signal into a frequency spectrum of the target scene at a low acquisition rate through a four-step phase-shift Fourier algorithm.

[0013] Furthermore, the expression of the reflected light intensity signal is as follows:

[0014] R p (k,l)=R n +h∫∫ S A(x,y)P(n,m;k,l)dxdy

[0015] P(n,m;k,l)=a+bsin[2π(nk+ml)+φ]

[0016] Among them, R p (k,l) represents the reflected light intensity signal, R n represents the intensity of ambient light, h represents a constant, S represents the projection area of ​​the modulation pattern, A(x, y) represents the surface albedo of the target scene, dx, dy represent the integration operation, S and A(x, y) are integrated, P(n, m; k, l) represents the modulation pattern, n, m represent the two-dimensional coordinates of the target scene, k, l represent the spatial frequency of the modulation pattern, a represents the DC component, b represents the contrast of the modulation pattern, and φ represents the initial phase of the modulation pattern.

[0017] Furthermore, the expression of the new spectrum of the target scene is as follows:

[0018] F=I4*H(u,v)

[0019]

[0020] D(u,ν)=[(uM / 2) 2 +(vN / 2) 2 ] 1 / 2

[0021] I4=(R p(0) -R p(π) )+i·(R p(π / 2) -R p(3π / 2) )

[0022] Where F represents the new spectrum of the target scene, I4 represents the spectrum obtained by the four-step phase shift Fourier algorithm, H(u,v) represents the Butterworth low-pass filter, D(u,v) represents the distance between the frequency point (u,v) and the center of the frequency domain (M / 2,N / 2), u,v represent the coordinate position of the frequency point on the spectrum graph, M and N represent the length and width of the spectrum graph respectively, D0 represents the cutoff frequency of the Butterworth low-pass filter, n represents the order of the Butterworth low-pass filter, R p(0) and R p(π) Both represent the real part, R p(π / 2) and R p(3π / 2) Both represent the imaginary part, and i is the imaginary unit.

[0023] Beneficial effects of the present invention:

[0024] The present invention is used to eliminate the problem of ringing artifacts when SPI reconstructs a target scene at a low sampling rate. This is because the spectrum at the low sampling rate is truncated. At this time, obvious ringing artifacts will appear when reconstructing the target scene. The present invention passes this truncated spectrum through a Butterworth low-pass filter, and the edge of the obtained new spectrum becomes smoother (no longer truncated), and the ringing artifact phenomenon is therefore eliminated. The present invention is different from the method based on deep learning to remove ringing artifacts, because the method based on deep learning requires a lot of training, and the arrangement of the data set is also a large workload. The whole process is quite time-consuming. It is also different from the method based on image displacement and image fusion technology. This method increases the complexity of the overall algorithm and the amount of calculation of the system. The present invention is more efficient than the currently proposed method and provides a method for subsequently realizing efficient and high-quality SPI. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Flow chart of the method of the present invention.

[0026] Figure 2 Schematic diagram of the experimental target scene.

[0027] Figure 3 This is the optical path diagram of the SPI experiment.

[0028] Figure 4 Schematic diagram of the spectrum obtained at low sampling rate (5%, 10%).

[0029] Figure 5 Schematic diagram of the reconstructed target scene at a 5% sampling rate.

[0030] Figure 6 Schematic diagram of the reconstructed target scene at a sampling rate of 10%.

[0031] Figure 7 A truncated low-sampling frequency perspective view.

[0032] Figure 8 Spectral perspective to remove ringing artifacts.

[0033] Figure 9 Schematic diagram of the reconstruction result after eliminating ringing artifacts at a 5% sampling rate.

[0034] Figure 10 The reconstructed result is obtained by eliminating ringing artifacts at a sampling rate of 10%. DETAILED DESCRIPTION

[0035] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0036] Example

[0037] like Figure 1 As shown, the present invention provides a method for eliminating ringing artifacts in single-pixel imaging, and its implementation method is as follows:

[0038] S1. Obtain the spectrum of the target scene at a low sampling rate. The implementation method is as follows:

[0039] S101, using the SPI optical system to collect a light intensity signal reflected when the target scene is illuminated by the modulated pattern, and saving the reflected light intensity signal to a computer via a data acquisition card;

[0040] S102, converting the stored light intensity signal into a spectrum of the target scene at a low acquisition rate through a four-step phase-shift Fourier algorithm;

[0041] S2. Obtain a new spectrum of the target scene through a first-order Butterworth low-pass filter according to the frequency of the target scene;

[0042] In this embodiment, based on the obtained spectrum of the target scene (the edge of the spectrum is truncated at this time, and if the corresponding inverse transform is used, the reconstructed target scene will have ringing artifacts), a first-order Butterworth low-pass filter is passed (n=1 in the formula, and n represents the order of the Butterworth low-pass filter) to obtain a new spectrum of the target scene (the edge of the new spectrum obtained at this time becomes smoother and is no longer truncated. If the corresponding inverse transform is used for reconstruction, the obtained target scene will not have ringing artifacts.

[0043] S3. Reconstructing the new spectrum of the target scene by using inverse transformation to eliminate ringing artifacts appearing in single-pixel imaging, thereby obtaining a restored target scene.

[0044] In this embodiment, the present invention proposes a new method for eliminating ringing artifacts at low sampling rates in the SPI field. The present invention is applicable to currently commonly used SPI technologies, such as Fourier SPI, Hadamard SPI, discrete cosine transform SPI, etc. The basic idea is: first, the spectrum of the target scene at a low sampling rate is obtained. At this time, the spectrum is truncated. Using the inverse transform to reconstruct the target scene will produce obvious ringing artifacts. The present invention passes the truncated spectrum through a Butterworth low-pass filter to make the truncated spectrum smoother, and the spectrum after removing the ringing artifact can be obtained. At this time, the shape of the spectrum is smoother than before. Finally, the corresponding inverse transform of SPI is used to reconstruct a high-quality target scene without ringing artifacts. Experimental results show that the proposed method has certain advantages and also obtains the expected results.

[0045] In this embodiment, the four-step phase shift Fourier SPI method is used as an example to verify the elimination of ringing artifacts. Figure 1 As shown, four pictures commonly used in image testing are selected. Figure 2 The SPI experiment optical path is shown. This optical path is used to acquire the spectrum of a target scene. The diagram includes a light source, a spatial light modulator (DMD) that generates the modulation pattern, two lenses with focal lengths of 50mm and 100mm, a single-pixel detector that receives the light intensity signal reflected from the target scene, and a data acquisition card that records the light intensity signal. A computer then processes the series of light intensity signals to reconstruct the target scene. The resulting modulation pattern is expressed as follows:

[0046] P(n,m;k,l)=a+bsin[2π(nk+ml)+φ] (1)

[0047] Where P(n,m;k,l) represents the modulation pattern, n and m represent the two-dimensional coordinates of the target scene, k and l represent the spatial frequency of the modulation pattern, that is, the frequency domain, a represents the DC component, b represents the contrast of the modulation pattern, a and b are used to adjust the brightness of the illumination pattern, and the setting value is both 0.5. φ represents the initial phase of the modulation pattern (the modulation pattern is a series of patterns with different spatial frequencies generated by the code), and the initial phase φ is 2kπ / N (where k = 0, 1, 2, 3, and N = 4), k represents the generation of four different initial phase values, and N represents the four-step phase shift.

[0048] The modulated pattern is then projected onto the target scene, and a series of different reflected light intensity signals are detected using a single-pixel detector and recorded using a data acquisition card. p It can be expressed as follows:

[0049] R p (k,l)=R n +h∫∫ SA(x,y)P(n,m;k,l)dxdy (2)

[0050] Among them, R p (k,l) represents the reflected light intensity signal, R n Represents the intensity of ambient light, h represents a constant, S represents the projection area of ​​the modulation pattern, A(x, y) represents the surface albedo of the target scene, dx, dy represent the integration operation, and integrating S (the projection area of ​​the modulation pattern) and A(x, y) (the surface albedo of the target scene) will give the light intensity value reflected when the modulation pattern is projected onto the target scene.

[0051] For the four-step phase-shifted Fourier SPI, that is, when N=4, the formula for obtaining each spectral coefficient is as follows. For simplicity, the spatial frequency coordinates are omitted in the given formula:

[0052] I4=(R p(0) -R p(π) )+i·(R p(π / 2) -R p(3π / 2) ) (3)

[0053] Where I4 represents the spectrum obtained by the four-step phase shift Fourier algorithm (if the spectrum at this time is used for the corresponding inverse transform, the reconstructed target scene will have ringing artifacts), R p(0) and R p(π) Both represent the real part, R p(π / 2) and R p(3π / 2) Both represent the imaginary part, i is the imaginary unit;

[0054] R p(0) represents the light intensity value obtained by projecting the modulation pattern onto the target scene, p (0) Indicates that the initial phase of the modulation pattern used at this time is 0;

[0055] R p(π) represents the light intensity value obtained by projecting the modulation pattern onto the target scene, p (π) Indicates that the initial phase of the modulation pattern used at this time is π;

[0056] R p(π / 2) represents the light intensity value obtained by projecting the modulation pattern onto the target scene, p (π / 2) Indicates that the initial phase of the modulation pattern used at this time is (π / 2);

[0057] R p(3π / 2) represents the light intensity value obtained by projecting the modulation pattern onto the target scene, p (3π / 2) This indicates that the initial phase of the modulation pattern used at this time is (3π / 2).

[0058] According to formula (3), the spectral coefficients of the target image are obtained in sequence and then combined into a complete Fourier spectrum. Finally, the target scene is reconstructed using a two-dimensional inverse Fourier transform.

[0059] Figure 3 The process of obtaining the target scene spectrum is demonstrated in the form of a plane diagram, and the spectrum diagrams obtained at low sampling rates (5% and 10%) are given. Figure 4 and Figure 5 The target scene is restored at low sampling rates (5%, 10%). From the reconstruction results, there are obvious ringing artifacts.

[0060] The obtained low sampling rate spectrum is passed through a Butterworth low-pass filter. The generation formula of the Butterworth low-pass filter is:

[0061]

[0062] Where H(u,v) represents a Butterworth low-pass filter, D0 represents the cutoff frequency of the Butterworth low-pass filter, D(u,v) represents the distance between the frequency point (u,v) and the center of the frequency domain (M / 2,N / 2), u and v represent the coordinate position of the frequency point on the spectrum graph, M and N represent the length and width of the spectrum graph, respectively, and n represents the order of the Butterworth low-pass filter. The larger n is, the steeper the filter shape is, that is, ringing artifacts will also appear. In this embodiment, the value of n is set to 1, which makes the filter shape more gentle and eliminates ringing artifacts.

[0063] Multiplying formula (3) and formula (4) yields formula (5).

[0064] F=I4*H(u,v) (5)

[0065] In this embodiment, Figure 6 The truncated low sampling rate spectrum is shown. This formula means that the spectrum is passed through a Butterworth low-pass filter to obtain a new spectrum F, which is also the spectrum with the ringing artifact removed, as shown in Figure 7 As shown in the figure, the spectrum is not truncated but flatter. Finally, the inverse transform is used to reconstruct the target scene with high quality and no ringing artifacts.

[0066] In this embodiment, after the above processing, the ringing artifacts in the reconstructed target scene can be eliminated well. The experimental results are as follows: Figure 8 、 Figure 9 As shown in Figure 2, the experimental results of removing ringing artifacts under 5% and 10% sampling are shown respectively.

[0067] In this embodiment, Figure 3This figure shows the optical path of an SPI experiment. In SPI imaging experiments, a series of modulated patterns with different spatial frequencies are projected onto the surface of a target scene. When the modulated patterns are projected onto the target scene, a single-pixel detector collects the intensity of the light reflected from the target scene and converts it into a corresponding voltage signal. A data acquisition card records these different voltage signals, which are then processed by a computer and reconstructed using appropriate algorithms.

[0068] Spatial light modulator: responsible for generating modulation patterns of different spatial frequencies.

[0069] Light source: Provides an illumination system to illuminate the modulation pattern generated by the spatial light modulator onto the target scene.

[0070] Lens 1: Focuses the modulated pattern onto the target scene.

[0071] Lens 2: Focuses the reflected light intensity signal onto a single-pixel detector.

[0072] Single-pixel detector: responsible for converting the reflected light intensity signal into a voltage signal, that is, converting the analog signal into a digital signal.

[0073] Data acquisition card: records the voltage signal converted by the single-pixel detector to facilitate subsequent processing.

[0074] Computer: The data acquisition card is connected to the computer via a USB cable to transmit the recorded signals to the computer. The computer reconstructs the target scene by using a single-pixel imaging reconstruction algorithm.

Claims

1. A method for eliminating ringing artifacts in single-pixel imaging, characterized in that: The following steps are involved: 4 S1, obtain the spectrum of the target scene at a low sampling rate; S2. Obtain a new spectrum of the target scene through a first-order Butterworth low-pass filter according to the frequency of the target scene; The expression of the new spectrum of the target scene is as follows: in, represents the new spectrum of the target scene, represents the spectrum obtained by the four-step phase-shift Fourier algorithm, represents a Butterworth low-pass filter, Indicates frequency point and the frequency domain center distance, Indicates the coordinate position of the frequency point on the spectrum graph, M 、 N Represent the length and width of the spectrum graph respectively, represents the cutoff frequency of the Butterworth low-pass filter, n represents the order of the Butterworth low-pass filter, and Both represent the real part, and Both represent the imaginary part, i is an imaginary unit; S3. Reconstructing the new spectrum of the target scene by using inverse transformation to eliminate ringing artifacts appearing in single-pixel imaging, thereby obtaining a restored target scene.

2. The method for eliminating ringing artifacts in single-pixel imaging according to claim 1, wherein: The step S1 comprises the following steps: S101, using the SPI optical system to collect a light intensity signal reflected when the target scene is illuminated by the modulated pattern, and saving the reflected light intensity signal to a computer via a data acquisition card; S102: Convert the stored light intensity signal into a frequency spectrum of the target scene at a low acquisition rate through a four-step phase-shift Fourier algorithm.

3. The method for eliminating ringing artifacts in single-pixel imaging according to claim 2, wherein: The expression of the reflected light intensity signal is as follows: in, Represents the reflected light intensity signal, Indicates the intensity of ambient light, represents a constant, S represents the projection area of ​​the modulation pattern, represents the surface albedo of the target scene, Represents the integral operation, S and Perform integration operations, represents the modulation pattern, Represents the two-dimensional coordinates of the target scene, represents the spatial frequency of the modulation pattern, represents the DC component, represents the contrast of the modulation pattern, Indicates the initial phase of the modulation pattern.

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