CN109685728B

CN109685728B - Digital image processing method based on local time-frequency domain transformation

Info

Publication number: CN109685728B
Application number: CN201811453794.1A
Authority: CN
Inventors: 谢振华
Original assignee: Central South University
Current assignee: Central South University
Priority date: 2018-11-30
Filing date: 2018-11-30
Publication date: 2023-01-31
Anticipated expiration: 2038-11-30
Also published as: CN109685728A

Abstract

The invention relates to a digital image processing method based on local time-frequency domain transformation, which comprises the following steps: acquiring a low-pass filter and a high-pass filter of a digital image by adopting a discrete wavelet analysis method; filtering the to-be-processed noise-containing digital image signal through a low-pass filter and a high-pass filter to obtain a de-noised digital image signal; and performing secondary denoising processing on the processed digital image signal by adopting a soft and hard wavelet threshold value. The invention adopts a mode of combining mixed nonlinear smooth filtering and single threshold wavelet filtering to solve the denoising problem of mixed Gaussian and pulse noise images.

Description

Digital image processing method based on local time-frequency domain transformation

Technical Field

The invention belongs to the technical field of image and signal processing, and particularly relates to a digital image processing method based on local time-frequency domain transformation.

Background

Due to the rapid development of current big data, cloud sharing and the situation of the internet of things, higher requirements are put on technologies such as information integration, software development and application, multimedia image processing and the like, the capture position of people for useful information (pictures and coded videos with different formats) is increasingly prominent in actual life, and generally, due to the fact that the images are collected to the transmission stage, due to the fact that the image capture environment or electronic component equipment and the like, the images are often doped with a plurality of high-frequency signals such as noise, dirt and the like, and therefore the picture quality and the overall visual perception effect are reduced; so that the receiving end user may make a misjudgment about such an "unreal image". Therefore, the patent aims at carrying out algorithm optimization expansion analysis such as early-stage denoising, signal enhancement, compression and the like on images containing noise, and provides early-stage basis for subsequent image segmentation and image restoration, thereby achieving the best satisfaction effect of users.

The characteristics of the digital image transmission process (image edge texture, peak and high and low frequency signal distribution) are different, which often interfere with the original information of the image, so that the useful information in the image is "buried" or "hidden". For a traditional denoising algorithm, although the mean filtering can effectively remove noise in a noise image, the quality is improved, and meanwhile, some special details in the image are removed, so that the image becomes chaotic; nonlinear smoothing filtering is often used in the aspect of impulse noise, and once the interference degree is slightly large, the filtering effect is not significant, and also the image fine nodes are lost, and the image quality is reduced. Both of the above-mentioned filters are slightly missing in the detail eigenprocessing.

Currently, the time-frequency domain-wavelet transform becomes one of the popular directions and fields of engineering subject research; also causes unprecedented bombing in the areas of computational mathematics and calculus. The method is used as a branch subject of the mathematical discipline and covers various aspects such as topological linear mapping, fourier She Diaohe analysis, curved surface line structure, difference quotient numerical theory and the like; the method is particularly applied to the fields of digital signal extraction, image textural feature recognition, ontology semantic mapping, machine intelligent vision and nonlinear diagnosis and calculation. The energy signal function is subjected to space and frequency local transformation on the basis of Fourier analysis, specifically translation and expansion, and the multi-scale thinning problem in the image or the voice can be objectively and really extracted and dispatched; the problem that the traditional Fourier function cannot solve at a microscopic angle is solved. Moreover, the time window function can be subdivided by a low frequency transformation; the high frequency presents the transient processes of the function changing along with the time one by one, namely, the signal transmission process removes noise pollution and fine impurity suspended particles, and any detail change can be accurately mastered in real time; wavelet analysis is of absolute advantage especially in processing non-stationary signal applications.

However, for non-stationary image transmission in practical application, the multi-resolution feature processing is single and not flexible enough. In the aspect of digital signal extraction, the algorithm can well reflect the whole image frequency domain information, but cannot objectively extract local time domain signals related to frequency and cannot comprehensively highlight the comprehensive characteristics of both the time domain and the frequency domain. For non-stationary image transmission in practical applications, the overall time function distribution must be considered, because the small variation of the signal in the time domain in the energy function must affect the spectrum variation trend of the signal in the whole windowing function. In addressing this problem, we originally proposed a short-time windowed Fourier transform, which aims to overcome the shortcomings of the conventional Fourier transform on the local time domain transform, and can slice the time function in the signal into several time intervals, thereby locking the frequencies corresponding to the intervals. However, once the windowing function is determined, the frequency domain window distribution is fixed, which causes inconvenience in stretching or stretching the window, and makes it increasingly difficult to change the resolution characteristics of the image, and the windowing independent variable and the windowing dependent variable must be selected again.

Therefore, it is necessary to provide a digital image processing method based on local time-frequency domain transformation.

Disclosure of Invention

Object of the invention

The invention provides a digital image processing method based on local time-frequency domain transformation, which can combine wavelet and filter to create certain superior condition for wavelet analysis and rapid extraction of discrete signals.

(II) technical scheme

In order to achieve the above object, the present invention provides a digital image processing method based on local time-frequency domain transformation, comprising:

s1, acquiring a digital image time-frequency domain filter by adopting a discrete wavelet analysis method;

s2, filtering the to-be-processed noise-containing digital image signal through a time-frequency domain filter to obtain a de-noised digital image signal;

and S3, performing secondary denoising treatment on the processed digital image signal by adopting a soft and hard wavelet threshold value.

The time-frequency domain filter comprises a low-pass filter h (omega) and a high-pass filter g (omega), and satisfies the following conditions:

|h(ω)| ² +|h(ω+2nπ)| ² ＝|g(ω)| ² +|g(ω+2nπ)| ² ＝2，

h(ω)g ^* (ω)+h(ω+2nπ)h ^* (ω+2nπ)＝0；

n belongs to Z, Z is the set of whole integers, h ^* (ω) is the conjugate function of h (ω), g ^* And (omega) is the conjugate function of g (omega).

The step S1 includes:

s1a, performing Hilbert transformation on a high-frequency signal part of an initial energy signal function F (t) to enable a function space L ² (R) is the square multiplicative of the Hilbert envelope function, for

Defining a continuous wavelet transform function; wherein R is the set of all real numbers;

s1b, performing discrete transformation on a continuous wavelet function based on discrete wavelet analysis to obtain a discrete dyadic wavelet transformation function;

and S1c, performing multi-resolution analysis on the obtained wavelet transformation function to obtain filtering parameters of a low-pass filter and a high-pass filter.

The step S3 includes:

s3a, carrying out gray level processing on the noise-containing digital image signal to be processed to obtain a gray level image;

s3b, selecting a threshold value for the gray level image to obtain a plurality of gray level images;

s3c, performing binary image processing and analysis on the gray level image to obtain a binary gray level image;

and S3d, extracting a low-frequency signal from the binary gray image by adopting a soft and hard threshold value, and then obtaining a real image signal by adopting a threshold value segmentation method.

The step S3d of extracting the low-frequency signal from the binarized grayscale image by using soft and hard thresholds includes:

and after the high-frequency signals in the binary gray-scale image are removed by adopting a hard threshold, extracting the low-frequency signals by adopting a soft threshold.

Optionally, before the step S3, at least one of the following steps is further included:

s30a, performing smooth filtering processing on the processed image signal;

s30b, compressing the processed image signal by adopting a wavelet transform method;

and S30c, performing image enhancement processing on the processed image signal by adopting wavelet transform of a frequency domain method.

The step S3b includes:

s3b1, decomposing the processed low-frequency signal and the processed high-frequency signal of the image signal to obtain an image signal slice;

s3b2, decomposing the image signal slice into a plurality of resolution grade sequences again after wavelet transformation;

s3b3, after the correlation of the minimum composition units in the resolution grade sequence is removed, a coding band transformation coefficient is obtained;

s3b4, quantizing the coding band transform coefficient matrix to obtain a compressed code stream, and adding a special identification symbol for repairing coding errors in the compressed code stream;

and S3b5, storing a segment header message for identifying the resolution grade sequence in front of the generated compressed code stream.

And the step S3a comprises the step of carrying out smooth filtering processing on the processed image signal by adopting a mean filtering method or a median filtering method.

And the step S3c comprises the steps of firstly carrying out Fourier transform on the processed image in the frequency domain, then carrying out digital filtering restoration on the frequency spectrum of the image, and finally carrying out inverse Fourier transform on the corrected image.

(III) advantageous effects

The invention has the beneficial effects that: the invention adopts a mode of combining mixed nonlinear smooth filtering and single threshold wavelet filtering to solve the denoising problem of mixed Gaussian and pulse noise images, and has certain practical significance on resolution analysis and detail feature extraction of the images.

Drawings

FIG. 1 is a flow chart of a digital image processing method based on local time-frequency domain transformation according to an embodiment of the present invention;

FIG. 2 is a graph of a spectrum after Hilbert transform of an initial function according to an embodiment of the present invention;

fig. 3 is a schematic diagram of the Hilbert transform envelope boosting effect according to an embodiment of the present invention;

fig. 4 is a schematic diagram of Hilbert transform envelope extraction and signal modulation according to an embodiment of the present invention;

FIG. 5 is a diagram illustrating the overall effect of the Hilbert transform arbitrary envelope image according to the embodiment of the present invention;

FIG. 6 is a schematic diagram of the effect before and after the gray level processing in the noise reduction processing according to the embodiment of the present invention;

FIG. 7 is a diagram illustrating a relationship between an initial position threshold and a signal in a denoising process according to an embodiment of the present invention;

FIG. 8 is a diagram illustrating a relationship between a threshold value of a terminal position and a signal in a denoising process according to an embodiment of the present invention;

FIG. 9 is a schematic diagram illustrating comparison of pre-and post-processing effects of binary signal processing in denoising processing according to an embodiment of the present invention;

FIG. 10 is a diagram illustrating comparison of pre-and post-denoising effects according to an embodiment of the present invention;

FIG. 11 is a diagram illustrating the relationship between signals before denoising and frequency domain according to an embodiment of the present invention;

FIG. 12 is a diagram illustrating the relationship between the denoised signal and the frequency domain according to the embodiment of the present invention;

FIG. 13 is a schematic diagram of a wavelet transform according to an embodiment of the present invention;

FIG. 14 is a diagram illustrating comparison between the pre-and post-wavelet transformation effects according to an embodiment of the present invention;

FIG. 15 is a diagram illustrating wavelet transform initial energy low-high frequency decomposition according to an embodiment of the present invention;

FIG. 16 is a diagram illustrating the relationship between the first compression size and the byte in the wavelet transform according to the embodiment of the present invention;

FIG. 17 is a diagram illustrating the relationship between the second compression size and the byte in the wavelet transform according to an embodiment of the present invention;

FIG. 18 is a schematic diagram illustrating comparison between the effects of a noisy image and a smoothed image according to an embodiment of the present invention;

FIG. 19 is a schematic diagram of a relationship between a time domain and a frequency domain of a noisy image before image smoothing according to an embodiment of the present invention;

FIG. 20 is a diagram illustrating a relationship between a time domain and a frequency domain after image smoothing according to an embodiment of the present invention;

FIG. 21 is a flowchart of a method for enhancing an image based on a frequency domain model according to the present invention;

FIG. 22 is a graph illustrating the comparison between the pre-image enhancement effect and the post-image enhancement effect according to an embodiment of the present invention;

FIG. 23 is a diagram illustrating the distribution of low frequency signals before image enhancement according to an embodiment of the present invention;

FIG. 24 is a diagram illustrating the distribution of the low-frequency signals after image enhancement according to an embodiment of the present invention.

Detailed Description

For a better understanding of the present invention, reference will now be made in detail to the present invention by way of specific embodiments thereof.

In the filtering process of the image signal, the signal initial energy function can be generally made into a complex and disturbed variable wave, however, the complex clutter is formed by laminating a plurality of sine waves with different phases, different amplitudes and different frequencies. The original Fourier algorithm is characterized in that the time and frequency relations of corresponding waves can be closely connected, and a spectrum with clear waveforms is adopted to analyze fuzzy nodes or scattered cakes in a corresponding time frequency range; but fourier algorithms are poor for localized time-frequency property analysis. If a receiving end of the method wants to obtain a signal point and a signal slice (very accurate signal) of a certain time point or a section where an image is located, meanwhile, the signals of the time frequency domain generally have redundancy or have the phenomenon of code disorder and the like, and the original Fourier algorithm can only process and analyze the signals of the whole time frequency domain. Therefore, the wavelet analysis has higher and more accurate analysis degree on the small-area image characteristics in the time domain and the frequency domain, and has stronger self-adaptability; therefore, wavelet analysis not only can meet the pulse sequence coding and electromagnetic effect of time-frequency domain signals, but also can be used for capturing and collecting various distortion and mutation characteristics which appear under any time node and any frequency condition in a sensitive manner.

The wavelet transform filtering can be approximately regarded as a low-pass filter, and compared with the traditional filtering, the low-pass filter can keep fine scales and texture intrinsic features in original signals especially in mixed Gaussian noise; meanwhile, the wavelet transform can be adjusted along with different signal waveforms in a local time-frequency domain window, and correlation characteristic signals between adjacent scales can be well maintained; in other words, the local information can be embodied completely; the concrete expression is as follows: (1) A stationary signal, which may take the form of a large time window to increase frequency domain resolution; (2) Non-stationary signals, as well as low frequency domain resolution, can be used to find precise time locations. Therefore, the method can solve the problem of image denoising of Gaussian mixture and pulse noise by adopting a mode of combining mixed nonlinear smooth filtering and single threshold wavelet filtering, and has certain practical significance on resolution analysis and detail feature extraction of the image. For non-stationary signals, the method adopts wavelet transformation and digital image processing based on local time-frequency domain transformation.

Several concepts of wavelet transforms are given below.

Assuming the initial energy signal function as f (x), the embodiment is set from the initial energy signal function f (x) epsilon L ² (R) starting with, bindingThe wavelet transform can highlight local time-frequency domain texture detail characteristics aiming at a non-stationary signal image; definition of

And is

Wavelet function

Fourier transform of

Satisfies the following conditions:

then

For a basic wavelet function or mother wavelet function, the mother wavelet function

After the stretching and the translation, the material is obtained,

a, b belongs to R; a ≠ 0,R is a real number.

For wavelet functions, a is the stretch or compression factor and b is the translation factor.

Performing stretching and translation mathematical modeling analysis on the signal sequence; the main characteristics are that:

(1) A stationary signal, which may take the form of a large time window to increase frequency domain resolution; (2) Non-stationary signals, as well as low frequency domain resolution, can be used to find precise time locations. Therefore, the method further promotes the image processing to have certain application value in the extraction and development of the local features of the time-frequency domain.

For an arbitrary function f (x) e L ² Continuous wavelet transform W of (R) _f (a, b) are:

for the same signal, the time domain and the frequency domain of any complete orthogonal set function follow the general law of energy conservation:

for a function g (x) of noisy, dirty high frequency signals,

for any x ∈ [ - π, π]So that the function f (x) can be integrated, f (x) epsilon R ² (x)；g(x)∈R ² (x) Is true. Therefore, the value of the wavelet transform function corresponding to the mother wavelet in the interval range is also a constant value; the discrete transform form of the wavelet function is changed, and can be expressed as follows:

the existence of an inverse recursion formula of f (x) is shown, and the signal loss in the processes of compressing, enhancing, filtering, denoising and the like of the signal during the local signal transformation of the time-frequency domain is almost 0; wherein R is ^* ≠0∪R ^* E is R; r is the set of all real numbers.

The present embodiment provides a digital image processing method based on local time-frequency domain transform, as shown in fig. 1, specifically, including the following steps:

s1, a time-frequency domain filter is obtained by adopting a discrete wavelet analysis method.

Wherein, the time-frequency domain filter includes a low-pass filter h (ω) and a high-pass filter g (ω), and satisfies:

|h(ω)| ² +|h(ω+2nπ)| ² ＝|g(ω)| ² +|g(ω+2nπ)| ² ＝2，

h(ω)g ^* (ω)+h(ω+2nπ)h ^* (ω+2nπ)＝0；

Specifically, the method comprises the following steps:

s1a, performing Hilbert transformation on a high-frequency signal part of an initial energy signal function F (t) to enable a function space L ² (R) is the square-multiplicative of the Hilbert envelope function, for

Defining a continuous wavelet transform function; where R is the set of all real numbers.

Let L ² (R) is the square-multiplicative product of the Hilbert envelope function and has

Therefore:

as shown in fig. 2, in Hilbert transform, the phase and convolution properties make the narrow-band filtering of fourier transform more prominent, and it is also a data processing method often used for envelope analysis, first, sin signal is changed into cos signal through H transform in Hilbert, then the obtained signal is Hilbert transformed into complex signal twice, and the negative signal is solved; and ensuring that the frequency spectrum of the composite signal of Hilbert transform is smaller than the Neisser frequency spectrum, and finally enabling the obtained composite signal to be orthogonal to the original signal. Through Hilbert transform, noisy dust particles are removed, but key texture intrinsic is preserved.

Then there is a function F (x), and the inner product of G (x) can be expressed as:

g (x) refers to a function of a noisy, dirty high-frequency signal.

At the same time, the function F (x) is epsilon L ² The Fourier transform of (R) can be set as:

fourier transform for function G (x)

For functions F (x), G (x) and

all satisfy Parseval identity:

therefore, in the center frequency narrowband signal analysis, the Hilbert transform is performed on the high frequency signal portion of the initial function F (x), G (x).

In Hilbert envelope analysis, the frequency is set to 20Hz, the waveform of the envelope signal is an absolute value signal of a cosine signal, and the absolute value is taken when the envelope is calculated, so that the signal frequency is doubled. The envelope is lifted away from 0 as shown in fig. 3.

Referring to fig. 4, it can be seen that Hilbert envelope analysis can effectively extract the envelope and modulated signal frequencies, with the same effect as detection. For an envelope of arbitrary shape, as shown in fig. 5, it can be seen that the overall effect is good, except for errors at the edges.

For the wavelet transform function: can be defined as f (x) epsilon L ² (x)，

If corresponding FourierConditional function of inner leaf transformation

Satisfies the following conditions:

then

Is a basic wavelet function. A basic wavelet function

The material is obtained through expansion and contraction and translation,

For an arbitrary function f (x) e L ² Continuous wavelet transform CT of (R) _f (a, b) are:

a is not equal to 0, b and x are continuous variable coefficients,

are conjugated; using fourier transform, we know: the coefficient of expansion a is the same as the coefficient of expansion a,

therefore, the smaller the a is, the smaller,

spectral function approaching peak, time domain function

Continuously compressing the waveform; on the contrary, the larger the a is,

spread of waveform, spectral function

Approaching to the trough; thus, a function

When x ≈ 0, the waveform shows a significant change, and the waveform gradually decreases and changes more significantly as the distance from the origin is increased. At the same time, for any parameter (a, b), the basic wavelet function will again show a significant variation at the x = b position, of course as the time-frequency domain increases, the function continues to decrease until it reaches the point where the time-frequency domain increases

Continuous wavelet transform CT _f The inverse transform of (a, b):

where f (t) is the continuous wavelet function after inverse transformation, CT _f Is a mother wavelet transform

The continuous wavelet function has the following properties:

the initial signal energy function is f (x), if the wavelet transform of f (x) is FT _a,b 。

The locality is as follows: the initial signal energy function is f (x), and a corresponding function value can be taken at the periphery of x =0, wherein f (x) =0 cannot be taken; therefore, in the time-frequency domain, a real number function or a complex number function can be used as a mother wavelet of the wavelet function, so that the time-frequency domain has locality.

Decomposability: the mother wavelet functional transform can be equated with the factorial composition of the two decompositions and summed and superimposed, then at this point, f (x) = f (x) ₁ )+f(x ₂ ) (ii) a Continuous wavelets, one function can be decomposed into two functions, represented as:

time shift invariance: if the wavelet transform of f (x) is FT _a,b (ii) a The wavelet transform of f (x-t) is FT _a,b-t (ii) a The relationship between the two can be expressed as:

fluctuation: it can be known that

The wavelet function exists in the wave alternation characteristic, and the wave alternation KT of the wavelet function _f (a, b) are:

in practical application, the continuous wavelet function transform has large redundancy, so KT _f The modulus maxima of the (a, b) function may be represented using MALLAT iterative signal reconstruction.

in the actual communication process, the signals are generally distributed in the form of discrete signals; therefore, the continuous wavelet must be discretized, and if the discretization of the continuous wavelet into wavelets needs to satisfy the following conditions, this section will focus on the detailed discussion and explanation of the problem.

For a dyadic wavelet, it is understood to be a semi-discrete wavelet transform, i.e. a discrete transform is applied to the scale coefficients, so that the displacement factor is continuously transformed.

For the continuous wavelet function:

A＝2 ^j ,j∈Z，

a is an image scale index function, Z is an integer or a focusing multiple

The dyadic wavelet function is:

for f (x) = L ² (R) corresponds to a dyadic wavelet transform function of

Wherein, j is a scale factor,

is a discrete transform function. The scale factor j is inversely proportional to the focusing multiple of the image, namely the smaller j is, the more detailed observation can be carried out on the local signal of the image; on the contrary, if the overall signal distribution of the image is adopted, the value of j can be increased; therefore, the value j is important for image signal analysis in the case of a dyadic wavelet.

Fourier transform function of

The requirements are as follows:

for the

Wherein G is ₁ ，G ₂ The finger receives the maximum index value with the minimum noise and dirt.

Is a sufficient condition to ensure that the wavelet function becomes a dyadic wavelet.

For discretized wavelet transform coefficients

If it is

Then the process of the first step is carried out,

at this time

The reconstruction formula of (c) can be expressed as:

wherein the content of the first and second substances,

is that

A reconstruction function is then

It should be noted that, in the above formula,

is a stable value, corresponding to a Fourier transform function

May not be constant when

In the case of a binary wavelet, the wavelet is,

neither a dyadic wavelet nor possibly a wavelet.

S1c, wavelet transformation function obtained

And performing multi-resolution analysis to obtain filter parameters of a low-pass filter h (omega) and a high-pass filter g (omega).

The multi-resolution analysis refers to a general term for revealing the overall condition and the process development essence of a thing; when the distance between the target source and the perceived visual field is large, all landscapes of a certain image in the visual field range can be truly, objectively and fairly reflected, and the prominent characteristics of the landscape are represented as large size in an area, full information content, fuzzy images, loose dot matrix in the area, only approximate panorama of a locked target can be achieved, and the detail fragmentary information of the individual target is not grasped carefully; on the contrary, the target range of the image area is smaller, the scale is finer, the pixels of the image are higher, the dot matrix is denser, the image essential features and the individual features can be finely embodied, but the image global features are difficult to grasp.

If the overall characteristics and the local details of the image are well mastered, different distances can be adopted to carefully observe the target object, and the specific details and the motion characteristics of the image can also have different changes and results due to different selection standards in the process; thus, a difference numerical approach can be used to observe dynamic changes between local and global. It should be noted that, because the development characteristics of objects at various stages are different, and the dimensions of the objects are different, it is also important to apply different numerical methods, and it is important to apply applicable qualitative numerical methods to specific objects.

According to the approximate characteristic property of the multiresolution characteristic, the initial energy signal function f (x) epsilon L must be ensured ² (R) closed subspace V _j The following requirements are met:

monotonicity:

complete progression:

the flexibility is as follows:

the translation is unchanged:

riesz group: if there is a function f (x) e V ₀ Riesz base that can constitute { f (x-i), i ∈ Z }, then for a unique sequence set a with respect to the Riesz base sequence set _k Comprises the following steps:

it V _j The set of spatial orthonormal vectors can be expressed as:

at the same time V _j Is comprised of

There will be a double scale equation:

wherein { h (i), i ∈ Z } ∈ L ² Is a scale series.

Definition V _j At V _j-1 Spatial quadrature compensation of W _j ,j∈Z,

Is recorded as:

then the subspace sequence W is orthogonally complemented _j J ∈ Z } is L ² (R)：

Wavelet function

Scale function of

Comprises the following steps:

if get

Then the

For wavelet transform functions

Comprises the following steps:

then f (x) is a fully asymptotic discrete function at a resolution of j and f (x) is at V _j The relationship between the target projections of (a) can be expressed as:

f (x) is in W, which is the local feature of j in resolution _j The orthogonal complement space projection of (a) is:

wherein the content of the first and second substances,

respectively f (x) at V _j 、W _j Is projected.

Order:

the discrete wavelet transform of the finite energy signal function f (x) is:

according to wavelet function

And scale function

The characteristics of the two can be expressed by a two-dimensional equation V _j 、W _j Respectively corresponding inner product diagonal matrices (orthonormal basis) are

Because of the scale function in the dual scale equation:

by V _j Basis function of j = -1

And (3) expanding terms in the dual-scale equation by series, and enabling h to be an expansion factor, so that the scale function is expressed as:

secondly, in terms of the wavelet function dual scale equation: v _-1 -V ₀ ＝W ₀ Wherein W is ₀ Is a double scale factor. In a clear view of the above, it is known that,

in other words

Available V _j Orthogonal basis of j = -1

And (3) expanding the series, and taking g as an expansion factor, the scale function is expressed as:

the first formula and the second formula are both scale functions and wavelet functionsA multiresolution analytical expression of numbers; expansion factors h and g in the equation are independent of j; and j is adjacent to any two

(ii) related; the filter parameters h (ω), g (ω) are:

continuous signal

Fourier transform;

h (omega), g (omega) are Fourier transforms of discrete signals h (x), g (x).

Therefore, h (ω) and g (ω) are parameters of the filter set, and the filter set coefficients have the following properties:

the filter coefficients of the two functions are summed to a constant value:

summing the initial values of the frequency domain to a constant value:

wherein h (ω) & gtdoes not pass through _ω＝0 、g(ω)| _ω＝0 Respectively low and high pass filter parametersAnd (4) counting.

And (3) recurrence property:

low-pass, high-pass filter specific requirements:

|h(ω)| ² +|h(ω+2nπ)| ² ＝|g(ω)| ² +|g(ω+2nπ)| ² ＝2

h(ω)g ^* (ω)+h(ω+2nπ)h ^* (ω+2nπ)＝0

and S2, filtering the to-be-processed noise-containing digital image signal through a low-pass filter and a high-pass filter to obtain a de-noised digital image signal.

The above characteristics are considered by combining the wavelet and the filter, which creates certain superior conditions for wavelet analysis and rapid extraction of discrete signals.

Based on the low-pass filter and the high-pass filter obtained in step S1, the denoised digital image signal may be obtained by filtering the noisy digital image signal to be processed through the low-pass filter and the high-pass filter.

The frequency domain where the signal function is distributed is obviously different from a signal area containing impurity noise, and certain particle suspension, image spikes, textures and edge features often exist in a high-frequency area; the useful signal distribution exists in a low-frequency area, the important features of the image cannot be lost only by properly processing the intersection area of the signal and the noise when the image is filtered, and the area category cannot be zoomed too small or expanded too much; therefore, how to better maintain some specific detail features of the image and to maximally eliminate noise becomes the focus of the image denoising header in image processing.

In the hard threshold, because the retained wavelet coefficient is large, a small factor removed in the method is set to be 0, and a large variance generally occurs, so that the position of a key node has large amplitude fluctuation. But also makes the function discontinuous at a suitable threshold gamma and does not result in a signal sample that is consistent with the original image. And (4) compared with a soft threshold, directly deleting the smaller wavelet parameters, and performing retraction processing on the reserved larger wavelet coefficients. In this process, wavelet coefficients larger than the threshold value gamma are also caused to have large errors when retracting, so that the denoised signal is generally made to be more smooth, but certain features in the image signal are more or less lost. Therefore, when the wavelet threshold is adopted to process the image problem, the soft and hard threshold combining method is used for improving the lifting.

Let the initial image be { f [ x, y ]: x, y =1,2

{g[x,y]:x,y＝1,2......N}

Meanwhile, let the noise interference value be { epsilon [ x, y ]: x, y =1,2.

{g[x,y]＝f[x,y]+ε[x,y]:x,y＝1,2......N}

Wherein, { ε [ x, y]N and { f [ x, y =1,2]X, y =1,2.. N } are independent of each other, and the final goal of denoising is to be from { g [ x, y ]]X, y =1,2]X, y =1,2

The error between the two is η, then:

after orthogonal transformation, the following can be obtained:

Y[x,y]＝X[x,y]+V[x,y]:x,y＝1,2......N

Y[x,y]as a noise-containing wavelet factor, X [ X, y ]]Is a noiseless wavelet factor, vx, y]Is a noise component and is distributed over N (0, σ) ² _n ) The above. Can be derived from a noisy wavelet factor Y x, Y]The wavelet factor of the signal is obtained, so that the noise wavelet factor is eliminated.

Specifically, the method comprises the following steps:

the signal energy is concentrated in a low frequency domain, namely the wavelet factor value is larger at the moment; and the noise is concentrated in a high frequency domain, and the wavelet coefficient is smaller in amplitude at the moment. Firstly, the original image is subjected to gray processing, that is, in the RGB model, if Red = Green = Blue, a specific color can be represented by a color at this time, and a value of R = G = B at this time is called a gray value, so that the image after the gray processing can only store one Bit gray value per dot matrix, and the gray value range is 0-255. Let the grayscale image at the coordinate (i, j) be f1 (i, j) = R (i, j) f2 (i, j) = G (i, j) f3 (i, j) = B (i, j); wherein, R component gray-scale map; a G component gray scale map; b component gray scale map. As shown in figure 6 of the drawings,

there are { g [ x, y ] = f [ x, y ] + epsilon [ x, y ]: x, y =1,2.. N } the initial image is { f [ x, y ]: x, y =1,2.... N }, the noisy contaminated image is { g [ x, y ]: x, y =1,2.... N }; let the noise interference value be { epsilon [ x, y ]: x, y =1,2.... N }; as the threshold value is increased, the signal function changes more and more significantly, as shown in fig. 7 and 8, for the wavelet transform method, a large wavelet coefficient is represented as signal energy, and a small wavelet factor is represented as noise, so that a coefficient with a large amplitude can be retained by the threshold value method, and a small amplitude of the wavelet coefficient can be removed.

for the image with good gray processing, the original RGB color pixels enable the original image to highlight a black-and-white dot matrix, the gray value can be set to be 0/255, and then a plurality of gray-scale images can be obtained by selecting a proper threshold value.

And S3c, performing binary image processing and analysis on the gray level image to obtain a binary gray level image.

The obtained result can still embody the binary image of the whole image and the local features. Because the digital image denoising generally needs to be processed and analyzed by binary images, the image with good gray level is binarized; the lattice location corresponding to 0/255 with respect to the image property may be made to be saved. As shown in fig. 9, other multi-level values related to the pixels are basically eliminated, so that the image processing becomes simpler, the image signal processing process is shortened, and the compression efficiency is high.

And S3d, extracting low-frequency signals from the binary gray level image by using a soft threshold and a hard threshold, and then obtaining real image signals by using a threshold segmentation method.

In order to obtain a more ideal binary digital image, the upper and lower threshold value ranges are usually delineated by shielding and cross-linking margins. That is, some wavelet coefficients ≧ the set threshold can be defined as a specific object (with a gray value of 255), and the rest of the pixels outside the region (with a gray value of 0); it can also be understood as the image background, if there is a consistent uniform gray value for a certain image essence and under a uniform background condition with a gray value of 0, the low-frequency signal can be extracted by using the soft and hard threshold values to divide the useful signal and the impurities, and then the useful signal can be screened out by using the threshold value division method, so as to realize the gray difference conversion.

The character map is subjected to secondary denoising processing by MATLAB, and the relationship between the signal and the frequency domain as shown in fig. 10, 11 and 12 is obtained: after the wavelet transformation processing is carried out on P (m, n) = P, gaussian distribution still exists, in other words, gaussian white noise is uniformly scattered in all the space of the frequency scale; the transformed signal is scattered in a frequency scale local space, and the energy is limited: i.e., the noise of the contaminated image is concentrated on all wavelet factors, while the signal energy is concentrated on part of the wavelet factors. For this reason, the wavelet factors can be roughly divided into two types: (1) The quantity of the polluted noise generated after wavelet transformation is small, and the distance from the wave crest to the wave trough is half (namely the amplitude is large); and (2) the amplitude of the converted signals is small, and the number of the converted signals is large. Therefore, a critical value can be set according to different amplitude parameters to remove the noise part of the image, and meanwhile, the local detail characteristics of the image are well preserved.

Because cloud computing and big data times are emerging at present, multimedia technologies such as image processing and machine vision are developed day by day, the code stream requirements for image transmission are higher and higher, and different steps such as suspended particle denoising, image compression, smoothing processing, signal enhancement, image fusion and the like are needed to be performed generally in the process of adopting wavelet transformation denoising.

Optionally, before step S3, at least one of the following steps is further included:

s30a, performing smooth filtering processing on the processed image signal;

in step S30a, the method of the smoothing filtering process includes a method of mean filtering and a method of median filtering.

Mean filtering-Gaussian noise

Mean filtering, also known as neighborhood averaging, is an algorithm for local spatial filtering. The purpose is to replace the initial gray value of a certain pixel point by the gray average value of all pixels in the neighborhood of the pixel point. The method has simple numerical operation but has obvious defects, and is characterized in that the image pixels are obviously reduced after the image is subjected to mean value filtering, and the main reason is that the gray value of the original whole domain pixels, especially the signals in a low-frequency region, is changed in the mean value replacing process, so that the original signals are distorted or distorted, and the processed image is in a fuzzy form. In addition, the smooth low-frequency filtering method also has a function of eliminating image noise (as shown in fig. 18), and determines the fuzziness of an image by calculating the average value of adjacent pixel points, namely, the larger the neighborhood value, the better the smoothness of the noise, and the clearer the image; however, once the neighborhood value is too large, the loss of the edge features of the image is more obvious, and the image is finally blurred; the method not only has very large computation amount, but also has difficulty in selecting proper neighborhood values, so that a low-pass smoothing filtering algorithm is not usually considered.

The specific principle is as follows:

let f (x, y) be an image of a lattice N × N, (x, y) denote a pixel in the selected region, S is a set of pixels in a central spatial domain near (x, y), M is the total number of pixels, and f (x, y) → g (x, y) be the image after mean filtering, then

Wherein (x, y) =0,1,2,3..... N-1; the radius in the S area is R, and the larger the R value is, the larger the ambiguity is; the average gray value of the neighborhood pixel point set replaces the original noise pollution pixel point, so that although the noise pollution is eliminated to a certain extent, the pixel coordinate value originally containing the noise pollution is changed, and the image edge blurring degree is increased.

Median filter-impulse noise

The median filtering is one of the common methods of the nonlinear filter, the processing method is similar to the neighborhood average method, and the processing method is also to operate on the neighborhood pixel coordinate set of a certain pixel point, and the difference is that the median of the neighborhood pixel point summation is not taken, but is replaced by the median of the neighborhood pixel point.

The method comprises the following specific steps:

firstly, in an N x N array of an image, if a central pixel point of a certain point (x, y) exists, selecting a proper square neighborhood pixel coordinate set S.

And secondly, sequentially sorting the gray values of the pixel points in the square neighborhood pixel coordinate set S according to the size, and selecting the middle value of the sequence group as the output value of the central pixel point (x, y).

The value taking principle in the process of screening the gray level intermediate value of the sequence is as follows:

if the total number M =2n +1 of the set pixel points in the neighborhood, N belongs to N ⁺ And recording the gray value of the middle pixel point of the sequence as an output value.

If the total number M =2n of the set pixel points in the neighborhood, N belongs to N ⁺ And recording the average gray value of two pixels in the middle of the sequence as an output value.

In summary, the median filtering expression can be summarized as:

y(n)＝medM＝med[x(n-N)..........x(n).......x(n+N)]

in the formula (I), the compound is shown in the specification, M = [ x (N-N) ·. And med [ ] indicates that all the numerical values of the sequence set are arranged in a monotonically increasing or decreasing order and then the middle gray value is taken.

The images of the person before and after comparison by using median filtering can be known from the image containing gaussian noise pollution in fig. 18; the median filtering is found to effectively remove Gaussian noise, and the image noise after smoothing processing is better suppressed, and the main reason is that the sorted median can convert the pixel values near the low-frequency useful signal to be approximately equal to the same pixel lattice of the region or the slice region, so as to achieve the effect of removing the noise. Also in fig. 19: x1=10, y1=50 and x2=18, y2=55 in the same time domain coordinates; however, in the time-frequency domain diagram of fig. 20, x1=10, y1=35 and x2=18, y2=30; the numerical value is obviously reduced, the noise disturbance is obviously reduced mainly, and the frequency domain coordinate numerical value is reduced no matter at the corresponding peak position or any other position; and the corresponding influence square grid of the image after the smoothing treatment is more obvious than that of the image shown in figure 19, and is far less than the dense disturbance before the initial smoothing, and the signal distribution is more uniform, and the redundant impurity suspended particles are all subjected to low-pass filtering, so that the noise can be inhibited in a certain range, important information such as image peaks, textures, image detail characteristics and contours can be kept intact, and the peripheral signals of the image are more obvious and clear.

because the digital image is composed of a large amount of set data, the common image has information redundancy, strong correlation and other factors, so that the low frequency (useful signals) can be effectively screened out, and redundant information (time redundancy, three-dimensional space redundancy, signal and knowledge redundancy and character redundancy) can be eliminated, so that the data can be compressed, and the attribute of the image can not be damaged. The image compression aims at representing the image by using the minimum Bit, and the pixel and the quality of the compressed image cannot be damaged in the process. The traditional DCT compression method is based on an orthogonal transformation method, and adopts a coordinate vector to express the symbol-related characteristics of data in an image; once the communication capacity is large and the image complexity is large, the DCT can only process a basic voice and knowledge module; therefore, the novel wavelet transform compression can effectively reduce or even eliminate 'mosquito interference', 'cellular noise', 'sheet noise' and 'accidental noise' on the basis of discrete transform; the image slice-shaped sub-quantity and the resolution of the visual effect of naked eyes are matched with the related coding of the signal frequency band by adopting a local time domain and frequency domain method, and the coefficient sub-band with a large wavelet factor can be collected, which can directly bring obvious effect to image compression.

According to the noise elimination evaluation method, the evaluation method for evaluating the quality of the image can be divided into the following steps: subjective consciousness evaluation and objective theorem evaluation. The former is a criterion established on the basis of (MSE) and (PSNR), and can be defined as:

in the formula N _x N _y Respectively representing the dot matrix of the image in the horizontal direction and the vertical direction, F (i, j) representing the gray scale function value of the image, and F (i-j) representing the gray scale value of the image after being processed.

Therefore, the objective evaluation method can more effectively make objective evaluation on the pixels and the quality of the image compared with subjective consciousness judgment, because the method can reflect the overall situation and the difference of the image before and after compression through the minimum mean square error, but the objective evaluation is general for all lattices of the image and has poor mobility.

The wavelet transform can mainly provide reliable image localization information, and fine time domain and frequency domain node calculation can be adopted for any detail features of the image without damaging the original characteristics of image signals; the specific process is shown in fig. 13, i.e. decomposing a signal into mother wavelets, and performing translation and scaling to obtain a series of wavelet sequences, wherein the formula is as follows:

wherein, scale and position are respectively a scaling coefficient and a translation position parameter, and a result after Fourier function sine-cosine wave transformation is replaced by a scaling and translation factor in a wavelet transformation signal f (t); only in discrete computation, the scale and position coefficients are small compared.

S30b, compressing the processed image signal by adopting a wavelet transform method; the method comprises the following steps:

and S30b1, decomposing the processed image signal to obtain an image signal slice.

Carrying out component decomposition on the initial image; meanwhile, the size of the image is often considered, if the image is large, the decomposed component image needs to be divided into a plurality of signal slices, and if the image is small, the whole image can be regarded as one signal slice. The smallest basic unit of the initial image and the component-decomposed image is a signal slice. Dividing the multiple segment signal slices in this way prevents the "square block" effect from occurring.

S30b2, decomposing the image signal slice into a plurality of resolution grade sequences again after wavelet transformation;

the signal slices are decomposed into a plurality of resolution level orders again after wavelet transform.

And S30b3, after the minimum composition units in the resolution grade order are subjected to decorrelation, obtaining the encoding band transform coefficient.

The minimum component unit of the resolution order is the decorrelated coding band of the signal band. It is worth paying attention to that the encoded band transform coefficients after the correlation removal can embody the frequency domain characteristics of resolution level and slice components.

And S30b4, quantizing the coding band transform coefficient matrix to obtain a compressed code stream, and adding a special identification symbol for repairing coding errors in the compressed code stream.

The coefficient is subjected to coding block matrix quantization, entropy coding of coefficient information quantity measurement is carried out on bit planes in the coding blocks from the primary to the secondary according to a key sequence in the process, a compressed code stream is obtained, and in order to repair coding errors conveniently, a special identification symbol is added in the code stream.

And S30b5, storing a segment header message for identifying the resolution grade sequence in front of the generated compressed code stream.

A section of header message exists in front of the generated code stream and is used for explaining the decomposition level order of the initial image; the decoding end can reconstruct the image of the initial image in a certain specific resolution and a certain specific area according to the above header information and by combining the actual situation of the decoding end without decoding all code streams.

After the threshold value is set, the partial large wavelet factor can be selected to match with the image suitable for the two-scale and multi-resolution characteristics; at the moment, two-dimensional wavelet denoising can be adopted to remove noise-containing parts in a targeted manner to highlight a useful signal image area. Generally, according to different scale characteristics, the wavelet transformation component characteristics can be divided into low-frequency vectors, transverse high-frequency, longitudinal high-frequency and diagonal high-frequency. The size of the wavelet coefficient, namely the energy function of the amplification signal, is adjusted by changing the space structure, the energy signal bearing and the vector direction by combining the actual vector characteristics of the image, so that the noise component is reduced. Therefore, the method can change the wavelet coefficient of the high-frequency vector until the wavelet coefficient is adjusted to the optimal parameter, and the wavelet coefficient is the image feature with clear image pixels and obvious outline.

Common wavelet transform image enhancement methods include a spatial domain method and a frequency domain method, wherein the former method is discussed in terms of pixel points of an image, namely:

g(x,y)＝h(x,y)*f(x,y)

f (x, y) is the initial image function, h (x, y) is the spatial transfer function, and g (x, y) represents the processed function.

As shown in fig. 21, the processed image is first fourier-transformed in the frequency domain, the spectrum of the image is then digitally filtered and restored, and finally the corrected image is inverse fourier-transformed.

The wavelet transformation enhancement principle of the frequency domain method is as follows: firstly, fourier transform is performed on the image in the frequency domain, then the frequency spectrum of the image is digitally filtered and restored, and finally, inverse fourier transform is performed on the corrected image, so that the interested features of the image are further enhanced as shown in fig. 22, 23 and 23.

It is to be understood that the invention is not limited to the specific arrangements and instrumentality described above and shown in the drawings. A detailed description of known methods is omitted herein for the sake of brevity. In the above embodiments, several specific steps are described and shown as examples. However, the method processes of the present invention are not limited to the specific steps described and illustrated, and those skilled in the art can make various changes, modifications and additions, or change the order between the steps, after comprehending the spirit of the present invention.

Finally, it should be noted that: the above-mentioned embodiments are only used for illustrating the technical solution of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for processing a digital image based on a local time-frequency domain transform, the method comprising:

and S3, carrying out secondary denoising treatment on the processed digital image signal by adopting a soft and hard wavelet threshold value.

2. The digital image processing method according to claim 1,

the time-frequency domain filter comprises a low-pass filter h (omega) and a high-pass filter g (omega) which satisfy the following conditions:

|h(ω)| ² +|h(ω+2nπ)| ² ＝|g(ω)| ² +|g(ω+2nπ)| ² ＝2，

h(ω)g ^* (ω)+h(ω+2nπ)h ^* (ω+2nπ)＝0；

n belongs to Z, Z is the set of whole integers, h ^* (ω) is the conjugate function of h (ω)，g ^* And (omega) is the conjugate function of g (omega).

3. The digital image processing method according to claim 2, wherein the step S1 comprises:

s1c, wavelet transformation function obtained

4. The digital image processing method according to claim 1, wherein the step S3 comprises:

5. The digital image processing method according to claim 4, wherein the extracting the low frequency signal for the binarized grayscale image using soft and hard thresholds in step S3d comprises:

6. The digital image processing method according to claim 1, further comprising, before said step S3, at least one of the steps of:

s30a, performing smooth filtering processing on the processed image signal;

7. The digital image processing method according to claim 5, wherein the step S3b comprises:

8. The method according to claim 5, wherein the step S3a comprises performing a smoothing filtering process on the processed image signal by using a mean filtering method or a median filtering method.

9. The digital image processing method according to claim 5, wherein said step S3c comprises,

firstly, fourier transform is carried out on the processed image in the frequency domain, then digital filtering restoration is carried out on the frequency spectrum of the image, and finally, fourier inverse transform is carried out on the corrected image.