Fast high-quality fourier ptychographic imaging method

Abstract

This invention discloses a single-pixel imaging method based on adaptive Fourier spectrum sampling and fast iterative adaptive reconstruction. By adaptively sampling low-frequency and important high-frequency spectra, the number of samplings is minimized while improving image quality. The obtained sampled spectra are solved using an image sparse prior and an alternating direction method is introduced in the gradient space. A fast Fourier transform is also introduced to accelerate the solution process, significantly reducing computational complexity and solving the problems of slow imaging and poor real-time performance in traditional single-pixel imaging methods. This single-pixel imaging method can quickly obtain high-quality images, solving the problem of high-quality and fast imaging under conditions of slow spatial light modulator modulation frequency and low sampling rate. It has wide application value in terahertz imaging, infrared imaging, single-photon imaging, and X-ray imaging.

Description

Technical Field

[0001] This field relates to single-pixel imaging technology, and in particular to a single-pixel sampling and reconstruction method based on Fourier analysis. Background Technology

[0002] Single-pixel imaging technology is widely used in terahertz imaging and single-photon imaging. The development of these fields is severely limited by the resolution and imaging time of single-pixel imaging. Fast, high-resolution single-pixel imaging technology relies on high-speed spatial light modulators and advanced algorithms. At the same time, the modulation speed of high-speed spatial light modulators limits the application and popularization of single-pixel imaging technology in various fields. How to obtain high-quality reconstructed images under the limitation of spatial light modulator modulation speed is an urgent problem to be solved.

[0003] Efficient sampling techniques and image reconstruction algorithms are key steps in high-quality and fast single-pixel imaging. Reasonable sampling of the Fourier spectrum can effectively reduce the number of samplings and improve imaging speed. Introducing image sparsity prior constraints into the reconstruction algorithm and optimizing the reconstruction process are key to fast and high-quality reconstruction. Currently, traditional single-pixel imaging methods use circular, spiral, or diamond-shaped sampling methods in the sampling step, and use inverse Fourier transform methods for image reconstruction.

[0004] Due to current technological limitations, the following bottlenecks still exist in the sampling and image reconstruction processes:

[0005] 1. Traditional sampling methods based on circular or spiral paths fail to fully utilize prior image information, resulting in a lot of redundant sampling during the sampling process, which reduces the imaging speed;

[0006] 2. Image reconstruction methods based on inverse Fourier transform can lead to severe ringing effects and image blurring in reconstructed images when the sampling rate is low;

[0007] 3. Iterative reconstruction-based algorithms suffer from slow image reconstruction speed and cannot be applied to imaging scenarios with high real-time requirements. Summary of the Invention

[0008] To address the above problems, this invention provides a single-pixel imaging method based on adaptive Fourier spectrum sampling and alternating direction optimization reconstruction.

[0009] The technical solution is as follows: 1. The spectrum is sampled in two stages. In the first stage, the low-frequency Fourier spectrum is sampled first.

[0010] 2. In the second stage, the location of the high-frequency spectrum is predicted using the sampling spectrum from the first stage, and the high-frequency spectrum is sampled.

[0011] 3. The high-frequency and low-frequency spectra from the above two stages are fused to obtain the final sampling spectrum.

[0012] 4. The sampled spectrum is reconstructed using the total variational regularization method.

[0013] 5. To accelerate the calculation speed during the reconstruction process, an alternating direction optimization algorithm is used in the gradient space for acceleration, and the fast Fourier transform is used to solve the inverse matrix to further accelerate the solution speed.

[0014] 6. After repeated iterations, the gradient image in the gradient space is obtained, and the original image is recovered using the Fast Fourier Transform combined with the divergence algorithm. Specific implementation methods

[0015] 1. Divide the sampling area into three circular regions C1, C2, and C3, with radii of respectively... , , The relationship between the three is as follows: First, the low-frequency Fourier spectrum in region C2 is sampled using circular path sampling technique.

[0016] 2. Estimate the distribution of the unsampled important high-frequency Fourier spectrum from the low-frequency sampled spectrum obtained in step 1.

[0017] 3. Set all the sampled spectral coefficients in region C1 to 0, and sort the remaining spectral coefficients in region C2 in descending order.

[0018] 4. Select the remaining s% of the larger spectral sparsity locations and expand their coordinate positions. The new coordinate position is obtained by moving to region C3.

[0019] 5. Sample the spectrum of the new coordinate position in region C3 to obtain the important high-frequency spectrum.

[0020] 6. Combine the low-frequency spectrum in region C2 with the high-frequency spectrum in region C1 to obtain the complete sampled spectrum.

[0021] 7. The sparse spectrum obtained from sampling is addressed by introducing total variational regularization for image solving, specifically as follows: , where x is the image to be reconstructed, D is the derivative sign, F is the Fourier transform, y is the sampling spectrum coefficient obtained by fusion in step 6, and R is the sampling matrix.

[0022] 8. To reduce the number of solutions, the formula in step 7 is transformed into the gradient domain for solution, i.e.: Where d is the gradient image, For the new penalty coefficient, The measurement spectral coefficients in the gradient domain are calculated using the following formula: .

[0023] 9. To further accelerate the solution process, the alternating direction optimization algorithm is used to solve the above problem. Therefore, the equation in step 8 can be written as: .

[0024] 10. Solve the equation in step 9 to obtain the image d in the gradient domain.

[0025] 11. After obtaining the gradient image d, the original image can be further solved using the divergence formula. ,Right now: This is the final reconstructed image.

Claims

1. A fast, high-quality Fourier single-pixel imaging method, Its features include the following steps: 1) Divide the sampling area into three circular regions C1, C2, and C3, with radii of respectively... , , The relationship between the three is as follows: First, the low-frequency Fourier spectrum in region C2 is sampled using circular path sampling technique; 2) Estimate the distribution of the unsampled important high-frequency Fourier spectrum from the low-frequency sampled spectrum obtained in step 1; 3) Set all the sampled spectral coefficients in region C1 to 0, and sort the remaining spectral coefficients in region C2 in descending order; 4) Take the remaining s% of the larger spectral sparsity positions and expand their coordinate positions. Double the coordinates to obtain the new coordinate position in region C3; 5) Sample the spectrum of the new coordinate position in region C3 to obtain the important high-frequency spectrum; 6) The low-frequency spectrum in region C2 is fused with the high-frequency spectrum in region C1 to obtain the complete sampled spectrum; 7) Introduce total variational regularization to solve the image problem for the sparse spectrum obtained from sampling, specifically: , where x is the image to be reconstructed, D is the derivative sign, F is the Fourier transform, y is the sampling spectrum coefficient obtained by fusion in step 6, and R is the sampling matrix; 8) To reduce the number of solutions, the formula in step 7 is transformed into the gradient domain for solution, i.e.: Where d is the gradient image, For the new penalty coefficient, The measurement spectral coefficients in the gradient domain are calculated using the following formula: ; 9) To further accelerate the solution process, the alternating direction optimization algorithm is used to solve the above problem. The equation in step 8 is written as follows: ; 10) Solve the equation in step 9 to obtain the image d in the gradient domain; 11) After obtaining the gradient image d, the original image is further solved using the divergence formula. ,Right now: This is the final reconstructed image.

Images