CN105760348B - A kind of equalization filtering deconvolution data reconstruction method - Google Patents

Abstract

The present invention relates to a kind of deconvolution data reconstruction method based on Fourier transformation.This method adds suitable noise in convolved data and convolution kernel, using filter function equilibrium convolution kernel, effectively inhibits the error of Deconvolution Algorithm Based on Frequency, and have the advantages that calculating speed is fast.

Description

A kind of equalization filtering deconvolution data reconstruction method

Technical field

The invention belongs to data processing field, in particular to a kind of deconvolution data reconstruction method.

Background technique

Convolution is a kind of common calculating of Data processing.In engineering, it features the defeated of a linear time invariant system Enter the relationship between output signal.It is cause fogging image important such as the nonindependence characteristic of optical detection element Reason.Convolution algorithm is also widely used for finite dimension signal processing, such as noise is eliminated.Its inverse problem deconvolution becomes research A hot spot, be a kind of important data reconstruction method, apply in fields such as astronomy, optics, medicine, realize and counter drops clear, height Resolution ratio and other effects.

Inverse problem is usually an ill-conditioning problem, i.e., small variation can cause the substantially deviation of solution.Deconvolution calculates Precision and convolution kernel, the noise profile and Deconvolution Algorithm Based on Frequency of data it is closely related.Convolution kernel is divided to two classes, normality convolution kernel and disease State convolution kernel.By discrete Fourier transform, the closer the frequency spectrum of convolution kernel the more ill from zero point；It is indicated by the matrix of convolution, The bigger the conditional number that convolution kernel represents matrix the more ill；By functional, the characteristic value of convolution operator the more goes to zero the more ill.Warp The noise that product calculates has convolution kernel noise, original signal noise and the cumulative noise of convolution process etc..Deconvolution is in frequency domain and sky Between domain be expressed as division and the inverse of a matrix operation of frequency spectrum.The method for solving deconvolution ill-conditioning problem has regular Operator Method, Total least square method, Algebraic Iterative Method, calculus of variations etc..These methods use quantic, computationally intensive.

Based on this, the present invention proposes a kind of accurate deconvolution data reconstruction method based on Fast Fourier Transform (FFT).

Summary of the invention

For the ill-conditioning problem that deconvolution calculates, the present invention proposes a kind of equalization filtering deconvolution calculation method, including with Lower step:

Convolution kernel b and convolved data c are filtered, B and C are updated to, wherein b and c is N-dimensional discrete data, and N is One natural number, meeting c=(a+d1) * (b+d2)+d3, a is initial data, and d1 is raw data, and d2 is that convolution kernel is made an uproar Sound, d3 are the noises of convolution algorithm；

The Fourier spectrum FC and FB for calculating convolved data C and convolution kernel B, are divided by obtain frequency spectrum quotient FA=FC./FB, frequency Compose the quotient that quotient FA is frequency spectrum FC and the FB frequency spectrum in corresponding frequencies；

The inverse Fourier transform of FA is calculated, deconvolution result A, the approximate solution as initial data a are exported.

It is described in one of the embodiments, that convolution kernel b and convolved data c are filtered, it is updated to B and C, including Following steps:

Convolved data c plus noise obtains c1=c+dc, and dc indicates the noise added when convolutional calculation；

Convolution kernel b plus noise obtains b1=b+db, and db indicates the noise of convolution kernel addition；

Select N-dimensional discrete filter F appropriate；

Convolved data c1 and convolution kernel b1 are done into convolution with F respectively, the convolved data C=c1*F and convolution kernel updated B=b1*F.

The convolved data c plus noise obtains c1=c+dc in one of the embodiments, when dc indicates convolutional calculation The noise of addition, wherein the noise dc of addition is selected as zero or white noise, and the norm of amplitude and original signal noise d1 are directly proportional.

The convolution kernel b plus noise obtains b1=b+db in one of the embodiments, and db indicates convolution kernel addition Noise, wherein the noise db of addition is selected as zero or white noise, and the norm of amplitude and b are directly proportional.

Selection filter F appropriate in one of the embodiments, wherein F is according to the property settings of convolution kernel b1 For the filter functions such as Hamming or Blacknam, or adaptive determination.

The convolved data c1 and convolution kernel b1 do convolution with F respectively in one of the embodiments, are updated Convolved data C=c1*F and convolution kernel B=b1*F, wherein make B and C have identical length by zero padding and do certain extension.

Above-described deconvolution data reconstruction method is suitable for limited dimension data, by suitably adding noise and right The equalization filtering of convolution kernel is handled, and effectively inhibits the Deconvolution Algorithm Based on Frequency error based on discrete Fourier transform；Under specific circumstances, The noise of initial data can also effectively be inhibited.The spy that this equalization filtering deconvolution data processing method has calculating speed fast Point.

Detailed description of the invention

For a better understanding of the present invention, it is described further with reference to the accompanying drawing.

Fig. 1 is the flow chart of equalization filtering deconvolution calculation method of the invention.

Fig. 2 is the flow chart of step S100 in Fig. 1.

Fig. 3 is the direct deconvolution of one-dimensional zero noise convolution kernel of one embodiment, Blacknam filtering algorithm and adaptive The comparison of filtering algorithm precision.

Fig. 4 is a width noisy image.

Fig. 5 is image obtained by the average convolution of image in Fig. 4.

Fig. 6 is image obtained by the direct deconvolution of image in Fig. 5.

Fig. 7 is image obtained by the Blacknam equalization filtering deconvolution of image in Fig. 6.

Fig. 8 is that the adaptive equalization of image in Fig. 7 filters image obtained by deconvolution.

Specific embodiment

The convolution algorithm of signal corresponds to it and calculates in the product of frequency domain, the direct Deconvolution Algorithm Based on Frequency based on Fourier transformation It can be because the morbid state of inverse operation generates biggish error.

Referring to attached drawing 1, the present invention provides a kind of quick equalization filtering deconvolution calculation methods, comprising the following steps:

S100: convolution kernel b and convolved data c are filtered, B and C are updated to, wherein b and c is N-dimensional dispersion number According to N is a natural number, and meeting c=(a+d1) * (b+d2)+d3, a is initial data, and d1 is raw data, and d2 is convolution Core noise, d3 are the noises of convolution algorithm；

S200: calculating the Fourier spectrum FC and FB of convolved data C and convolution kernel B, be divided by obtain frequency spectrum quotient FA=FC./ FB, frequency spectrum quotient FA are the quotient of frequency spectrum FC and the FB frequency spectrum in corresponding frequencies；

S300: calculating the inverse Fourier transform of FA, exports deconvolution result A, the approximate solution as initial data a.

Above-mentioned steps S200 and S300 are combined into direct Deconvolution Algorithm Based on Frequency, to special convolution kernel, can reach good data Recovery effect；But the ill-conditioning problem of deconvolution can not be handled.

Step S100 optimizes convolution kernel processing by equalization filtering, reduces and calculates error.Step S200, the calculating C and B Fourier spectrum, make B and C have identical length by zero padding and do certain extension.The extension of data B and C are that processing is non- Recycle a kind of method of de-convolution operation.

Referring to attached drawing 2, convolution kernel b and convolved data c is filtered in above-mentioned steps S100, obtains B and C, including with Lower step:

S110: convolved data c plus noise obtains c1=c+dc, and dc indicates the noise added when convolutional calculation；

S120: convolution kernel b plus noise obtains b1=b+db, and db indicates the noise of convolution kernel addition；

S130: N-dimensional discrete filter F appropriate is selected；

S140: doing convolution with F respectively for convolved data c1 and convolution kernel b1, the convolved data C=c1*F updated and Convolution kernel B=b1*F.

Convolved data c plus noise described in step S110 obtains c1=c+dc, and dc indicates the noise added when convolutional calculation, The noise dc of addition is selected as zero or white noise, and the norm of amplitude and raw data d1 are directly proportional.

Convolution kernel b plus noise described in step S120 obtains b1=b+db, and db indicates the noise of convolution kernel addition, addition Noise db is selected as zero or white noise, and the norm of amplitude and b are directly proportional.

Selection filter F appropriate described in step S130, F are Hamming or Bu Laike according to the property settings of convolution kernel b1 Graceful equal filter functions, or it is adaptive determining.

The effect of filtering is regular convolution kernel, makes its normalization.The filter functions such as Hamming or Blacknam pass through at frequency spectrum Reason achievees the purpose that regular convolution kernel.The selection of filter function relies on the frequency spectrum of convolution kernel.Sef-adapting filter is according to convolution kernel The frequency spectrum of b1 determines that the spectral magnitude of such as balanced convolution kernel achievees the purpose that regular convolution kernel.The error that deconvolution calculates is very The characteristic of convolution kernel is depended in big degree, can also be optimized convolution kernel by smoothing processing, be reduced error.Convolved data and volume Product core filtering processing in noise be properly added there are two effect, one is to aid in regular convolution kernel, second is that reduce direct computation of DFT The error that leaf deconvolution calculates.

Fig. 3 shows that under identical signal-to-noise ratio, one-dimensional random convolution signal filters warp in direct deconvolution, Blacknam The distribution map for the maximum error percentage that data under long-pending and three kinds of algorithms of adaptive-filtering deconvolution are restored.Error rate distribution Mean value and maximum value all show that equalization filtering deconvolution is better than direct Deconvolution Method.

Fig. 4 is a width noisy image, and Fig. 5 is that the approximation of Fig. 4 is averaged convolution results.Fig. 6 is the direct deconvolution figure of Fig. 5 Picture, very big absolute error are 0.97.Fig. 7 is the Blacknam filtering deconvolution image of Fig. 5, and very big absolute error is 0.54.Fig. 8 It is the adaptive-filtering deconvolution image of Fig. 5, very big absolute error is 0.51.This example illustrates that filtering Deconvolution Algorithm Based on Frequency is better than Direct Deconvolution Method.

Finally, it should be noted that obviously, the above embodiment is merely an example for clearly illustrating the present invention, and It does not limit the embodiments.It for those of ordinary skill in the art, on the basis of the above description can be with It makes other variations or changes in different ways.There is no necessity and possibility to exhaust all the enbodiments.And thus institute The obvious changes or variations amplified out are still in the protection scope of this invention.

Claims (1)

1. a kind of equalization filtering deconvolution data reconstruction method, comprising the following steps:

Convolution kernel b and convolved data c are filtered, are updated to B=F* (b+db) and C=F* (c+dc), wherein b is N-dimensional Discrete convolution Nuclear Data, c are the N-dimensional signal datas obtained on application apparatus, and N is a natural number, meet c=(a+d1) * (b+ D2)+d3, a are initial data, and d1 is raw data, and d2 is convolution kernel noise, and d3 is the noise of convolution algorithm, and F is appropriate The N-dimensional discrete filter of selection, db and dc are the amplitude and signal b of selection addition, and the norm of c distinguishes directly proportional white noise letter Number；

The Fourier spectrum FC and FB for calculating convolved data C and convolution kernel B, are divided by obtain frequency spectrum quotient FA=FC./FB, frequency spectrum quotient FA is the quotient of frequency spectrum FC and the FB frequency spectrum in corresponding frequencies；

The inverse Fourier transform of FA is calculated, deconvolution result A, the approximate solution as initial data a are exported.