CN111968032A - Self-adaptive sampling single-pixel imaging method - Google Patents
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Abstract
The invention belongs to the technical field of single-pixel imaging; the existing compression imaging method needs to select a proper sampling rate after a known target scene is imaged by trying different sampling rates for multiple times, the sampling rate is not always the most proper after the scene is changed, and the imaging quality and efficiency cannot be considered; the invention provides a self-adaptive sampling single-pixel imaging method, which is used for carrying out self-adaptive sampling single-pixel imaging on different target scenes, detecting the dispersion degree of each frequency band on a transform domain during imaging and the trend of the variation of the dispersion degree in real time in the transform domain with energy concentration and sparsity, determining whether to stop sampling according to the variation trend, reducing the number of measurements and the occupation amount of a memory, having stronger self-adaptability and meeting the requirements of both imaging time and imaging quality.
Description
Technical Field
The invention relates to the technical field of single-pixel imaging, in particular to a self-adaptive sampling single-pixel imaging method.
Background
Single pixel imaging utilizes an imaging technique in which an object is encoded with a series of temporally varying spatial light, and a series of encoded time-varying information of the object is converted into spatial information by a detector without spatial resolution. Single pixel imaging techniques have evolved from earlier ghost imaging techniques, ranging from initial quantum ghost imaging, to thermo-optic ghost imaging, to computational ghost imaging. Because the signal acquisition system has a series of advantages of depth resolution capability, diffraction imaging capability, certain noise resistance, capability of imaging in low-light conditions, low manufacturing cost and the like, the signal acquisition system is gradually combined into an image by a plurality of detectors, and the development is made to image by only using one single-pixel detector. The system has the limitations of imaging time and imaging quality because single-pixel imaging requires a large amount of time-varying spatial light in the encoding stage of the object. With the normalized and differential ghost imaging proposed by the researchers later, the quality of the imaging is significantly improved. On the other hand, with the development of compressed sensing, researchers combine it with single-pixel imaging, which greatly reduces the acquisition time of signals. But because the computational complexity of compressed sensing is high, the problem of long image reconstruction time is inevitable. Two solutions to the problem exist, one is convex optimization, and the other is a greedy algorithm, and the methods reduce the computational complexity of compression imaging to a certain extent and improve the imaging efficiency. These current methods of compression imaging still have the disadvantage that they require several attempts to image a given target scene at different sampling rates, and finally determine to select a suitable sampling rate, but if a scene with a greater complexity difference than before is replaced, the selected sampling rate is not necessarily the most suitable, and therefore a good tradeoff between imaging quality and imaging efficiency cannot be achieved.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a self-adaptive sampling single-pixel imaging method, which carries out self-adaptive sampling single-pixel imaging on different target scenes, determines whether to stop sampling according to the change trend and meets the requirements of simultaneously considering imaging time and imaging quality.
In order to achieve the purpose, the invention provides the following technical scheme:
a self-adaptive sampling single-pixel imaging method is characterized in that in a transform domain with energy concentration and sparsity, the discrete degree of each frequency band on the transform domain and the trend of variation of the discrete degree during imaging are detected in real time, and whether sampling is stopped or not is determined according to the variation trend, and specifically comprises the following steps:
step 1, configuring an initial imaging resolution parameter M multiplied by N of an imaging system and a frequency band number j for starting to fit0And the maximum value k of the variation fluctuation of the slope k of the fitting curve of the first Delta j fitting frequency bands when stopping fitting and sampling0Selecting one of the structural illumination basic modes from the range of the structural illumination basic modes as a structural illumination basic mode for projecting the target scene;
step 2, under the condition of the structural illumination basic mode selected in the step 1, according to the coefficient matrix DM×NGenerating an illumination basis matrix P corresponding to the selected mode according to the sequence of the elements in the target scene, gradually projecting and collecting the illumination basis matrix P to a position with low energy of a transform domain from the highest point of the energy of the transform domain, coding the projection illumination basis matrix P of the target scene, and synchronously collecting coding signals carrying object information by using a single-pixel detector;
step 3, grouping the signals collected in the step 2 according to frequency bands, and calculating the average signal intensity a of each group of frequency bandsjSum signal deviation ajDegree of dispersion v ofj；
Step 4, the frequency band number j formed by the collected signals and the frequency band number j beginning to be fitted0Comparing, if the frequency band number j is larger than or equal to j0Degree of dispersion v of the acquired signal bandjPerforming polynomial fitting to form a fitting curve, and calculating the slope k of the fitting curve; if the number of frequency bands j < j0Repeating the operation of the step 3;
and 5, judging whether the sampling stopping condition is met: in the interval delta j, the gradient k satisfies that k is 0 or delta k is less than or equal to k0Stopping sampling, and performing image reconstruction on the sampled signals, wherein Δ k is the change fluctuation value of the slope k in the first Δ j frequency bands, namely Δ k is kmax-kmin(ii) a Otherwise, repeating the operation of the step 4.
Further, the method of grouping by band in step 3 is as follows: and according to the sparse distribution characteristic of the signals of the selected structural illumination base mode in the corresponding transform domain, dividing the acquired signals on the region formed around the energy concentration point into a frequency band according to the same regular shape.
Further, the structural illumination basis mode ranges include a Hadamard (Hadamard) illumination basis, a discrete cosine illumination basis, a Krawtchouk illumination basis, and a fourier illumination basis.
Further, in step 4, the degree of dispersion v is measuredjThe polynomial fitting method is as follows: the discrete degrees of all frequency bands of the acquired signal are logarithmically transformed and the polynomial f (x) c is used1xn+c2xn-1+…+cnx+cn+1Fitting, determining all coefficients of the polynomial according to fitting results, substituting the coefficients into the polynomial to determine a fitting function f (x), deriving the fitting function f (x) to obtain a first derivative polynomial function f' (x) of the fitting function f (x), calculating the slope k of each fitted frequency band, and predicting the change of a fitting curve according to the slope k.
Further, the number of frequency bands j to start fitting0In the range of 0 < j0≤jmax/2，jmaxThe maximum number of fitted bands.
Further, the maximum value k of the variation fluctuation of the slope k of the fitting curve0Has a value range of 0 < k0≤0.2。
Further, the value range of the delta j is more than or equal to 5 and less than or equal to 20.
In conclusion, the invention has the following beneficial effects:
(1) the method utilizes the centralization of image energy information in a transform domain, samples important transform domain coefficients and greatly reduces the number of measurements;
(2) according to the characteristics of the target image, the sampling rate is self-adapted, all measurement bases do not need to be generated in advance and stored in a computer, and the occupation amount of a memory is reduced for the image needing to be reconstructed with high resolution;
(3) the invention has stronger environmental adaptivity, and meets the requirements of simultaneously considering both imaging time and imaging quality for different target images;
(4) the method is suitable for various measurement illumination bases, such as a Hadamard illumination base, a discrete cosine illumination base, a Krawtchouk illumination base and a Fourier illumination base, and is suitable for the measurement bases with the characteristic of energy concentration after the target image is transformed.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of the spectral grouping principle of discrete cosine or Hadamard sampled signals;
FIG. 3 is a schematic diagram of the spectral grouping principle of a Krawtchouk sampled signal;
FIG. 4 is a schematic diagram of a Fourier sampled signal spectrum grouping principle;
fig. 5 shows the result of the adaptive sampling simulation reconstruction in embodiment 1.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1 to 5, the present invention discloses a self-adaptive sampling single-pixel imaging method, which detects the dispersion degree of each frequency band and the variation trend of the dispersion degree in the transform domain during imaging in real time in the transform domain with energy concentration and sparsity, determines whether to stop sampling according to the variation trend, meets the requirements of simultaneously considering both imaging time and imaging quality, is suitable for different target scenes, and specifically comprises the following steps:
step 1, configuring an initial imaging resolution parameter M multiplied by N of an imaging system and a frequency band number j for starting to fit0Number of frequency bands j0In the range of 0 < j0≤jmax/2，jmaxIs the maximum number of fitting frequency bands and the maximum value k of the variation fluctuation of the slope k of the fitting curve of the first delta j fitting frequency bands when the fitting and the sampling are stopped0The value range is 0 < k0Is less than or equal to 0.2, and delta j is less than or equal to 20 and is less than or equal to 5; and selecting one of the structural illumination basic mode ranges as a structural illumination basic mode projected to the target scene, wherein the structural illumination basic mode ranges comprise a Hadamard illumination basis, a discrete cosine illumination basis, a Krawtchouk illumination basis and a Fourier illumination basis.
Step 2, under the condition of the structural illumination basic mode selected in the step 1, according to the coefficient matrix DM×NBy the orthogonal basis matrix phi of the selected structural illumination basis patternAnd generating a corresponding illumination basis matrix P, generating a light pattern for illuminating (or scanning or coding) the target object to be imaged by the projection system according to the numerical value in the illumination basis matrix P, gradually projecting and collecting the light pattern to a position with low energy in a transform domain from the highest point of the energy in the transform domain by using a projector or other projection equipment which can be acquired by a person skilled in the art by the projection system, coding the projection illumination basis matrix P of the target scene, and synchronously collecting the coding signal carrying the object information by using a single-pixel detector.
Step 3, grouping the signals acquired in the step 2 according to frequency bands, dividing the acquired signals on the region formed around the energy concentration point according to the same regular shape into a frequency band according to the signal sparse distribution characteristics of the selected structural illumination base mode in the corresponding transform domain, and calculating the average signal intensity a of each group of frequency bandsjSum signal deviation ajDegree of dispersion v ofj。
Step 4, the frequency band number j formed by the collected signals and the frequency band number j beginning to be fitted0Comparing, if the frequency band number j is larger than or equal to j0Degree of dispersion v of the acquired signal bandjPerforming polynomial fitting to form a fitting curve, and calculating the slope k of the fitting curve; if the number of frequency bands j < j0Repeating the operation of the step 3; for degree of dispersion vjThe polynomial fitting method is as follows: the discrete degrees of all frequency bands of the acquired signal are logarithmically transformed and fitted with a polynomial formula as follows:
f(x)＝c1xn+c2xn-1+…+cnx+cn+1 (1)
determining all coefficients of the polynomial according to the fitting result, substituting the coefficients into the polynomial to determine a fitting function f (x), and deriving the fitting function f (x) to obtain a first derivative polynomial function f' (x) of the fitting function f (x), namely
f'(x)＝c1xn-1+c2xn-2+…+cn (2)
The slope k of each fitted band is calculated and the change of the fitted curve is predicted from the slope k.
And 5, judging whether the sampling stopping condition is met: in the interval delta j, the gradient k satisfies that k is 0 or delta k is less than or equal to k0Stopping sampling, and performing image reconstruction on the sampled signals, wherein Δ k is the change fluctuation value of the slope k in the first Δ j frequency bands, namely Δ k is kmax-kminFirst Δ j bands, kmaxIs the maximum value of the slope, kminIs the slope minimum; otherwise, repeating the operation of the step 4.
The invention is further illustrated by the following 4 examples.
Example 1: the initial imaging resolution is 128 x 128, the number of initial bands j of the fit0＝40，k00.005, the structural illumination basis pattern P selects the discrete cosine illumination basis, the discrete cosine transform energy is concentrated at the upper left corner of the transform domain matrix, as shown in FIG. 2, according to the coefficient matrix D in the figureM×NThe illumination base mode is generated by the sequence specified by the subscripts of the elements, and the discrete cosine transform principle is utilized to generate the illumination base mode, wherein the formula is as follows:
wherein, u-0, 1, 2.., M-1; v-0, 1,2, ·, N-1,
f (u, v) is the coefficient of the digital image F (u, v) in the transform domain, and defines M × N binary matrices Θ that contain only 0 and 1 elements and are different from each other, namely:
substituting formula (5) into formula (4), and performing inverse DCT on each coefficient matrix to obtain orthogonal basis matrix phi of discrete cosine transformi DFor adaptation to the output of the projection system, the orthogonal basis matrix phi isi DNormalization is performed by mean value, and the formula is as follows:
wherein, BmFor the ith orthogonal basis matrix phii DInverse of the element of medium maximum, illumination basis matrix Pi DThe value range of the medium element is 0-1, an illumination base for projection is obtained according to a formula (6), and a single illumination base carrying object information encoding signal d is obtained through synchronous acquisition and operation of a single-pixel detectoriD can also be determined by differential measurementi＝di +-di -。
Average signal strength ajAnd degree of dispersion vjThe calculation formula is as follows:
where e is the number of elements per band, c is the index of the starting element of each band, and j denotes the number of bands; the first reconstruction method of this embodiment is as follows:
wherein the set Ψ of illumination basis matrices consists of M × N different DCT orthogonal basis matrices Φi HComposition, Ψ { u, v } represents the orthogonal basis matrices at the u and v positionsΦi HOrthogonal basis matrix phii HThe size is M × N, the size of the illumination basis matrix set Ψ is M2×N2D is a matrix of measurement signals,
to reconstruct an image; the second reconstruction method can perform reconstruction through the inverse transformation equation of step two. Fig. 5 shows the original images and results of 5 of the reconstructed images by adaptive sampling, and the simpler the target scene is, the lower the sampling rate is, on the premise of ensuring high quality.
Example 2: the structural illumination basis pattern P selects a Hadamard illumination basis, other initial configurations are the same as embodiment 1, Hadamard transform energy is concentrated at the upper left corner of a transform domain matrix, and a transform formula is as follows:
wherein b isi(x) Is the ith bit of the binary representation of x, the formula (5) is substituted into the formula (11), and the inverse Hadamard transform is carried out on the binary matrix theta of the formula (5) to obtain the orthogonal basis matrix phi of the Hadamard transformi HContaining only the binary elements +1 and-1, for adapting to the output of the projection system and for performing a differential measurement, the orthogonal basis matrix Φ is subjected toi HThe following transformations are performed:
wherein the positive illumination group Pi +Containing only binary elements +1 and 0, the anti-lighting base Pi -Containing only binary elementsElement-1 and 0. Obtaining two groups of opposite illumination bases actually used for projection according to the formula (12) and the formula (13), and carrying out matrix D on the target scene according to coefficientsM×NThe corresponding illumination bases are projected in the sequence specified by the subscript of the middle element, synchronous acquisition is carried out by a single-pixel detector, and differential operation is carried out to obtain a coded signal d of the object information carried by the single illumination basei＝di +-di -。
The conditions for stopping sampling are the same as in example 1, and the image reconstruction calculation formula is as follows:
example 3: the structural illumination basis pattern P selects the Krawtchouk illumination basis, other initial configurations are the same as those of embodiment 1, and the Krawtchouk moment transform energy is concentrated at the upper left corner of the transform domain matrix, as shown in FIG. 3, and is expressed as the coefficient matrix D in the graphM×NThe illumination base mode is generated according to the sequence specified by the subscripts of the elements in the (1), and the Krawtchouk moment transformation principle is utilized to generate the illumination base mode, wherein the formula is as follows:
wherein u-0, 1,2, …, M-1, v-0, 1,2, …, N-1, p1And p2Polynomial weights for controlling image locality properties, Krawtchouk moment transform
The calculation formula of (2) is as follows:
where ω (x; p, M) is a weight function, ρ (u; p, M) is a square norm, Ku(x; p, M) is the Uth order Krawtchouk polynomial, (-M)tFor Pochhammer (power of order) notation, the calculation formula is as follows:
wherein () is a gamma function; the individual Krawtchouk illumination basis is expressed as:
at this time, the orthogonal basis matrix Φ of the krawtchook transformi KOr can be calculated quickly by a three-item recursive algorithm, and the orthogonal basis matrix phi is subjected to adaptive calculation to the output of the projection systemi KIs changed over
Wherein the parameter Bm KFor orthogonal basis matrix phii KInverse of the element of medium maximum, illumination basis matrix Pi KThe value range of the illumination base for actual projection is-0.5, and the target scene is subjected to coefficient matrix D in the graphM×NThe corresponding illumination base of the projection designated by the subscript of the middle element is synchronously collected and operated by a single-pixel detector to obtain a coded signal d of the object information carried by the single illumination baseiOr d can also be determined by differential measurementi＝di +-di -。
The collected signals are grouped by frequency band in step 3 as shown in fig. 3, and the rest is the same as in embodiment 1.
Example 4: the Fourier illumination basis is selected in the structural illumination basis pattern P, and other initial configurations are the same as those in embodiment 1, and Fourier transform energy is concentrated at the center of a transform domain matrix, as shown in FIG. 4, according to a coefficient matrix D in the graphM×NThe illumination base pattern is generated by the sequence specified by the subscripts of the elements in the (1), and the Fourier transform principle is utilized to generate the illumination base pattern, wherein the formula is as follows:
defining M x N mutually different complex matrices thetacThe following were used:
adopting three-step Fourier imaging, wherein beta is 0, 2 pi/3 and 4 pi/3; if four-step fourier imaging is used, then β is 0,1 pi/2, 3 pi/2, 1 pi, equation (25) is substituted into equation (24), and for each complex matrix ΘcPerforming inverse Fourier transform and taking a real part to obtain a result, namely an orthogonal basis matrix of Fourier
To adapt to the output of the projection system, the orthogonal basis matrix is transformed as follows:
according toEquation (26) yields the basis for actual projection illumination
For the target scene, the coefficient matrix D in FIG. 4 is shownM×NCorresponding illumination bases are projected in sequence specified by subscripts of the elements in the (A), and a single pixel detector is used for synchronously acquiring coded signals d of the single illumination bases carrying object informationβ(ii) a For three-step Fourier imaging there are
For four-step Fourier imaging there is di＝dπ-d0+i(d3π/2-dπ/2)。
Step 3 groups the acquired signals by frequency band as shown in fig. 4, and the rest is the same as embodiment 1.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may occur to those skilled in the art without departing from the principle of the invention, and are considered to be within the scope of the invention.
Claims (7)
1. A self-adaptive sampling single-pixel imaging method is characterized in that: in a transform domain with energy concentration and sparsity, detecting the dispersion degree of each frequency band on the transform domain during imaging and the trend of variation of the dispersion degree in real time, and determining whether to stop sampling according to the variation trend, specifically comprising the following steps:
step 1, configuring an initial imaging resolution parameter M multiplied by N of an imaging system and a frequency band number j for starting to fit0And the maximum value k of the variation fluctuation of the slope k of the fitting curve of the first Delta j fitting frequency bands when stopping fitting and sampling0Selecting one of the structural illumination basic modes from the range of the structural illumination basic modes as a structural illumination basic mode for projecting the target scene;
step 2. under the condition of the structure illumination base mode selected in the step 1,by coefficient matrix DM×NGenerating an illumination basis matrix P corresponding to the selected mode according to the sequence of the elements in the target scene, gradually projecting and collecting the illumination basis matrix P to a position with low energy of a transform domain from the highest point of the energy of the transform domain, coding the projection illumination basis matrix P of the target scene, and synchronously collecting coding signals carrying object information by using a single-pixel detector;
step 3, grouping the signals collected in the step 2 according to frequency bands, and calculating the average signal intensity a of each group of frequency bandsjSum signal deviation ajDegree of dispersion v ofj；
Step 4, the frequency band number j formed by the collected signals and the frequency band number j beginning to be fitted0Comparing, if the frequency band number j is larger than or equal to j0Degree of dispersion v of the acquired signal bandjPerforming polynomial fitting to form a fitting curve, and calculating the slope k of the fitting curve; if the number of frequency bands j < j0Repeating the operation of the step 3;
and 5, judging whether the sampling stopping condition is met: in the interval delta j, the gradient k satisfies that k is 0 or delta k is less than or equal to k0Stopping sampling, and performing image reconstruction on the sampled signals, wherein Δ k is the variation fluctuation value of the slope k in the first Δ j fitting frequency bands, namely Δ k is kmax-kmin(ii) a Otherwise, repeating the operation of the step 4.
2. The method of adaptively sampled single pixel imaging according to claim 1, wherein: the method of grouping by band in step 3 is as follows: and according to the sparse distribution characteristic of the signals of the selected structural illumination base mode in the corresponding transform domain, dividing the acquired signals on the region formed around the energy concentration point into a frequency band according to the same regular shape.
3. The method of adaptively sampled single pixel imaging according to claim 1, wherein: the structural illumination basis mode ranges include a Hadamard (Hadamard) illumination basis, a discrete cosine illumination basis, a krawttchouk illumination basis, and a fourier illumination basis.
4. The method of adaptively sampled single pixel imaging according to claim 1, wherein: in step 4, the method of performing polynomial fitting on the discrete degree is as follows: degree of dispersion v for all frequency bands of the acquired signaljLogarithmic transformation is carried out and the polynomial f (x) is c1xn+c2xn-1+...+cnx+cn+1Fitting, determining all coefficients of the polynomial according to fitting results, substituting the coefficients into the polynomial to determine a fitting function f (x), deriving the fitting function f (x) to obtain a first derivative polynomial function f' (x) of the fitting function f (x), calculating the slope k of each fitted frequency band, and predicting the change of a fitting curve according to the slope k.
5. The adaptively sampled single-pixel imaging method of claim 1,2, 3 or 4, wherein: the number of bands to start fitting j0In the range of 0 < j0≤jmax/2，jmaxThe maximum number of fitted bands.
6. The adaptively sampled single-pixel imaging method of claim 1,2, 3 or 4, wherein: maximum value k of variation fluctuation of slope k of the fitting curve0Has a value range of 0 < k0≤0.2。
7. The adaptively sampled single-pixel imaging method of claim 1,2, 3 or 4, wherein: the value range of the delta j is more than or equal to 5 and less than or equal to 20.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112345424A (en) * | 2020-11-27 | 2021-02-09 | 太原理工大学 | Method and device for detecting gas diffusion and concentration distribution by wavelength tuning single pixel |
| CN114414050A (en) * | 2022-01-18 | 2022-04-29 | 中国人民解放军国防科技大学 | Self-adaptive Fourier calculation correlation imaging method and system |
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