CN107123100B - FiDrizzle multi-sampling image reconstruction technology - Google Patents

FiDrizzle multi-sampling image reconstruction technology Download PDF

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CN107123100B
CN107123100B CN201710307681.XA CN201710307681A CN107123100B CN 107123100 B CN107123100 B CN 107123100B CN 201710307681 A CN201710307681 A CN 201710307681A CN 107123100 B CN107123100 B CN 107123100B
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王蕾
李国亮
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Purple Mountain Observatory of CAS
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Abstract

The FiDrizzle multi-sampling image reconstruction technology is technological upgrades after the realization method is improved on the basis of our prior invention patents, mainly integrates the advantages of fast calculation of the fiDrizzle method and fast convergence speed of a low frequency band and the strong term of high fidelity of the iDrizzle method in a high frequency band, adds low-pass filtering of a frequency domain on the basis of the prior fiDrizzle algorithm, thereby integrating the advantages of the two methods.

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FiDrizzle multi-sampling image reconstruction technology
September 30，2019
1 technical field
In the field of digital signal communication and image acquisition and processing, data is acquired by collectors such as CCD (charge coupled device), CMOS (complementary metal oxide semiconductor) and the like, the collectors are photon counter arrays in principle, that is, the sampling is discrete, and infinite and fine continuous sampling cannot be realized practically, so that sampling rates are involved.
2 background of the invention
As mentioned earlier, because of the considerations of process limitations and economic costs, many imaging devices have sampling rates which are not 2 times higher than the highest optical resolution of the device, namely, the lowest sampling rate required by the sampling rate theorem (Nyquist theorem) and capable of completely describing signals, namely, the so-called low sampling rate (under sampling), low sampling rate causes the final image to show blurring, mosaicing (i.e., pixelation) and the like, pixelation is equivalent to filters, is the expression of analog signal discretization sampling, and although sampling rates are low, shooting the target object at different positions by recording the tremor (diatherm) of the instrument results in many samples with low sampling rates, and overlaying the samples through reasonable techniques can obtain high resolution which breaks through the convolution constraints of the instrument or simultaneously realize the inverse of pixelation filters, namely, the de-pixelation technique which is used by the former de-pixelation technique and the inverse-convolution technique which is equivalent to the high resolution of the original image obtained by the original image by the instrument collector or the original image obtained by the inverse-mesh reconstruction method (i.e) through the inverse-mesh reconstruction of the inverse-mesh reconstruction method, namely, the high-mesh-based method is not much more effective than the original-mesh-based-convolution method (i.e-based-method, i.e-i-i.e-to-i.e-to-i.e-i.e.e.e-i.e.e-i.e-i.e.e-i.g. the characteristics of the fast-i.g. the original-i.e-i.g. the fast-i.e-i.e. the fast-i.e-i.e. the fast-i.e-i.e.e-i-i.e-i-i.e.e-i.e. the fast-i.e-i.e. the fast-i.e-i..
Disclosure of the invention
3.1 FiDrizzle technology our goal is to gather the advantages of fiDrizzle and iDrizzle from the steps of FiDrizzle are as follows:
step (1): obtaining an original observation image
Will be paired withN tremored original images obtained by observing a quasi-region are marked as g1(m，n)，g2(m，n)...gN(m, n) }, in gk(m, N) represents the kth, wherein N, m, N and k are positive integers, k is more than or equal to 1 and less than or equal to N, and (m, N) is the image pixel position;
step (2): reconstructing an image
Step (2.1): the original observation image { g1(m，n)，g2(m，n)，g3(m，n)…gN(m, n) }, which is superimposed on predetermined high resolution standard grids by using a Drazzle method, i.e. an upsampling operation, to generate a reconstructed image f1Subscript 1 of (x, y), f represents that this is the result of the 1 st reconstructed image, (x, y) is the high resolution pixel position, and x, y is a positive integer;
step (2.2): to f1(x, y) low-pass filtering, i.e. attenuating the power of the high-frequency part, to obtain a reconstructed image
Figure GDA0002224629370000021
Here, LF () indicates that the image in parentheses is subjected to a low-pass filtering operation, and then proceeds to the next step;
and (3): iterative processing
Step (3.1): reconstructing the high-resolution image obtained from the ith image
Figure GDA0002224629370000023
Performing N times of resampling under the same sampling condition as the step (1), namely, down-sampling operation, thereby obtaining N imagesBy using
Figure GDA0002224629370000025
Representing the kth of the N resampled images, where i is a natural number,
Figure GDA0002224629370000026
namely the reconstructed image obtained in step (2.2), and then the next step is carried out;
step (3.2): using N original images gk(m, n) subtracting the corresponding resampled images, respectively
Figure GDA0002224629370000027
Obtaining N residual images
Figure GDA0002224629370000028
Wherein
Figure GDA0002224629370000029
Proceeding to step ;
step (3.3): n residual images
Figure GDA0002224629370000031
Superimposed on the standard grid by the Drizzle method and low-pass filtered, and then addedTo obtain a new reconstructed imageIf it is
Figure GDA0002224629370000034
If the requirement is not met, the step is entered;
and (3.4) returning to the step (3.1) to carry out times of iterative loop operation until the image meeting the requirement is output.
Comparing the iDrizzle, the FiDrizzle of the improved version adds the filtering step omitted by the previous fiDrizzle into the process, increases part of calculation amount, but improves precision and effect greatly, and effectively inhibits high-frequency noise, then we perform visual appearance aspect, comprehensive comparison in quantitative aspect and time complexity aspect on the Drizzle, iDrizzle, fiDrizzle and FiDrizzle four image reconstruction technologies, and finally output low-resolution original images (diathermimages) by resampling in order to control and compare the four methods, then we perform reconstruction on the low-resolution original images by using the four methods, finally output the result to the same resolution, namely output the result, and simulate the real exposure rate of each time, wherein the simulation is performed on the real exposure rate of each time, and the simulation is performed on the real exposure rate of 0 percent.
Before the beginning, we first demonstrated "OverSampling deceleration Convergence effect" (OSDC), which we newly discovered, let T be real signals of a two-dimensional plane space, after passing through an observation device (such as a telescope, a microscope, a camera, etc.), discretized digital signal images I are obtained on a CCD plane, and have a tremor displacement ds (including translation and rotation angles) relative to our standard grid:
Figure GDA0002224629370000035
here G has integrated all effects before T is sampled, such as seeing, CCD deformation, pixelation, etc.Now we resample I two times, is a standard grid of resampled to oversampled resolution
Figure GDA0002224629370000037
Another are resampled to the critical sample rate standard gridThe tremor displacement ds is taken into account. Namely:
Figure GDA00022246293700000310
where P isOSOr PCSIs a resampling matrix that contains the effect of resampling pixelation. And also
Figure GDA00022246293700000311
Figure GDA00022246293700000312
Here sinc (P)OS→PCS) Is a lossless sinc interpolation from the over-sampling rate to the critical sampling rate. Thus, the device is provided with
Figure GDA00022246293700000313
Is equal to
Figure GDA00022246293700000314
Here, the
Figure GDA00022246293700000315
It is the result of Drizzle. From the above iterative reconstruction procedure, we use the observed sampling rate to align two standard meshes
Figure GDA00022246293700000316
And
Figure GDA00022246293700000317
resampling to down-sample to I-grid, thus obtaining th approximation of original observation image I
Figure GDA00022246293700000318
And
Figure GDA00022246293700000319
then the difference of the th approximation from the original observed image I can be written as:
Figure GDA00022246293700000320
Figure GDA00022246293700000321
due to the fact thatHas a ratio of
Figure GDA0002224629370000042
Higher resolution (meaning more detail), then the corresponding margin
Figure GDA0002224629370000043
Just has a ratio
Figure GDA0002224629370000044
Less power, especially at the low frequency end at extremes, if we oversample the original observed image to an infinitely high resolution
Figure GDA0002224629370000045
complete I's will be retained, resulting in
Figure GDA0002224629370000046
That is to say
Figure GDA0002224629370000047
After the th iteration, we get a second approximation of the real imageAnd
Figure GDA0002224629370000049
Figure GDA00022246293700000410
Figure GDA00022246293700000411
from the last steps of iDrizzle, we need to interpolate the oversampled standard grid Eq. (4) to the Critical sampling Rate grid by sine interpolation
Figure GDA00022246293700000412
Comparing equations (6) and (5), we find that for a comparison of the same coarse grid (here the critical resolution grid), an iterative reconstruction directly into the critical resolution grid yields higher power, i.e. more signal, in the margin than a reconstruction that undergoes oversampling and then interpolation back into the critical sample rate grid. This means that for reconstructions of the same tremor observation number and the same number of iterations, the iterative convergence rate is reduced by the oversampling mechanism. We call this new effect the Over-Sampling induced deceleration Convergence effect (OSDC). The reader can also prove this effect on his own in the case of other dimensions and any number of tremor observations and iterations greater than 1. So even if we neglect the filtering mechanism, fiDrizzle is more efficient in deconvolution than it is. Of course, from the steps of FiDrizzle we can also see that FiDrizzle is not affected by OSDC effects like it is, so that image deconvolution can be done quickly and efficiently.
3.2 results
In fig. 1 we have used a test image Miss Lena (size 512 x 512 pixels and assuming that the resolution reaches the critical sampling rate, i.e. the Nyquist sampling rate) known from the field of image processing as the real image, left image, i.e. the optically highest resolution of the imaging device is 0.5 times the critical sampling rate we resample the real image reducing the resolution of the 5 original observed images byOf which is the right image, we can see that there is low samplingThe eyes and eyelashes of Lena in the low-resolution image are blurred, the edges of the hat are severely jagged, the stripes on the hat disappear, the images are pixilated, all details are mosaicized, and the images are expressed by real observation images in reality.
The top left image is the result of the Drizzle reconstruction after undergoing "oversampling-filtering-sine interpolation" to facilitate comparison, and we use the exact same low pass filter in the iDrizzle and FiDrizzle, as in FIG. 2, the top right image is the result of the Drizzle reconstruction, the top right image is the result of the iDrizzle, the bottom left image is the result of the FiDrizzle of the present invention, the bottom right image is the result of the FiDrizzle of the present invention, the top right image is 5 iterations, the image of the significant Drizzle reconstruction has been more than the original observed image, yet has significantly more detail than the original Drizzle, the difference between the two top left images is found to be significant left and left, and the difference between the two top left images is found to be significant left and right, and the difference between the top left and right images is found to be significant left and left significant residual error of the Drizzle is found to be significant difference between the top left and right significant Drizzle, and the top left significant residual error of the top left significant Drizzle is found to be significant drag, and the difference between the top left significant drag image, i 3, and the top left significant drag image, and the significant drag image is found to be significant residual error, the difference between the significant drag image, i-3.
To see the difference between fiducizle and fiducizle, we use Reduced Power Spectrum (RPS) tools, that is, to do fast fourier transform FFT on the other images of the residual fig. 3 except for the fiducizle (only the middle area, i.e., the middle 256 × 256pixel area, which is to avoid pixels not completely covered by 5 dither images) to get a two-dimensional power spectrum with low frequency power concentrated in the center area and high frequency area on the periphery, so we do a radial average density profile of the power spectrum, called Reduced Power Spectrum (RPS), that can roughly reflect the power change from low to high frequency, as in fig. 4, we easily see that the high frequency band of the OSDC effect fiducizle (dotted line) at low frequency is not as good as the low frequency band but better than the fiducizle (solid line) at low frequency band, which we can see that the high frequency band of the fiducizle is slightly better than the high frequency band of the fiducizle (dashed line) and the high frequency filter (. the high frequency band of the fiducizle is better than the fiducizle.
A more detailed graph can be seen in fig. 5, which is a graph of power difference using fidrizle as a reference, i.e., a 0-value line in the graph, where three lines are the solid line in fig. 4 minus the three lines in fig. 4, respectively. That is, the difference between fiDrizzle and fiDrizzle, iDrizzle and fiDrizzle, respectively. If the graph line is larger than zero, the reconstruction effect of the frequency band is better than that of the fiDrizzle, otherwise, the reconstruction effect of the frequency band is not as good as that of the fiDrizzle. The overall effect of FiDrizzle is best as is evident from fig. 5.
3.3 computational complexity comparison
It is needless to say that the speed of Drizzle is fastest, since re-samples are calculated in an amount equivalent to Drizzle calculations, FiDrizzle actually consumes 2N-1 times more calculations (N is the number of iterations) than Drizzle, and in fig. 1, the real image has a size of 512 × 512, and the original image has
Figure GDA0002224629370000051
Figure GDA0002224629370000052
The size of the pixel. The amount of Drizzle calculation depends not only on the number of original pixels of 5 × 120 × 120 but also on the resolution of the output image, and thus Drizzle consumes
Figure GDA0002224629370000053
The second calculation (on average, 2900 operations including polygon clipping, integration are performed for every original pixels.) thus its complexity is O (800 n)2) (let n be 512). While fiDrizzle requires 4.5 more iterations, the complexity is therefore probably O (8000 n)2). FiDrizzle only has more filtering processes per iteration than the FiDrizzle, and the computational complexity is
Figure GDA0002224629370000054
Figure GDA0002224629370000055
I.e. O (20 n)2log2n) the operational expenditure of the iDrizzle is that the iDrizzle needs oversampled output grids, e.g. 4 x 4 times higher than the critical sampling rate in this context, the total operation time is 15 times more than that of the FiDrizzle, and in addition, since the interpolation from the oversampled grid to the critical sampling rate grid will contribute to the computational complexity of O (256n2) (we use 16 surrounding grid points for operation per interpolation), so in this example, FiDrizzle saves at least 15 times the amount of computation compared to the idlizle, but only 1/50 is increased compared to the fidlizle, in exchange for the superior performance of the idlizle in the high frequency band.
3.4 discussion and conclusions
By combining the advantages of each of iDrizzle and fidDrizzle and abandoning the disadvantages, we have developed a new fidDrizzle deconvolution technique. The progress and advantages of FiDrizzle over isdizzle and FiDrizzle are mainly reflected in the following 3 aspects:
FiDrizzle is more efficient and the reconstruction results are more fidelity, both to irdizzle and FiDrizzle.
FiDrizzle saves a lot of computing resources compared to iDrizzle.
FiDrizzle reduces high band noise compared to FiDrizzle.
In the near future many new telescope devices are put into observation: such as the Wide field marked free surface Telescope (WFIRST) by NASA, Euclid, Large Synthetic Surface Telescope (LSST) sponsored by the national science foundation of the United states, and the Chinese astronomical Telescope (CSST). At that time, massive data is generated, and how to process the data quickly and with high fidelity becomes an urgent need. In practice this is just a big place for FiDrizzle.
Astronomical field:
1. for a telescope with an insufficiently kept tracking posture, a multi-exposure technology can be used, the exposure time is shortened, the image contour blurring caused by unstable posture can be greatly reduced, and then a high-resolution observation image is reconstructed by using FiDrizzle.
2. Whether a space telescope or a ground telescope, multiple exposures can be selected to align the observed source for a selected period of time, and then a high resolution image of the source can be reconstructed using FiDrizzle. This avoids adverse weather conditions or the spatial telescope being affected by factors such as the earth's moon.
3. Since astronomical observations are mostly seen with dark and weak sources, FiDrizzle can use a considerable number of dark and weak sources that have been discarded before to perform astronomical studies in deeper spaces.
4. As long as the hardware condition of the shooting telescope is known, parameters such as the position and the like can process observation data of sources from different telescopes in different historical periods and generate high-resolution images with the assistance of FiDrizzle, so that the aim of fully utilizing the historical data is fulfilled.
5. Astronomical observations are necessary in some cases to perform multiple exposures, since in the case of multiple signal sources and widely varying intensities, multiple exposures must be used to enhance the signal intensity of weak sources while ensuring that strong sources are not saturated, at which time it is necessary to reconstruct images of sources with higher fidelity quickly and efficiently using FiDrizzle, at least faster than the best current FiDrizzle.
In the field of digital image monitoring, the FiDrizzle technology can reconstruct a high-definition image of a monitored object by using continuous multi-frame video pictures.
The fields of micro-physics, microorganisms, medical imaging, etc. can be used to obtain high resolution images of viruses, bacteria or organic molecules using multiple exposures in combination with FiDrizzle with limited pixel resolution.
Finally, the technique provides approaches to the field of digital imaging, where low-sample-rate images can be reconstructed by multiple exposures and the FiDrizzle technique to reach the highest resolution limit of the optical device.
Detailed description of the preferred embodiments
Program software based on the FiDrizzle technology is developed by using the C language, and a high-resolution source image can be reconstructed by knowing parameters (such as position, rotation, CCD deformation and the like) of an imaging instrument when the imaging instrument captures an image, so that more detailed information is given.
Thank you: the invention is supported by national items 973 (No.2015CB857003, No.2015CB857000, No.2013CB834900), national fund committee (No.11333008, No.11233005, No.11273061), the outstanding youth item in Jiangsu province (No. BK20140050) and the space science structure leader item in Chinese academy (No. XDB09010000), and the inventor herein represents thank you for these supporting items.
Description of the drawings 5
This patent shares 5 figures to compare the different effects of the four reconstruction methods Dirzle, iDirzle, fiDrizzle and FiDriz-zle in visual appearance and quantification. The drawings illustrate the following:
FIG. 1: we used Miss Lena as the true image (left image), and generated the original observed image (right image) by resampling, where the right image is reduced in resolution compared to the left imageThe detail corresponding substantially to 3x 3 pixels in the left image would be replaced by pixels in the right image.
FIG. 2: the results of the four different methods of reconstruction are ascribed to the comparison at the critical sampling rate. The upper left graph is the result of the Drizzle reconstruction, the upper right graph is the result of the idrzzle, the lower left graph is the result of the fiDrizzle, and the lower right graph is the result of the fiDrizzle of the present invention. These were all 5 iterations of iDrizzle, fiDrizzle and FiDrizzle.
FIG. 3: residual images of four reconstruction methods. Upper left drawing Drizzle, upper right drawing idmizle, lower left drawing fidizzle and lower right drawing fidizzle.
FIG. 4: reduced Power Spectrum (RPS) of the residual map. Dotted lines are the result for fiDrizzle, solid lines are the result for fiDrizzle, and dashed lines are the result for fiDrizzle.
FIG. 5: reduced Power Spectrum (RPS) versus residual plot of fiDrizzle. Dotted lines are the result for fiDrizzle, solid lines are the result for fiDrizzle, and dashed lines are the result for fiDrizzle.

Claims (1)

  1. A FiDrizzle multi-sampling image reconstruction technique, characterized by comprising the steps of:
    step (1): obtaining an original observation image
    Marking N tremor original images obtained by aiming at a certain region to be { g1(m，n)，g2(m，n)...gN(m, n) }, in gk(m, N) represents the kth, wherein N, m, N and k are positive integers, k is more than or equal to 1 and less than or equal to N, and (m, N) is the image pixel position;
    step (2): reconstructing an image
    Step (2.1): the original observation image { g1(m，n)，g2(m，n)，g3(m，n)...gN(m, n) }, which is superimposed on predetermined high resolution standard grids by using a Drazzle method, i.e. an upsampling operation, to generate a reconstructed image f1Subscript 1 of (x, y), f represents that this is the result of the 1 st reconstructed image, (x, y) is the high resolution pixel position, and x, y is a positive integer;
    step (2.2): to f1(x, y) low-pass filtering, i.e. attenuating the power of the high-frequency part, to obtain a reconstructed image Where LF (.) denotes a pairThe images in brackets are subjected to a low-pass filtering operation, and then the step is carried out;
    and (3): iterative processing
    Step (3.1): reconstructing the high-resolution image obtained from the ith image
    Figure FDA0002224629360000013
    Performing N times of resampling under the same sampling condition as the step (1), namely, down-sampling operation, thereby obtaining N images
    Figure FDA0002224629360000014
    By using
    Figure FDA0002224629360000015
    Representing the kth of the N resampled images, where i is a natural number,
    Figure FDA0002224629360000016
    namely the reconstructed image obtained in step (2.2), and then the next step is carried out;
    step (3.2): using N original images gk(m, n) subtracting the corresponding resampled images, respectively
    Figure FDA0002224629360000017
    Obtaining N residual images
    Figure FDA0002224629360000018
    Wherein
    Figure FDA0002224629360000019
    Proceeding to step ;
    step (3.3): n residual images
    Figure FDA00022246293600000110
    Superimposed on the standard grid by the Drizzle method and low-pass filtered, and then added
    Figure FDA00022246293600000111
    To obtain a new reconstructed imageIf it isIf the requirement is not met, the step is entered;
    and (3.4) returning to the step (3.1) to carry out times of iterative loop operation until the image meeting the requirement is output.
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