CN104077751B - High spectrum image reconstructing method based on mixing norm tracing algorithm - Google Patents

Abstract

The invention discloses a kind of high spectrum image reconstructing method based on mixing norm tracing algorithm: combine high spectrum image property analysis existing compressed sensing restructing algorithm, select corresponding 0 norm algorithm and 1 norm algorithm, prove there is the mixed strategy that can the two be combined and find optimal mixed strategy, obtain mixing norm tracing algorithm, and then the high spectrum image of sparse sampling is reconstructed, finally export the reconstruct high spectrum image obtained through sparse inverse transformation.The method has Man Machine Interface module, mixed strategy analyzes module, high spectrum image reconstructed module, reconstruct these four functional modules of image output module.Mixing norm tracing algorithm, compared to traditional reconstructing method, all improves significantly in speed and precision, alleviates the transmission of EO-1 hyperion big data, stores the hardware pressure brought, improves the capacity of resisting disturbance of data transmission.

Description

High spectrum image reconstructing method based on mixing norm tracing algorithm

Technical field

The present invention relates to a kind of high spectrum image reconstructing method based on mixing norm tracing algorithm, it is adaptable to EO-1 hyperion number According in processing system, belong to hyperspectral data processing field.

Background technology

High-spectrum remote-sensing is an empty sky earth observation technology developed rapidly in recent decades, the character of its collection of illustrative plates unification There is great Research Significance and be widely applied prospect, being used widely in business, field military and among the people.Compare In conventional remote sensing images, what high spectrum image can be finer portrays characters of ground object, detects in conventional remote sensing and cannot detect Material, for later stage terrain classification and detection provide precondition.But, its good character is set up in huge data volume On, the size of a high spectrum image is often the hundred times of normal image, and it is superfluous that substantial amounts of wave band number brings huge information Remaining.This is collection of high spectrum image, transmits and store and bring unnecessary trouble.

Compressed sensing is the technology of the searching under determined system sparse solution proposed in recent years, and this technology is by exploitation signal Sparse characteristic under conditions of much smaller than nyquist sampling rate, utilize stochastical sampling obtain signal discrete sample, then By nonlinear reconstruction algorithm perfect reconstruction signal.Compressive sensing theory is once proposing just by theory of information, image procossing, the earth The highest attention in the fields such as science, optics, microwave imaging, pattern recognition, wireless telecommunications, and it is widely used in electronic engineering Especially in signal processing, carry out low sampling rate sampling and High precision reconstruction is sparse or compressible signal.The most widely used Compressed sensing restructing algorithm mainly have two classes: greedy algorithm based on 0 norm and convex optimized algorithm based on 1 norm.Based on 0 The greedy algorithm of norm includes matching pursuit algorithm, orthogonal matching pursuit algorithm, hard-threshold iterative algorithm etc., based on 1 norm Convex optimized algorithm includes base tracing algorithm, gradient project algorithms, interior point method, Homotopy Method etc..This two classes algorithm have his own strong points but also All there is its weak point: algorithm speed corresponding to 0 norm is fast but precision is the highest；Arithmetic accuracy corresponding to 1 norm be high but speed Unhappy.

Hyperspectral image data huge and obtain be difficult to, in order to alleviate hardware transport, storage pressure need alap enter Row sampling and High precision reconstruction；On the other hand, the shortcoming of the restructing algorithm of low velocity can because of big data quantity by amplification drastically, The time loss caused often allows people stand.It is, thus, sought for a kind of reconstruction accuracy is sufficiently high and reconstructed velocity foot Enough fast algorithms, meet the demand that high spectrum image processes in real time.

Summary of the invention

It is desirable to provide a kind of high spectrum image reconstructing method based on mixing norm tracing algorithm, specifically a kind of In conjunction with existing 0 norm algorithm and the new type of compression sensing reconstructing method of 1 norm algorithm advantage.This method has stronger robust Property, it is possible in the case of ensureing reconstruction accuracy, quickly reconstruct original high spectrum image, the height to differently substance environment Spectrum picture all shows good experiment effect.

Method flow involved in the present invention specifically includes following four step: 1, obtain initial information and relevant initialization Operation；2, mixed strategy analysis；3, high spectrum image reconstruct；4, reconstruction result output.Step each to the method flow process is entered below Row describes in detail:

Step one obtains initial information and relevant initialization operation

Utilize man-machine interactively interface module input high spectrum image sparse sampling result and two class algorithm examples, and arrange such as Formula (1) arrives the algorithm iteration end condition shown in (3), to whether termination algorithm judges.

|norm(x_k-1, 0) and-norm (x_k, 0) | ＜ ε₀ (1)

$\frac{\left|\right|x_k-x_{k-1}\left|\right|}{\left|\right|x_k\left|\right|}\≤{\mathrm{\ϵ}}_1---\left(2\right)$

$\frac{\left|\right|f\left(x_k\right)-f\left(x_{k-1}\right)\left|\right|}{\left|\right|f\left(x_k\right)\left|\right|}\≤{\mathrm{\ϵ}}_2---\left(3\right)$

Wherein, norm (x, 0) represents nonzero element number in x, ε₀, ε₁, ε₂Being selected normal number, x is that kth walks iteration As a result, f is object function.

Step 2 mixed strategy is analyzed

Assuming that primary signal is n dimensional signal sparse for k, its sparse transformation result is x, and the approximation solved is x '. It practice, either algorithm based on 0 norm is also based on the algorithm of 1 norm, their iterative process is all to force on n-dimensional space One broken line of close-target.Assuming that the base of n-dimensional space is

Algorithm based on 0 norm meets following constrained optimization problems:

$\underset{x}{\min }{\left|\right|x\left|\right|}_{l_0},s.t.\mathrm{\Φ\Ψx}=y---\left(4\right)$

Wherein, y represents observation, and x is the result that we need to solve, Φ be observing matrix Ψ be sparse matrix.Based on 0 Each step of the greedy algorithm of norm all can obtain the approximation in certain result dimension, is iterated according to the following steps:

1st step, obtains the approximation of one-component from initial point along coordinate axes

2nd step, from x₁' set out obtains the approximation of second component along coordinate axes

N-th step, from x_n-1' set out obtains the approximation of the n-th component along coordinate axes

Algorithm based on 1 norm meets following convex optimization problem:

$\underset{x}{\min }{\left|\right|x\left|\right|}_{l_1},s.t.\mathrm{\Φ\Ψx}=y---\left(5\right)$

It can be written as form to utilize Lagrangian method:

$\underset{x}{\min }({\left|\right|x\left|\right|}_{l_1}+\mathrm{\τ}||y-\mathrm{\Φ\Ψx}|\left|\right)---\left(6\right)$

Wherein, τ represents a non-negative constant for balanced signal degree of rarefication and reconstructed error.Convex optimized algorithm each Step iteration all can make iteration result from target more recently.In order to more directly illustrate, utilize the algorithm that gradient guides as one Individual example, this kind of algorithm carries out iterative process with below step:

1st step, from initial point, along gradient direction advance α now⁰Step-length

2nd step, from x₁' set out, along gradient direction advance α now¹Step-length

M walks, from x_m-1' set out, along gradient direction advance α now^m-1Step-length

Wherein, parameter alphaⁱRepresent the step-length of the i-th step,Represent object function.

Analysis based on step 2, is defined as being obtained the result of approximation by 0 norm by mixing norm tracing algorithm, then by 1 Norm algorithm is adjusted obtaining two step iterative process of precise results.Mixing norm tracing algorithm has been effectively combined 0 norm Speed and the precision of 1 norm, it is possible at a high speed reconstruction signal the most accurately.Whether the problem existed now has two: 1, exist Excellent mixed strategy；2, how optimal mixed strategy is found.

Whether the mixed strategy first analyzing optimum exists, say, that whether exchange point t exists.Define 0 norm algorithm Velocity Time function be v₀T (), the Velocity Time function of 1 norm algorithm is v₁(t).For easy analysis, it is assumed that two class speed Time function all smooth enoughs.

As in figure 2 it is shown, the distance of the initial point of an iteration to impact point is denoted as d₁, the distance of terminating point to impact point It is denoted as d₂, the distance that current iteration is walked is denoted as d₁-d₂.So Velocity Time function of the algorithm between the two time point Meet formula (7).

${\∫}_{t_1}^{t_2}v\left(t\right)\mathrm{dt}=d_1-d_2---\left(7\right)$

Select timing node t as the alternately node of two class algorithms.Before node t, 0 norm algorithm obtain result Approximation, is adjusted by 1 norm algorithm pairing approximation value afterwards, and concrete condition is as shown in Figure 3.Due to two class algorithms speed not Equally, the distance that in the identical time, 0 norm algorithm advances is more than 1 norm algorithm, so iteration initial time corresponding to 1 norm should F (t) should be denoted as more than t.Identical from forward travel distance, then both meet the relation shown in formula (8).

${\∫}_{t_0}^t{v}_0\left(t\right)\mathrm{dt}={\∫}_{t_0}^{f\left(t\right)}{v}_1\left(t\right)\mathrm{dt}---\left(8\right)$

The average speed of definition new algorithm isSo it meets the equilibrium relationships shown in formula (9).

$\stackrel{\‾}{v\left(t\right)}=\frac{{\∫}_{t_0}^t{v}_0\left(t\right)\mathrm{dt}+{\∫}_{f\left(t\right)}^{t_{\mathrm{end}}}{v}_1\left(t\right)\mathrm{dt}}{t-t_0+t_{\mathrm{end}}-f\left(t\right)}---\left(9\right)$

Combinatorial formula (8) and formula (9), can obtain result below:

$\stackrel{\‾}{v\left(t\right)}=\frac{{\∫}_{t_0}^{t_{\mathrm{end}}}{v}_1\left(t\right)\mathrm{dt}}{t_{\mathrm{end}}-t_0-(f\left(t\right)-t)}---\left(10\right)$

From formula (10), the distance that new algorithm runs isThis means that it can reach and 1 norm algorithm Identical precision.Along with the degree of rarefication of test sample increases, the iteration time of 0 norm algorithm substantially increases, but 1 norm algorithm Time change and inconspicuous.Such as, when the degree of rarefication of test sample increases to 200 when, orthogonal matching pursuit algorithm The CPU operation time substantially increases, but the CPU of gradient project algorithms runs the time and do not has much changes.The mixing of two kinds of algorithms Make new algorithm that the CPU of test sample is run the time more stable.On the other hand, most of 1 norm algorithms are at the beginning of iteration Initial point is had ready conditions requirement, but 0 norm algorithm seldom requires.The approximation utilizing 0 norm algorithm to obtain is calculated as 1 norm The iteration initial value of method often more meets the requirement of 1 norm algorithm than the initial value randomly choosed.Described on end, mixing norm chases after Track algorithm has higher robustness compared with 0 original norm algorithm and 1 norm algorithm.

Due to new algorithm operation it has been determined that the timing node of the only algorithm of relation new algorithm efficiency is chosen.Therefore Problem is converted into following optimization problem:

$\underset{t}{\max }(f\left(t\right)-t)$

$s.t.{\∫}_{t_0}^t{v}_0\left(t\right)\mathrm{dt}={\∫}_{t_0}^{f\left(t\right)}{v}_1\left(t\right)\mathrm{dt}---\left(11\right)$

Continuously and optimal mixed strategy is at open interval (t to prove now function f (t) in formula (11) respectively₀, t_end) Upper existence.

First defined function F (t): $F\left(t\right)={\∫}_{t_0}^t{v}_0\left(t\right)\mathrm{dt}={\∫}_{t_0}^{f\left(t\right)}{v}_1\left(t\right)\mathrm{dt}$

ForSelect open interval (t₀, t_endAny one some t in)_c, then

$\left|\right|F\left(t\right)-F\left(t_c\right)\left|\right|=\left|\right|{\∫}_{t_c}^t{v}_0\left(t\right)\mathrm{dt}\left|\right|\≤\left|\right|t-t_c\left|\right|*\underset{t}{\max }\left|\right|v_0\left(t\right)\left|\right|---\left(12\right)$

ChooseWhen | | t-t_c| | during ＜ δ, have | | F (t)-F (t_c) | | ＜ ε.That is F (t) is at t_c Point is continuous, due to t_cThe arbitrariness of point, F (t) is at open interval (t₀, t_end) upper continuous.

So, forThere is a normal number δ ＞ 0, when | | t-t_c| | during ＜ δ

$\left|\right|F\left(t\right)-F\left(t_c\right)\left|\right|=\left|\right|{\&Integral;}_{f\left(t_c\right)}^{f\left(t\right)}{v}_1\left(t\right)\mathrm{dt}\left|\right|=\left|\right|f\left(t\right)-f\left(t_c\right)\left|\right|*\left|\right|v_1\left(\mathrm{\&eta;}\right)\left|\right|<\mathrm{\&epsiv;}---\left(13\right)$

$\left|\right|f\left(t\right)-f\left(t_c\right)\left|\right|<\frac{\mathrm{\&epsiv;}}{\left|\right|v_1\left(\mathrm{\&eta;}\right)\left|\right|}---\left(14\right)$

In formula (13), η is that a constant meets η ∈ [f (t), f (t_c)].Therefore, f (t) is at an open interval (t₀, t_end) Upper arbitrfary point t_cPlace is continuous, so f (t) is at open interval (t₀, t_end) place is continuous.

For optimization problem (11), function f (t)-t is at interval (t₀, t_end) upper continuous.Therefore, for arbitrarilyFunction f (t)-t is at interval [t₀+ ε, t_end-ε] on all there is maximum.Problem is converted into function f now T ()-t is at interval [t₀, t_endMaximum value position on] is not at t₀And t_endPlace.

Being known by analysis before, the speed of 0 norm is faster than 1 norm, it means that there is 1 t₀', 0 model before this point The speed of number all can be more than 1 norm.Corresponding, it is longer than 0 norm that 1 norm runs the time, it means that in the operation of 0 norm During stopping, 1 norm speed is still being run.I.e. there is 1 t_end', the speed of 1 norm is more than 0 norm speed after this point. So have:

$\stackrel{\&OverBar;}{v\left({t_0}^{\&prime;}\right)}=\frac{{\&Integral;}_{t_0}^{{t_0}^{\&prime;}}-v_0\left(t\right)\mathrm{dt}+{\&Integral;}_{f\left({t_0}^{\&prime;}\right)}^{t_{\mathrm{end}}}{v}_1\left(t\right)\mathrm{dt}}{(t_{\mathrm{end}}-t_0)-(f\left({t_0}^{\&prime;}\right)-{t_0}^{\&prime;})}=\frac{{\&Integral;}_{t_0}^{t_{\mathrm{end}}}{v}_1\left(t\right)\mathrm{dt}}{(t_{\mathrm{end}}-t_0)-(f\left({t_0}^{\&prime;}\right)-{t_0}^{\&prime;})}>\frac{{\&Integral;}_{t_0}^{t_{\mathrm{end}}}{v}_1\left(t\right)\mathrm{dt}}{t_{\mathrm{end}}-t_0}=\stackrel{\&OverBar;}{v\left(t_0\right)}---\left(15\right)$

$\stackrel{\&OverBar;}{v\left({t_{\mathrm{end}}}^{\&prime;}\right)}=\frac{{\&Integral;}_{t_0}^{{t_{\mathrm{end}}}^{\&prime;}}-v_0\left(t\right)\mathrm{dt}+{\&Integral;}_{f\left({t_{\mathrm{end}}}^{\&prime;}\right)}^{t_{\mathrm{end}}}{v}_1\left(t\right)\mathrm{dt}}{(t_{\mathrm{end}}-t_0)-(f\left({t_{\mathrm{end}}}^{\&prime;}\right)-{t_{\mathrm{end}}}^{\&prime;})}=\frac{{\&Integral;}_{t_0}^{t_{\mathrm{end}}}{v}_1\left(t\right)\mathrm{dt}}{(t_{\mathrm{end}}-t_0)-(f\left({t_{\mathrm{end}}}^{\&prime;}\right)-{t_{\mathrm{end}}}^{\&prime;})}>\frac{{\&Integral;}_{t_0}^{t_{\mathrm{end}}}{v}_0\left(t\right)\mathrm{dt}}{t_{\mathrm{end}}-t_0}=\stackrel{\&OverBar;}{v\left(t_{\mathrm{end}}\right)}---\left(16\right)$

I.e. function f (t)-t is at interval [t₀, t_endMaximum value position on] is not at t₀And t_endPlace.

According to conclusion above, optimal mixed strategy is chosen and is analyzed.Formula (11) is carried out derivation,

[f (t)-t] '=f ' (t)-1=0 (17)

Formula (8) is analyzed, has

${\left[{\&Integral;}_{t_0}^t{v}_0\left(t\right)\mathrm{dt}\right]}^{\&prime;}=v_0\left(t\right)---\left(18\right)$

${\left[{\&Integral;}_{t_0}^{f\left(t\right)}{v}_1\left(t\right)\mathrm{dt}\right]}^{\&prime;}=v_1\left[f\left(t\right)\right]f^{\&prime;}\left(t\right)=v_1\left[f\left(t\right)\right]---\left(19\right)$

Therefore, it can obtain:

v₀(t)=v₁[f(t)] (20)

So, the essential condition in the moment that efficiency is the highest is that when running identical distance, speed is identical.It is to say, operation phase It is that there is a strong possibility is exactly optimum mixed strategy point for the point that speed is identical with distance.

Step 3 reconstruct high spectrum image

By the analysis of step 2, the algorithm flow obtaining mixing norm tracing algorithm can be arranged.Understand for convenience, The algorithm guided by gradient is as the example of 1 norm algorithm:

Step 1, utilizes the approximation of the one-component of 0 norm algorithm acquisition signal to be solved

Step 2, utilizes the approximation of second component of 0 norm algorithm acquisition signal to be solved

Step p, utilizes the approximation of pth the component of 0 norm algorithm acquisition signal to be solved

Step p+1, utilizes 1 norm algorithm to obtain along the gradient direction of current location and solves the position of signal ${x_{p+1}}^{\&prime;}={x_p}^{\&prime;}-{\mathrm{\&alpha;}}^{p+1}\&dtri;f\left({x_p}^{\&prime;}\right);$

Step q, utilizes 1 norm algorithm to obtain the position solving signal along current location gradient direction $x^{\&prime;}={x_q}^{\&prime;}={x_{q-1}}^{\&prime;}-{\mathrm{\&alpha;}}^q\&dtri;f\left({x_{q-1}}^{\&prime;}\right).$

P ∈ in superincumbent algorithm flow 1,2 ... k}, k are the degree of rarefications of primary signal, αⁱIt it is the i-th step iteration stepping； New algorithm will the biggest probability reach optimum state, if, with 0 norm algorithm iteration p step time spent t meet (8) and (20)。

Mixing norm tracing algorithm is utilized the low sampling rate hyperspectral image data of input to be reconstructed, according to input End condition terminates iterative step, it is thus achieved that the sparse approximate solution of needs.According to the feature of high spectrum image, select the most sparse Base, the sparse sampling that Man Machine Interface module is obtained by the mixing norm restructing algorithm obtained by mixed strategy analysis module Result is reconstructed, and utilizes sparse inverse transformation to obtain the reconstruction result of high spectrum image.

Step 4 reconstruction result exports

By reconstruction result output module, the high spectrum image that output has reconstructed.

The present invention is high spectrum image reconstructing method based on mixing norm tracing algorithm, has an advantage in that: can be relatively High spectrum image sample to low sampling rate reconstructs accurately in the short time, for the ground object target and not of different background Same sample rate all can reach good quality reconstruction, and more original algorithm has higher robustness.

Accompanying drawing explanation

Fig. 1 show high spectrum image reconstructing method flow chart based on mixing norm tracing algorithm

Fig. 2 tri-class restructing algorithm compares

Fig. 3 show the definition of speed

Fig. 4 show the Velocity Time relation of three class algorithms

Fig. 5 show emulation experiment data

Fig. 6 show the simulation experiment result

Detailed description of the invention

With emulation experiment, the technical method of this invention is further detailed below in conjunction with the accompanying drawings.

Developing emulation prototype system based on the present invention, this system includes: Man Machine Interface module, mixed strategy analysis Module, high spectrum image reconstructed module, reconstruct these four functional modules of image output module.

The high-spectral data after sparse sampling is obtained by Man Machine Interface module.This example uses Indiana Pine The part that high-spectral data and Washington D.C.Mall high-spectral data intercept, concrete condition is as shown in Figure 4.Wherein, Indiana Pine high-spectral data size is 145 × 145, and wave-length coverage is 400～2400nm, remove water vapor absorption wave band and After low signal-to-noise ratio wave band, retaining 220 wave bands, the part that Washington D.C.Mall high-spectral data intercepts, size is 100 × 100, wave-length coverage is 0.4～2.4 μm, after removing water vapor absorption wave band and low signal-to-noise ratio wave band, retains 191 wave bands, Sampling matrix is Gaussian random matrix.

Parameter about stopping criterion for iteration is carried out initialization process, parameter ε being used for termination algorithm is set₀, ε₁, ε₂, When algorithm meets formula (1) (2) (3), out of service.

In conjunction with high spectrum image sparse sampling result, select suitable 0 norm algorithm and 1 norm algorithm, analyze theirs Specific algorithm flow process, finds their optimum incorporation time node, it is thus achieved that the algorithm flow of mixing norm tracing algorithm.

Assuming that primary signal is n dimensional signal sparse for k, its sparse transformation result is x, and the approximation solved is x '. It practice, either algorithm based on 0 norm is also based on the algorithm of 1 norm, their iterative process is all to force on n-dimensional space One broken line of close-target.Assuming that the base of n-dimensional space isExplain for convenience, the following is and guided by gradient Algorithm as the example of 1 norm algorithm:

Step 1: utilize 0 norm algorithm to obtain the approximation of one-component of signal to be solved:

Step 2: utilize 0 norm algorithm to obtain the approximation of second component of signal to be solved:

Step p: utilize 0 norm algorithm to obtain the approximation of pth component of signal to be solved:

Step p+1: utilize 1 norm algorithm to obtain along the gradient direction of current location and solve the position of signal: ${x_{p+1}}^{\&prime;}={x_p}^{\&prime;}-{\mathrm{\&alpha;}}^{p+1}\&dtri;f\left({x_{p+1}}^{\&prime;}\right);$

Step q: utilize 1 norm algorithm to obtain along current location gradient direction and solve the position of signal: $x^{\&prime;}={x_q}^{\&prime;}={x_{q-1}}^{\&prime;}-{\mathrm{\&alpha;}}^{q-1}\&dtri;f\left({x_{q-1}}^{\&prime;}\right);$

P ∈ in superincumbent algorithm flow 1,2 ... k}, k are the degree of rarefications of primary signal, αⁱIt it is the i-th step iteration stepping； New algorithm will the biggest probability reach optimum state, if, with 0 norm algorithm iteration p step time spent t meet (8) and (20)。

According to the feature of high spectrum image, select corresponding sparse base, analyze, by mixed strategy, the mixing that module obtains The sparse sampling result that Man Machine Interface module is obtained by norm restructing algorithm is reconstructed, and utilizes sparse inverse transformation to obtain height The reconstruction result of spectrum picture；

By reconstruction result output module, the high-spectrum remote sensing that output has reconstructed.

The inventive method being embodied as through analogue system, test result indicate that and can reconstruct difference by high-speed, high precision Under sample rate, the atural object high spectrum image of different background, has good robustness.

Claims (1)

1. a high spectrum image reconstructing method based on mixing norm tracing algorithm, and based on emulating prototype system accordingly, This system has Man Machine Interface module, mixed strategy analyzes module, high spectrum image reconstructed module, reconstruct image output mould These four functional modules of block, specifically include following steps:

The first step, obtains primary data and relevant initialization operation；

Utilize Man Machine Interface module obtain low sampling rate hyperspectral image data, initialization algorithm stopping criterion for iteration, And relevant parameter is set: primary signal is n dimensional signal sparse for k, and its sparse transformation result is x, and the approximation solved is X ', the base of n-dimensional space is

Second step, is analyzed restructing algorithm based on 0 norm and restructing algorithm based on 1 norm, obtains corresponding mixing Strategy；

In conjunction with high spectrum image feature, analyzing 0 norm algorithm and 1 norm algorithm characteristic and set up mixed strategy model, analysis is ground Study carefully optimal mixed strategy, obtain mixing the algorithm flow of norm tracing algorithm, with the algorithm of gradient guiding as 1 norm algorithm The algorithm flow obtaining mixing norm tracing algorithm is:

Step 1, utilizes approximation ξ of the one-component of 0 norm algorithm acquisition signal to be solved_i' and first step iteration result

Step 2, utilizes approximation ξ of second component of 0 norm algorithm acquisition signal to be solved_j' and second step iteration result

Step p, utilizes approximation ξ of pth the component of 0 norm algorithm acquisition signal to be solved_p' and pth step iteration result

Step p+1, utilizes 1 norm algorithm to obtain along the gradient direction of current location and solves the position of signal

Step q, utilizes 1 norm algorithm to obtain the position solving signal along current location gradient direction

P ∈ in superincumbent algorithm flow 1,2 ... k}, k are the degree of rarefications of primary signal, αⁱIt it is the i-th step iteration stepping；Mixing Norm tracing algorithm will the biggest probability reach optimum state, if, with 0 norm algorithm iteration p step time spent t meet:

${\&Integral;}_{t_0}^t{v}_0\left(t\right)dt={\&Integral;}_{t_0}^{f\left(t\right)}{v}_1\left(t\right)dt---\left(1\right)$

v₀(t)=v₁[f(t)] (2)

Wherein, t₀It is iteration initial time, v₀T () is the speed of 0 norm algorithm, v₁T () is the speed of 1 norm algorithm, t is 0 model The time that number algorithm iteration p step spends, f (t) is the time that 1 norm walks that 0 norm algorithm p step journey spends；

3rd step, high spectrum image reconstructs；

According to the feature of high spectrum image, select corresponding sparse base, analyze, by mixed strategy, the mixing norm that module obtains The sparse sampling result that Man Machine Interface module is obtained by restructing algorithm is reconstructed, and utilizes sparse inverse transformation to obtain EO-1 hyperion The reconstruction result of image；

4th step: by reconstruction result output module, exports high spectrum image reconstruction result.