CN111932473A - Phase information noise reduction algorithm of multi-resolution sparse coding and storage medium - Google Patents

Phase information noise reduction algorithm of multi-resolution sparse coding and storage medium Download PDF

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CN111932473A
CN111932473A CN202010748233.5A CN202010748233A CN111932473A CN 111932473 A CN111932473 A CN 111932473A CN 202010748233 A CN202010748233 A CN 202010748233A CN 111932473 A CN111932473 A CN 111932473A
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郝红星
于荣欢
胡华全
吴玲达
郭静
巩向武
朱帅
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Peoples Liberation Army Strategic Support Force Aerospace Engineering University
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Abstract

The invention discloses a phase information noise reduction algorithm of multiresolution sparse coding and a storage medium, and provides a phase image noise reduction technology based on multiresolution sparse coding in a complex domain by realizing a multiresolution adaptive dictionary training algorithm in the complex domain according to the self-similarity and multiresolution similarity of interference phase images, thereby improving the noise reduction effect of the complex phase and laying a foundation for realizing phase noise reduction in synthetic aperture radar interferometry and phase noise reduction in magnetic resonance images.

Description

一种多分辨率稀疏编码的相位信息降噪算法及存储介质A phase information noise reduction algorithm and storage medium for multi-resolution sparse coding

技术领域technical field

本发明涉及复数域干涉测量技术领域,特别是涉及一种多分辨率稀疏编码的相位信息降噪算法及计算机可读存储介质。The present invention relates to the technical field of interferometry in complex number domain, in particular to a multi-resolution sparse coding phase information noise reduction algorithm and a computer-readable storage medium.

背景技术Background technique

目前,复数域的相位图像广泛应用于实际测量中,例如通过合成孔径雷达的干涉测量能够进行地形高程的测量,美国航天飞机雷达地形测绘任务SRTM系统是运用该测量方法获取了全球数字高程数据。通过干涉测量还能够测量由于地震或者资源开发等导致的地形的变化等。在医学领域,核磁共振复数图像通过复数的相位图像指导诊断。At present, phase images in the complex domain are widely used in practical measurements. For example, terrain elevation can be measured by interferometry of synthetic aperture radar. The SRTM system of the US space shuttle radar terrain mapping mission uses this measurement method to obtain global digital elevation data. Changes in terrain due to earthquakes or resource development can also be measured by interferometry. In the medical field, complex MRI images guide diagnosis through complex phase images.

但是无论是运用合成孔径雷达干涉测量还是核磁共振图像测量,由于测量设备的固有因素和测量环境的干扰等因素的存在,在最终的复数测量图像中存在噪声,这些噪声影响了测量的精度,并且可能导致后续的处理无法进行。所以如何实现去噪成为现在亟待需要解决的问题。However, whether using synthetic aperture radar interferometry or nuclear magnetic resonance image measurement, due to the inherent factors of the measurement equipment and the interference of the measurement environment, there is noise in the final complex measurement image, which affects the measurement accuracy, and It may cause subsequent processing to fail. Therefore, how to achieve denoising has become an urgent problem to be solved.

发明内容SUMMARY OF THE INVENTION

本发明提供了一种多分辨率稀疏编码的相位信息降噪算法及计算机可读存储介质,以解决现有技术中由于复数测量图像中存在噪声而影响测量精度的问题。The present invention provides a multi-resolution sparse coding phase information noise reduction algorithm and a computer-readable storage medium, so as to solve the problem in the prior art that the measurement accuracy is affected by the existence of noise in the complex measurement image.

第一方面,本发明提供了一种多分辨率稀疏编码的相位信息降噪算法,该方法包括:获取待降噪相位图像对应复数的多分辨率图像,分别将各个分辨率图像进行图像块分割得到图像块集合,其中,所述图像块集合为多个,且所述图像块集分别与所述分辨率图像相唯一对应;对任一所述图像块集合均别分执行以下步骤:将所述图像块集合中的图像块,通过在线训练获得编码字典,通过所述编码字典对所述图像块集合进行编码,获得与所述图像块集合所对应的稀疏编码系数,并将所述编码字典与所述稀疏编码系数相乘,得到降噪后图像块,并对所述图像块集合按照分割的逆操作进行拼合,得到降噪后的图像;将不同分辨率的降噪后的图像进行融合,得到最终的复数的降噪后的相位图像,将复数取相位操作得到最终的相位降噪结果。In a first aspect, the present invention provides a multi-resolution sparse coding phase information noise reduction algorithm, the method comprising: acquiring complex multi-resolution images corresponding to phase images to be denoised, and dividing each resolution image into image blocks respectively Obtaining a set of image blocks, wherein there are multiple sets of image blocks, and the sets of image blocks are uniquely corresponding to the resolution images respectively; respectively perform the following steps for any set of image blocks: the image blocks in the image block set, obtain a coding dictionary through online training, encode the image block set through the coding dictionary, obtain sparse coding coefficients corresponding to the image block set, and use the coding dictionary Multiplying the sparse coding coefficients to obtain image blocks after noise reduction, and combining the set of image blocks according to the inverse operation of segmentation to obtain a noise-reduced image; fuse the noise-reduced images of different resolutions , obtain the final complex phase image after noise reduction, and obtain the final phase noise reduction result by taking the complex phase operation.

可选地,所述获取待降噪相位图像对应复数的多分辨率图像,包括:Optionally, the acquiring a complex multi-resolution image corresponding to the phase image to be denoised includes:

将所述待降噪相位图像通过z=e转换为对应复数的分辨率图像,其中,φ为待降噪相位图像,e为自然底数,j为虚数单位;The phase image to be denoised is converted into a resolution image corresponding to a complex number by z=e , wherein φ is the phase image to be denoised, e is a natural base, and j is an imaginary unit;

根据所需要获取的多分辨率的层数,运用二维Harr小波变换方式,获取不同分辨率的待降噪复数图像z(1),z(2),…z(R),R为分辨率层数。According to the number of multi-resolution layers to be acquired, the two-dimensional Harr wavelet transform method is used to obtain complex images z (1) , z (2) ,...z (R) of different resolutions to be denoised, where R is the resolution layers.

可选地,分别将所述多分辨率图像进行图像块分割得到图像块集合,包括:Optionally, the multi-resolution images are divided into image blocks to obtain image block sets, including:

将待降噪复数图像z(1),z(2),…z(R)按照逐列拼接方式转化为列向量,根据分割图像块的大小,首先将原始图像对应向量进行图像块的分割,定义选择矩阵Mi使得zi=Miz,矩阵Mi每一行只有一个非零元素并且其值为1,其中zi为第i个图像块;定义以下矩阵

Figure BDA0002609121050000021
其中,Np为图像z能够分割的图像块个数,T为转置;Convert the complex images z (1) , z (2) ,...z (R) to be denoised into column vectors according to the column-by-column splicing method. According to the size of the divided image blocks, firstly, the corresponding vectors of the original image are divided into image blocks, Define the selection matrix M i such that zi = M i z, each row of the matrix M i has only one non-zero element and its value is 1, where zi i is the ith image block; define the following matrix
Figure BDA0002609121050000021
Among them, N p is the number of image blocks that the image z can be divided into, and T is the transposition;

同理对于不同分辨率的z(1),z(2),…z(R),分别定义对应的分割矩阵M(1),M(2),…M(R),通过选择矩阵以将原始的图像对应向量分割为大小为

Figure BDA0002609121050000022
的图像块的集合,m一般取整数的平方,如81,100等,即:Similarly, for z (1) , z (2) ,…z (R) of different resolutions, define the corresponding partition matrices M (1) , M (2) ,…M (R) respectively. The original image corresponding vector is divided into a size of
Figure BDA0002609121050000022
The set of image blocks, m generally takes the square of the integer, such as 81, 100, etc., namely:

Figure BDA0002609121050000031
Figure BDA0002609121050000031

Figure BDA0002609121050000032
Figure BDA0002609121050000032

可选地,将所述待降噪相位图像对应复数的图像块,通过在线训练获得编码字典,包括:Optionally, a coding dictionary is obtained through online training for the complex-numbered image blocks corresponding to the phase image to be denoised, including:

从集合

Figure BDA0002609121050000033
中随机获取图像块组zt,t=1,…,Ng,Ng为所选择的图像块组中图像块的个数,按照预定顺序根据所述图像块组进行词典学习,训练的每一个循环采用其中的一个图像块组进行字典元素更新,即通过最小化下式进行字典训练:from the collection
Figure BDA0002609121050000033
Randomly obtain image block groups z t , t=1,...,N g , where N g is the number of image blocks in the selected image block group, and perform dictionary learning according to the image block groups in a predetermined order. A loop uses one of the image block groups to update dictionary elements, that is, dictionary training by minimizing the following formula:

Figure BDA0002609121050000034
Figure BDA0002609121050000034

可选地,获取多分辨率图像块集合的编码的步骤包括:Optionally, the step of obtaining the encoding of the multi-resolution image block set includes:

对于每一个分辨率下的图像块集合,对图像块集合中的每一个图像块对应的列向量进行稀疏编码,对于训练得到的字典D,如果对

Figure BDA0002609121050000035
中的每一个向量zi进行稀疏编码通过求解下面的最优化问题来获得For the image block set at each resolution, the column vector corresponding to each image block in the image block set is sparsely encoded. For the dictionary D obtained by training, if the
Figure BDA0002609121050000035
Each vector z i in the sparse coding is obtained by solving the following optimization problem

Figure BDA0002609121050000036
Figure BDA0002609121050000036

对于分辨率r,通过求解

Figure BDA0002609121050000037
来获得最优化编码。αi是zi在字典D的编码,
Figure BDA0002609121050000038
Figure BDA0002609121050000039
在字典D上的编码。For resolution r, by solving
Figure BDA0002609121050000037
to get the optimal encoding. α i is the encoding of zi in dictionary D,
Figure BDA0002609121050000038
Yes
Figure BDA0002609121050000039
encoding on dictionary D.

可选地,将所述编码字典与所述稀疏编码系数相乘,得到降噪后图像块,包括:Optionally, multiplying the coding dictionary with the sparse coding coefficients to obtain image blocks after noise reduction, including:

Figure BDA00026091210500000310
Figure BDA00026091210500000310

其中,Nr为第r分辨率的图像块的个数,

Figure BDA0002609121050000041
为zi降噪后图像块,
Figure BDA0002609121050000042
Figure BDA0002609121050000043
降噪后图像块。Among them, N r is the number of image blocks of the rth resolution,
Figure BDA0002609121050000041
is the image block after denoising for z i ,
Figure BDA0002609121050000042
for
Figure BDA0002609121050000043
Image block after noise reduction.

可选地,将所述图像块集合按照分割的逆操作进行拼合,得到不同分辨率下降噪后的图像,包括:Optionally, the image block set is assembled according to the inverse operation of the segmentation to obtain denoised images at different resolutions, including:

将同一分辨率下的图像块集合按照下式进行拼合,得到不同分辨率下降噪后的图像;The image block sets under the same resolution are combined according to the following formula to obtain denoised images under different resolutions;

Figure BDA0002609121050000044
Figure BDA0002609121050000044

Figure BDA0002609121050000045
Figure BDA0002609121050000045

其中,

Figure BDA0002609121050000046
是z的降噪结果,
Figure BDA0002609121050000047
是z(r)的降噪结果in,
Figure BDA0002609121050000046
is the noise reduction result of z,
Figure BDA0002609121050000047
is the noise reduction result of z (r)

可选地,将不同分辨率的降噪后的图像进行融合,得到最终的复数的降噪效果,包括:Optionally, the denoised images of different resolutions are fused to obtain a final complex denoising effect, including:

按照从高分辨率到低分辨率的顺序,运用假设检验方式获取最终的融合结果,每一步的融合结果作为下一分辨率的融合输入;According to the order from high resolution to low resolution, the final fusion result is obtained by means of hypothesis testing, and the fusion result of each step is used as the fusion input of the next resolution;

首先将

Figure BDA0002609121050000048
进行上采样,获取与
Figure BDA0002609121050000049
同样大小N1×N2的降噪结果,N1
Figure BDA00026091210500000410
的长,N2
Figure BDA00026091210500000411
的宽,假设如下:First put
Figure BDA0002609121050000048
Upsampling is performed to obtain the
Figure BDA0002609121050000049
The noise reduction results of the same size N 1 × N 2 , N 1 is
Figure BDA00026091210500000410
The length of N2 is
Figure BDA00026091210500000411
width, assuming the following:

Figure BDA00026091210500000412
Figure BDA00026091210500000412

Figure BDA00026091210500000413
Figure BDA00026091210500000413

假设

Figure BDA00026091210500000414
服从零均值高斯分布,高斯分布的标准差为σ,则在置信度为0.95的情况下,对于图像中的每一个像素点,应当满足如下条件Assumption
Figure BDA00026091210500000414
It obeys the zero-mean Gaussian distribution, and the standard deviation of the Gaussian distribution is σ, then when the confidence level is 0.95, for each pixel in the image, the following conditions should be met

Figure BDA00026091210500000415
Figure BDA00026091210500000415

若满足上式,则认为分辨率为r=1的情况下,估计

Figure BDA00026091210500000416
是可用的,反之,则可以认为估计不可用,因此将
Figure BDA0002609121050000051
Figure BDA0002609121050000052
的融合结果为If the above formula is satisfied, it is considered that when the resolution is r=1, it is estimated that
Figure BDA00026091210500000416
is available, otherwise, it can be considered that the estimate is not available, so the
Figure BDA0002609121050000051
and
Figure BDA0002609121050000052
The fusion result is

Figure BDA0002609121050000053
Figure BDA0002609121050000053

其中i=1,2,…,N1,j=1,2,…,N2where i=1,2,...,N 1 ,j=1,2,...,N 2 ;

同理,按照上述方法将zr1

Figure BDA0002609121050000054
进行融合得到zr2,并得到与最后一级分辨率R的降噪结果的融合结果zrR。Similarly, according to the above method, zr 1 and
Figure BDA0002609121050000054
Perform fusion to obtain zr 2 , and obtain a fusion result zr R with the noise reduction result of the last-level resolution R.

可选地,所述将复数取相位操作得到最终的相位降噪结果,包括:Optionally, obtaining the final phase noise reduction result by taking the complex phase operation, including:

根据最终的复数图像的融合结果zrR,获取复数zrR的相位角最为最终相位的估计值:According to the fusion result zr R of the final complex number image, the phase angle of the complex number zr R is obtained as the estimated value of the final phase:

Figure BDA0002609121050000055
其中imag(·)和real(·)分别为计算实部和虚部。
Figure BDA0002609121050000055
where imag( ) and real( ) are the real and imaginary parts of the calculation, respectively.

第二方面,本发明提供了一种计算机可读存储介质,其特征在于,所述计算机可读存储介质存储有信号映射的计算机程序,所述计算机程序被至少一个处理器执行时,以实现上述任一种所述的多分辨率稀疏编码的相位信息降噪算法。In a second aspect, the present invention provides a computer-readable storage medium, characterized in that, the computer-readable storage medium stores a computer program for signal mapping, and when the computer program is executed by at least one processor, the above-mentioned computer program is implemented. Any one of the multi-resolution sparse coding phase information noise reduction algorithms.

本发明有益效果如下:The beneficial effects of the present invention are as follows:

本发明是根据干涉相位图像的自相似性与多分辨率相似性,通过复数域中多分辨率自适应词典训练算法的实现,提出复数域中一种基于多分辨率稀疏编码的相位图像降噪技术,提高复数相位的降噪效果,从而实现合成孔径雷达干涉测量中的相位降噪以及磁共振图像中的相位降噪奠定基础。According to the self-similarity and multi-resolution similarity of the interference phase image, the invention proposes a phase image noise reduction based on multi-resolution sparse coding in the complex number domain through the realization of the multi-resolution adaptive dictionary training algorithm in the complex number domain. technology to improve the noise reduction effect of complex phase, thus laying the foundation for phase noise reduction in synthetic aperture radar interferometry and phase noise reduction in magnetic resonance images.

附图说明Description of drawings

图1是本发明实施例提供的一种多分辨率稀疏编码的相位信息降噪算法的流程示意图;1 is a schematic flowchart of a phase information noise reduction algorithm for multi-resolution sparse coding provided by an embodiment of the present invention;

图2是本发明实施例提供的另一种多分辨率稀疏编码的相位信息降噪算法的流程示意图;2 is a schematic flowchart of another multi-resolution sparse coding phase information noise reduction algorithm provided by an embodiment of the present invention;

图3是本发明实施例提供的多分辨率稀疏编码的相位信息降噪算法示意图;3 is a schematic diagram of a phase information noise reduction algorithm for multi-resolution sparse coding provided by an embodiment of the present invention;

图4是本发明实施例提供的稀疏编码示意图。FIG. 4 is a schematic diagram of sparse coding provided by an embodiment of the present invention.

具体实施方式Detailed ways

随着信号变换理论的发展,特别是离散傅里叶变换、离散余弦变换和离散小波变换的提出,其在计算机系统中的离散信号降噪中发挥着重大作用。这些算法的本质就是稀疏编码,其表明自然信号能够通过表示基(也被称为字典)中的少量元素进行表示。运用稀疏编码进行降噪的基本原理是信号空间包含于信号的观察空间,稀疏编码技术中的字典应当为信号空间的支撑基,但是并不是信号观察空间的支撑基。换句话说,信号观察空间包含信号和噪声,优良的字典能够很好地对信号进行稀疏编码,但是不能对噪声进行稀疏编码,通过编码和解码过程,能够有效滤除观察信号中的噪声,进而实现去除噪声,提高精度的目的。通过上述分析可以得到要想实现基于稀疏编码的信号降噪问题,需要首先具有优良的表示字典,其次能够进行有效的编码和解码过程。因此本发明重点关注在这三方面进行专利申请与维护。With the development of signal transform theory, especially the proposal of discrete Fourier transform, discrete cosine transform and discrete wavelet transform, it plays an important role in the noise reduction of discrete signals in computer systems. The essence of these algorithms is sparse coding, which shows that natural signals can be represented by a small number of elements in a representation base (also known as a dictionary). The basic principle of using sparse coding for noise reduction is that the signal space is included in the observation space of the signal, and the dictionary in the sparse coding technique should be the support base of the signal space, but not the support base of the signal observation space. In other words, the signal observation space contains both signal and noise. A good dictionary can sparsely encode the signal, but cannot sparsely encode the noise. Through the encoding and decoding process, the noise in the observation signal can be effectively filtered out, and then To achieve the purpose of removing noise and improving accuracy. Through the above analysis, it can be concluded that in order to realize the signal noise reduction problem based on sparse coding, it is necessary to have an excellent representation dictionary first, and secondly, to be able to perform effective encoding and decoding processes. Therefore, the present invention focuses on patent application and maintenance in these three aspects.

稀疏编码最初提出时,字典是固定的,例如在离散余弦变换中通过余弦基分解信号。但是,固定的表示基并不能获得较高的稀疏度,并不能得到较好的降噪或者压缩效果。然而通过待表示信号训练得到的表示字典具有较好的自适应性,因此能够获取更加满意的表示结果。一些智能算法被提出用于训练自适应字典。一种基于冗余表示的K-SVD算法被提出用于图像降噪中,其中表示字典通过噪声图像中提取的图像块进行训练得到。后来,该算法被扩展到三维领域用来解决彩色图像的修复问题。有些研究者将字典训练算法通过随机近似进行改进,用于成百万训练样本的大数据中。在2012年,一种有监督字典训练算法的一般方法被提出用于不同类别的任务中。后期的字典也开始逐步适应于组稀疏编码,即相似的信号块基于同样的编码字典应当具有相似的编码,或者说编码具有相同的特征。When sparse coding was first proposed, the dictionary was fixed, for example in discrete cosine transforms decomposing the signal by cosine basis. However, a fixed representation base cannot obtain a higher sparsity, and cannot obtain a better noise reduction or compression effect. However, the representation dictionary obtained by training the signal to be represented has better adaptability, so it can obtain more satisfactory representation results. Some intelligent algorithms have been proposed for training adaptive dictionaries. A redundant representation-based K-SVD algorithm is proposed for image denoising, in which the representation dictionary is trained from image patches extracted from noisy images. Later, the algorithm was extended to the 3D domain to solve the inpainting problem of color images. Some researchers have improved the dictionary training algorithm by random approximation and used it in large data with millions of training samples. In 2012, a general approach to supervised dictionary training algorithms was proposed for different classes of tasks. Later dictionaries also began to gradually adapt to group sparse coding, that is, similar signal blocks should have similar coding based on the same coding dictionary, or the coding has the same characteristics.

关于编码和解码问题中,为了实现编码算法能够较好地对信号进行编码而避免对噪声进行编码,一般训练得到的表示字典是冗余字典,这样对信号的编码就是稀疏的,即编码中少量的元素非零,编码向量中的大多数元素为0。在实际的编码过程中,一般采用零范数正则化方式实现对零元素个数的约束。但是由于在编码最优化问题中,采用零范数正则化方法所得到的最优化问题是非凸的,因此需要将问题松弛为凸优化问题或者运用贪婪算法进行求解获取观察信号的编码。获得稀疏编码后,可以通过编码字典和稀疏编码恢复原始信号,由于稀疏编码过程中避免了对噪声的编码,因此在恢复后会滤除噪声的干扰,进而实现降噪。Regarding the encoding and decoding problems, in order to realize that the encoding algorithm can better encode the signal and avoid encoding the noise, the representation dictionary obtained by general training is a redundant dictionary, so the encoding of the signal is sparse, that is, a small amount of encoding The elements of is non-zero, and most of the elements in the encoded vector are 0. In the actual encoding process, the zero-norm regularization method is generally used to realize the constraint on the number of zero elements. However, in the encoding optimization problem, the optimization problem obtained by using the zero-norm regularization method is non-convex, so it is necessary to relax the problem into a convex optimization problem or use a greedy algorithm to solve the encoding of the observed signal. After the sparse coding is obtained, the original signal can be restored through the coding dictionary and sparse coding. Since the coding of noise is avoided in the sparse coding process, the interference of noise will be filtered out after restoration, thereby realizing noise reduction.

在运用稀疏编码对复数值的相位信息进行降噪的算法中,目前存在三类重要的算法:一类是直接针对相位图像通过稀疏编码技术进行降噪,由于复数相位的不连续性,且被截断于区间[-π,π)中,该类算法取得的效果并不是很理想,降噪算法在滤除噪声的同时滤除了部分信号中的细节信息,导致信号的精度降低了。第二类算法是分别针对复数值的实部和虚部分别通过稀疏编码技术进行降噪,将两个部分的降噪结果进行融合,获得降噪后的复数值,获取复数值得相位作为原始复数值中相位信息的降噪结果。该类算法的主要缺点是将复数的实部和虚部进行单独处理,忽略了实部和虚部之间的关联关系,导致最终的相位降噪结果精度值仍然有提升的空间。第三类算法是将复数值作为一个整体通过稀疏编码技术进行降噪,该类算法充分考虑了复数中实部和虚部之间的相关性,通过将降噪以后的复数获得的降噪相位能够取得较好的降噪效果。本发明提出的算法属于第三种类型降噪算法。本发明算法与以前算法的不同之处在于通过多分辨率字典训练与稀疏编码的方式实现降噪从而进一步提高相位图像的降噪效果。Among the algorithms for denoising complex-valued phase information using sparse coding, there are currently three types of important algorithms: one is to denoise the phase image directly through sparse coding technology. Truncated in the interval [-π,π), the effect of this type of algorithm is not very ideal. The noise reduction algorithm filters out the details of the signal while filtering out the noise, which reduces the accuracy of the signal. The second type of algorithm is to denoise the real part and imaginary part of the complex value through sparse coding technology, fuse the noise reduction results of the two parts to obtain the denoised complex value, and obtain the phase of the complex value as the original complex value. The noise reduction result of the phase information in the value. The main disadvantage of this type of algorithm is that the real and imaginary parts of complex numbers are processed separately, ignoring the correlation between the real and imaginary parts, resulting in the final phase noise reduction result accuracy value still has room for improvement. The third type of algorithm is to denoise the complex value as a whole through sparse coding technology. This type of algorithm fully considers the correlation between the real part and the imaginary part of the complex number. The noise reduction phase obtained by denoising the complex number Can achieve better noise reduction effect. The algorithm proposed by the present invention belongs to the third type of noise reduction algorithm. The difference between the algorithm of the present invention and the previous algorithm is that noise reduction is realized by means of multi-resolution dictionary training and sparse coding, thereby further improving the noise reduction effect of the phase image.

本发明实施例的目的是根据干涉相位图像的自相似性与多分辨率相似性,通过复数域中多分辨率自适应词典训练算法的实现,提出复数域中一种基于多分辨率稀疏编码的相位图像降噪技术,提高复数相位的降噪效果,从而实现合成孔径雷达干涉测量中的相位降噪以及磁共振图像中的相位降噪奠定基础。在本发明中,运用二维小波变换方式获取待降噪相位图像对应复数的多分辨率形式,分别将获得的多分辨率图像进行图像块分割得到图像块集合。然后通过原始相位图像对应复数图像块运用在线训练方式获得复数编码字典,运用训练得到的字典对多分辨率的图像块集合进行编码获得稀疏编码系数。通过编码字典与编码系数相乘的方式获取降噪后图像块。将图像块集合依据分割方式的逆操作进行拼合得到不同分辨率下的降噪结果,将不同分辨率的降噪结果进行融合得到最终的复数的降噪效果,将复数取相位操作得到最终的相位降噪结果。The purpose of the embodiment of the present invention is to propose a multi-resolution sparse coding based multi-resolution sparse coding method in the complex number domain through the realization of the multi-resolution adaptive dictionary training algorithm in the complex number domain according to the self-similarity and the multi-resolution similarity of the interference phase image. The phase image noise reduction technology improves the noise reduction effect of complex phases, thereby laying the foundation for phase noise reduction in synthetic aperture radar interferometry and phase noise reduction in magnetic resonance images. In the present invention, a two-dimensional wavelet transform method is used to obtain the complex multi-resolution form of the phase image to be denoised, and the obtained multi-resolution images are divided into image blocks to obtain an image block set. Then, the complex coding dictionary is obtained by using the online training method corresponding to the complex image blocks of the original phase image, and the sparse coding coefficients are obtained by encoding the multi-resolution image block set using the dictionary obtained by training. The denoised image block is obtained by multiplying the coding dictionary and the coding coefficients. The image block sets are assembled according to the inverse operation of the segmentation method to obtain the noise reduction results under different resolutions, the noise reduction results of different resolutions are fused to obtain the final complex noise reduction effect, and the complex number is obtained by taking the phase operation to obtain the final phase. Noise reduction results.

具体实施时,本发明实施例的多分辨率稀疏编码的相位信息降噪算法,参见图1,包括:During specific implementation, the phase information noise reduction algorithm of multi-resolution sparse coding according to the embodiment of the present invention, referring to FIG. 1 , includes:

S101、获取待降噪相位图像对应复数的多分辨率图像,分别将各个分辨率图像进行图像块分割得到图像块集合,其中,所述图像块集合为多个,且所述图像块集分别与所述分辨率图像相唯一对应;S101. Acquire complex multi-resolution images corresponding to the phase image to be denoised, and perform image block segmentation on each resolution image to obtain an image block set, wherein the image block sets are multiple, and the image block sets are The resolution images are uniquely corresponding;

S102、对任一所述图像块集合均别分执行以下步骤:将所述图像块集合中的图像块,通过在线训练获得编码字典,通过所述编码字典对所述图像块集合进行编码,获得与所述图像块集合所对应的稀疏编码系数,并将所述编码字典与所述稀疏编码系数相乘,得到降噪后图像块,并对所述图像块集合按照分割的逆操作进行拼合,得到降噪后的图像;S102. Perform the following steps on any of the image block sets: obtaining a coding dictionary for the image blocks in the image block set through online training, and encoding the image block set by using the coding dictionary to obtain the sparse coding coefficients corresponding to the set of image blocks, and multiplying the coding dictionary with the sparse coding coefficients to obtain image blocks after noise reduction, and stitching the set of image blocks according to the inverse operation of segmentation, Get the denoised image;

S103、将不同分辨率的降噪后的图像进行融合,得到最终的复数的降噪后的相位图像,将复数取相位操作得到最终的相位降噪结果。S103 , fuse the denoised images of different resolutions to obtain a final complex denoised phase image, and obtain a final phase denoising result by taking the complex phase operation.

也就是说,本发明实施例是针对相位图像的噪声干扰问题,运用多分辨率稀疏编码技术对信号进行编码,但是不能对随机噪声进行编码的特点。通过编码和解编码过程与方法设计,滤除复数测量信号中噪声,提高复数测量信号中的相位信息的精度,为后期的信号应用奠定基础。That is to say, the embodiment of the present invention is aimed at the noise interference problem of the phase image, and uses the multi-resolution sparse coding technology to encode the signal, but cannot encode random noise. Through the coding and decoding process and method design, the noise in the complex measurement signal is filtered, the accuracy of the phase information in the complex measurement signal is improved, and the foundation for later signal applications is laid.

下面将结合图2和图3通过一个具体的例子对本发明所述的方法进行详细的解释和说明:The method described in the present invention will be explained and described in detail below with reference to Fig. 2 and Fig. 3 through a specific example:

本发明实施例中,所述多分辨率图像块集合获取具体包括:In the embodiment of the present invention, the acquisition of the multi-resolution image block set specifically includes:

(a)多分辨率复数图像获取:(a) Multi-resolution complex image acquisition:

若提供相位图像对应的复数图像z进行相位降噪,则直接对其进行操作,若提供含噪相位图像φ进行相位降噪,则运用If the complex image z corresponding to the phase image is provided for phase noise reduction, then operate it directly; if the noisy phase image φ is provided for phase noise reduction, use

z=e 式1z=e Formula 1

转化为复数进行下面操作。Convert to complex numbers and do the following.

根据所需要获取的多分辨率的层数,运用二维Harr小波变换方式,获取不同分辨率的待降噪复数图像z(1),z(2),…z(R),其中低分辨率图像仅仅取小波变换后的低频分辨。由于通过二维小波变换获取,因此下一级分辨率图像的长和宽都是上一级分辨率图像的二分之一。According to the number of multi-resolution layers to be acquired, the two-dimensional Harr wavelet transform method is used to obtain complex images z (1) , z (2) ,...z (R) of different resolutions to be denoised, among which the low resolution The image only takes the low frequency resolution after wavelet transformation. Because it is obtained by two-dimensional wavelet transform, the length and width of the next-level resolution image are both half of those of the previous-level resolution image.

(b)多分辨率图像块分割:(b) Multi-resolution image patch segmentation:

将图像矩阵z,z(1),z(2),…z(R)按照逐列拼接方式转化为列向量。根据分割图像块的大小,首先将原始图像对应向量进行图像块的分割,定义选择矩阵Mi使得zi=Miz(矩阵Mi每一行只有一个非零元素并且其值为1),其中zi为第i个图像块。定义以下矩阵Convert the image matrices z, z (1) , z (2) ,...z (R) into column vectors in a column-by-column stitching manner. According to the size of the divided image block, firstly, the corresponding vector of the original image is divided into image blocks, and the selection matrix M i is defined so that zi = M i z (each row of the matrix M i has only one non-zero element and its value is 1), where z i is the ith image block. Define the following matrix

Figure BDA0002609121050000101
Figure BDA0002609121050000101

其中,Np为图像z能够分割的图像块个数。例如对于N=N1×N2大小的图像z,若要分割为

Figure BDA0002609121050000102
的图像块,则分割的个数为
Figure BDA0002609121050000103
Among them, N p is the number of image blocks that the image z can be divided into. For example, for an image z of size N=N 1 ×N 2 , to be divided into
Figure BDA0002609121050000102
image blocks, the number of divisions is
Figure BDA0002609121050000103

同理对于不同分辨率的z(1),z(2),…z(R),定义分割矩阵M(1),M(2),…M(R)。通过选择矩阵可以将原始的图像对应向量分割为大小为

Figure BDA0002609121050000104
的图像块的集合,即Similarly, for z (1) , z (2) ,…z (R) of different resolutions, define partition matrices M (1) , M (2) ,…M (R) . By selecting the matrix, the original image corresponding vector can be divided into the size of
Figure BDA0002609121050000104
a collection of image blocks, i.e.

Figure BDA0002609121050000105
Figure BDA0002609121050000105

Figure BDA0002609121050000106
Figure BDA0002609121050000106

本发明实施例中编码字典的训练具体包括:根据集合

Figure BDA0002609121050000107
训练得到稀疏编码字典,采用字典训练算法获取自适应词典的目的是能够需找到一个编码字典,运用其中的较少数目字典原子的线性组合就可以实现对训练集中图像块的表示,其训练过程可以通过下面的最优化问题进行描述。The training of the coding dictionary in the embodiment of the present invention specifically includes: according to the set
Figure BDA0002609121050000107
The sparse coding dictionary is obtained by training, and the purpose of using the dictionary training algorithm to obtain the adaptive dictionary is to find a coding dictionary, and use the linear combination of a small number of dictionary atoms to realize the representation of the image blocks in the training set. The training process can be It is described by the following optimization problem.

Figure BDA0002609121050000108
Figure BDA0002609121050000108

其中

Figure BDA0002609121050000109
其中前面的一项为表示误差,后面的一项为稀疏约束项,两项通过正则化参数λ>0来进行平衡。约束条件D∈C是为了防止字典中的元素趋于任意大。在式(5)中,后一项稀疏约束是通过L1范数来进行约束的,这是因为在实际的实验中,L1范数方式获取的编码字典对于复数的降噪具有更好的效果。in
Figure BDA0002609121050000109
The former term is the representation error, the latter term is the sparse constraint term, and the two terms are balanced by the regularization parameter λ>0. The constraint D∈C is to prevent the elements in the dictionary from tending to be arbitrarily large. In Equation (5), the latter sparse constraint is constrained by the L1 norm, because in the actual experiment, the coding dictionary obtained by the L1 norm method has a better effect on the denoising of complex numbers.

通常解决问题式5的方法是交互地对字典D和编码

Figure BDA00026091210500001010
分别进行最优化求解。对D最优化求解是一个凸集上的二次优化问题,对
Figure BDA00026091210500001011
最优化是凸优化问题且可分解的。最优化问题式5对于字典D求最优化问题相对较简单,但是对于编码
Figure BDA0002609121050000111
最优化求解非常耗时。为了提高计算效率,降低字典训练的解决这个问题,本发明采用在线词典训练方法。首先从集合
Figure BDA0002609121050000112
中随机获取图像块组zt,t=1,…,Ng,然后按照一定顺序根据这些图像块组进行词典学习。训练的每一个循环采用其中的一个图像块组进行字典元素更新。即通过最小化下式进行字典训练。The usual way to solve Equation 5 is to interactively encode the dictionary D and
Figure BDA00026091210500001010
The optimization solutions are carried out separately. The optimal solution to D is a quadratic optimization problem on a convex set.
Figure BDA00026091210500001011
The optimization is a convex optimization problem and decomposable. The optimization problem Equation 5 is relatively simple to find the optimization problem for the dictionary D, but for the encoding
Figure BDA0002609121050000111
The optimization solution is very time consuming. In order to improve computing efficiency and reduce dictionary training to solve this problem, the present invention adopts an online dictionary training method. First from the collection
Figure BDA0002609121050000112
Randomly obtain image block groups z t , t=1, . . . , N g , and then perform dictionary learning according to these image block groups in a certain order. Each loop of training uses one of the image block groups to update dictionary elements. That is, dictionary training is performed by minimizing the following equation.

Figure BDA0002609121050000113
Figure BDA0002609121050000113

本发明实施例中获取多分辨率图像块集合的编码具体包括:In the embodiment of the present invention, the encoding for acquiring the multi-resolution image block set specifically includes:

对于每一个分辨率下的图像块集合,对图像块集合中的每一个图像块对应的列向量进行稀疏编码,具体如图4所示。对于训练得到的字典D,如果对

Figure BDA0002609121050000114
中的每一个向量zi进行稀疏编码通过求解下面的最优化问题来获得For the image block set at each resolution, sparse coding is performed on the column vector corresponding to each image block in the image block set, as shown in FIG. 4 . For the dictionary D obtained by training, if the
Figure BDA0002609121050000114
Each vector z i in the sparse coding is obtained by solving the following optimization problem

Figure BDA0002609121050000115
Figure BDA0002609121050000115

对于分辨率r,可以通过求解下面的最优化问题来获得。For the resolution r, it can be obtained by solving the following optimization problem.

Figure BDA0002609121050000116
Figure BDA0002609121050000116

可以运用贪婪算法对上述最优化问题进行求解。The above optimization problem can be solved using a greedy algorithm.

本发明实施例中多分辨率图像块的融合具体包括:The fusion of multi-resolution image blocks in the embodiment of the present invention specifically includes:

(a)多分辨率复数图像降噪图像块的获取:(a) Acquisition of multi-resolution complex image denoised image blocks:

通过上面的步骤,我们已经获取了稀疏编码字典D和各个分辨率下编码,可以通过将编码字典与稀疏编码相乘的方式获取分割的图像块的降噪结果。Through the above steps, we have obtained the sparse coding dictionary D and the codes at various resolutions. The noise reduction results of the segmented image blocks can be obtained by multiplying the coding dictionary with the sparse coding.

which is

Figure BDA0002609121050000121
Figure BDA0002609121050000121

Figure BDA0002609121050000122
Figure BDA0002609121050000122

(b)图像块集合的拼合:(b) Flattening of image patch sets:

获取了图像块的降噪集合以后,针对多个分辨率进行图像块分割的逆操作,将同一分辨率下的图像块结合合成整一幅图像。其拼合过程为式3和式4的逆运算。After obtaining the noise reduction set of image blocks, the inverse operation of image block segmentation is performed for multiple resolutions, and the image blocks under the same resolution are combined into a whole image. The stitching process is the inverse operation of Equation 3 and Equation 4.

Figure BDA0002609121050000123
Figure BDA0002609121050000123

Figure BDA0002609121050000124
Figure BDA0002609121050000124

通过上述运算,获取了原始的相位图像对应的复数的降噪估计结果

Figure BDA0002609121050000125
以及对应于分辨率r的降噪估计结果
Figure BDA0002609121050000126
在本发明下面的步骤中是如何将
Figure BDA0002609121050000127
以及不同分辨率的降噪结果
Figure BDA0002609121050000128
进行融合,得到最终的降噪结果。这是本发明重点维护的部分。Through the above operations, the complex noise reduction estimation result corresponding to the original phase image is obtained
Figure BDA0002609121050000125
and the noise reduction estimation result corresponding to the resolution r
Figure BDA0002609121050000126
In the following steps of the present invention, how
Figure BDA0002609121050000127
and noise reduction results at different resolutions
Figure BDA0002609121050000128
Fusion is performed to obtain the final noise reduction result. This is the important maintenance part of the present invention.

(c)多分辨率降噪结果的融合:(c) Fusion of multi-resolution noise reduction results:

在不同分辨率降噪结果的融合过程中,本发明采用从高分辨率到低分辨率方式运用假设检验方式获取最终的融合结果。每一步的融合结果作为下一分辨率的融合输入。In the fusion process of noise reduction results of different resolutions, the present invention adopts a hypothesis test method from high resolution to low resolution to obtain the final fusion result. The fusion result of each step is used as the fusion input for the next resolution.

首先看

Figure BDA0002609121050000129
Figure BDA00026091210500001210
首先将
Figure BDA00026091210500001211
进行上采样,获取与
Figure BDA00026091210500001212
同样大小N1×N2的降噪结果,。假设如下:first look
Figure BDA0002609121050000129
and
Figure BDA00026091210500001210
First put
Figure BDA00026091210500001211
Upsampling is performed to obtain the
Figure BDA00026091210500001212
The noise reduction results of the same size N 1 × N 2 , . Suppose the following:

Figure BDA00026091210500001213
Figure BDA00026091210500001213

Figure BDA00026091210500001214
Figure BDA00026091210500001214

可以假设

Figure BDA00026091210500001215
服从零均值高斯分布,高斯分布的标准差为σ,则在置信度为0.95的情况下,对于图像中的每一个像素点,应当满足如下条件It can be assumed
Figure BDA00026091210500001215
It obeys the zero-mean Gaussian distribution, and the standard deviation of the Gaussian distribution is σ, then when the confidence level is 0.95, for each pixel in the image, the following conditions should be met

Figure BDA0002609121050000131
Figure BDA0002609121050000131

若式14满足,则可认为分辨率为r=1的情况下,估计

Figure BDA0002609121050000132
是可用的,反之,则可以认为估计不可用,因此将
Figure BDA0002609121050000133
Figure BDA0002609121050000134
的融合结果为If Equation 14 is satisfied, it can be considered that when the resolution is r=1, it is estimated that
Figure BDA0002609121050000132
is available, otherwise, it can be considered that the estimate is not available, so the
Figure BDA0002609121050000133
and
Figure BDA0002609121050000134
The fusion result is

Figure BDA0002609121050000135
Figure BDA0002609121050000135

其中i=1,2,…,N1,j=1,2,…,N2。下面运用同样的方式将zr1

Figure BDA0002609121050000136
进行融合得到zr2,如此继续得到与最后一级分辨率R的降噪结果的融合结果zrR。where i=1,2,...,N1,j= 1,2 ,..., N2 . The following applies the same method to zr 1 to
Figure BDA0002609121050000136
Perform fusion to obtain zr 2 , and then continue to obtain the fusion result zr R with the noise reduction result of the last-level resolution R.

(d)获取相位图像降噪结果:(d) Obtain the phase image noise reduction results:

根据最终的复数图像的融合结果zrR,获取复数zrR的相位角最为最终相位的估计值。According to the fusion result zr R of the final complex number image, the phase angle of the complex number zr R is obtained, which is the estimated value of the final phase.

Figure BDA0002609121050000137
Figure BDA0002609121050000137

其中imag(·)和real(·)分别为计算实部和虚部。where imag( ) and real( ) are the real and imaginary parts of the calculation, respectively.

本发明方法中主要的要点是运用假设检验方法对多分辨率的降噪结果进行融合,即式15的计算方式。在进行降噪结果的融合之前,运用小波变换进行多分辨率的分解,并且分辨运用式6进行稀疏编码字典的训练,运用式7和式8进行稀疏编码,最后通过分块的逆运算将降噪后的块进行合并,得到不同分辨率下的降噪结果。The main point of the method of the present invention is to use the hypothesis testing method to fuse the multi-resolution noise reduction results, that is, the calculation method of Equation 15. Before the fusion of the noise reduction results, the wavelet transform is used to perform multi-resolution decomposition, and the training of the sparse coding dictionary is performed by using the formula 6, and the sparse coding is performed by using the formula 7 and formula 8. Finally, the inverse operation of the block will reduce the The denoised blocks are merged to obtain denoising results at different resolutions.

本发明方法主要执行以下步骤:The method of the present invention mainly performs the following steps:

(1)将输入相位图像转化为复数形式,若已知其幅值,则将其作为复数幅值,若未输入幅值,则将幅值设置为1,将相位图像运用小波变化方式获取不同分辨率的相位图像,其中不同分辨率的层数至少为2,即至少应当具有两个分辨率的图像。(1) Convert the input phase image into a complex number form. If its amplitude is known, take it as a complex amplitude value. If no amplitude value is input, set the amplitude to 1, and use the wavelet transformation method to obtain different phase images. Resolution phase images, where the number of layers with different resolutions is at least 2, that is, there should be at least two resolution images.

(2)设定图像块大小为m=64,运用式3和式4将不同分辨率的图像分割为8×8大小的图像块集合,并且将每一个图像块按照列堆叠方式转化为64×1大小的列向量。(2) Set the image block size to m=64, use Equation 3 and Equation 4 to divide images of different resolutions into 8×8 image block sets, and convert each image block into 64× A column vector of size 1.

(3)指定训练字典的维度为64×256,选择最高的分辨率图像对应的图像块向量集合,运用最小化式6的方式求解稀疏编码字典D。其中最小化式6采用如下两个方法求解,对于稀疏编码字典的训练集编码算法采用变量分解和增广拉格朗日稀疏回归方法求解如下问题:(3) Specify the dimension of the training dictionary as 64×256, select the image block vector set corresponding to the highest resolution image, and solve the sparse coding dictionary D by minimizing Equation 6. Among them, the minimization formula 6 is solved by the following two methods. For the training set encoding algorithm of the sparse encoding dictionary, the variable decomposition and the augmented Lagrangian sparse regression method are used to solve the following problems:

Figure BDA0002609121050000141
Figure BDA0002609121050000141

运用编码进行字典元素的更新,具体如下:Use encoding to update dictionary elements, as follows:

Figure BDA0002609121050000142
Figure BDA0002609121050000142

Figure BDA0002609121050000143
Figure BDA0002609121050000143

其中dj为字典D的第j列。where d j is the jth column of dictionary D.

(4)运用稀疏编码方法对不同分辨率的图像块向量集合进行稀疏编码,稀疏编码的算法为求解式7和式8的算法,在本发明执行中采用贪婪算法来进行稀疏编码的求解,即首先从编码字典中选择一个元素,是的该元素能够表示待编码向量的误差最小,然后再从字典中选的一个元素,使得该元素的加入能够最大限度地降低表示误差,如此循环,直至编码误差小于给定的阈值。如此能够得到编码所需要的字典的元素以及稀疏编码。(4) Use sparse coding method to carry out sparse coding on image block vector sets of different resolutions. The algorithm of sparse coding is the algorithm for solving equations 7 and 8. In the implementation of the present invention, a greedy algorithm is used to solve the sparse coding, that is, First select an element from the encoding dictionary, yes, this element can represent the smallest error of the vector to be encoded, and then select an element from the dictionary so that the addition of this element can minimize the representation error, and so on until the encoding error less than the given threshold. In this way, the elements of the dictionary required for encoding and sparse encoding can be obtained.

(5)根据稀疏编码计算图像块向量组的降噪结果以及编码字典,运用式9和式10求解每一个分割图像块的降噪结果。(5) Calculate the noise reduction result of the image block vector group and the coding dictionary according to the sparse coding, and use Equation 9 and Equation 10 to solve the noise reduction result of each segmented image block.

(6)运用式11和式12计算得到不同分辨率下的降噪结果,将不同分辨率下的降噪结果运用上采样方式获取同样大小图像,并且运用式15将不同分辨率下的降噪结果进行融合。(6) Use Equation 11 and Equation 12 to calculate the noise reduction results at different resolutions, use the upsampling method to obtain the same size image, and use Equation 15 to calculate the noise reduction results at different resolutions The results are fused.

(7)运用式16获取降噪后融合图像的相位,从而获得相位图像的降噪结果。(7) Use Equation 16 to obtain the phase of the fused image after noise reduction, so as to obtain the noise reduction result of the phase image.

本发明方法的优势主要是与现阶段的技术相比,本发明提出了多分辨率复数域自适应词典训练算法和稀疏编码算法进行降噪估计,该方法能够有效降低降噪图像中平滑区域的伪边缘,充分利用相位图像的多分辨率下的自相似性进行降噪。本发明创新之处是提出了一种多分辨率降噪结果的融合方法,运用假设检验的方法将不同分辨率的降噪结果融合,该算法能够有效地滤除由于多分辨率采样过程中的信息损耗,并且有效利用多分辨率的降噪结果。The advantage of the method of the present invention is that compared with the current technology, the present invention proposes a multi-resolution complex number domain adaptive dictionary training algorithm and a sparse coding algorithm for noise reduction estimation, and the method can effectively reduce the noise of the smooth area in the noise reduction image. Pseudo-edge, taking full advantage of the self-similarity of the phase image at multiple resolutions for denoising. The innovation of the present invention is that it proposes a fusion method of multi-resolution noise reduction results. The method of hypothesis testing is used to fuse the noise reduction results of different resolutions. The algorithm can effectively filter out the noise caused by the multi-resolution sampling process. Information loss, and effectively use the multi-resolution noise reduction results.

总体来说,本发明实施例是根据干涉相位图像的自相似性与多分辨率相似性,通过复数域中多分辨率自适应词典训练算法的实现,提出复数域中一种基于多分辨率稀疏编码的相位图像降噪技术,提高复数相位的降噪效果,从而实现合成孔径雷达干涉测量中的相位降噪以及磁共振图像中的相位降噪奠定基础。在本专利中,运用二维小波变换方式获取待降噪相位图像对应复数的多分辨率形式,分别将获得的多分辨率图像进行图像块分割得到图像块集合。然后通过原始相位图像对应复数图像块运用在线训练方式获得复数编码字典,运用训练得到的字典对多分辨率的图像块集合进行编码获得稀疏编码系数。通过编码字典与编码系数相乘的方式获取降噪后图像块。将图像块集合依据分割方式的逆操作进行拼合得到不同分辨率下的降噪结果,将不同分辨率的降噪结果进行融合得到最终的复数的降噪效果,将复数取相位操作得到最终的相位降噪结果。In general, according to the self-similarity and multi-resolution similarity of the interference phase image, the embodiment of the present invention proposes a multi-resolution sparse algorithm in the complex domain through the realization of the multi-resolution adaptive dictionary training algorithm in the complex domain. The coded phase image noise reduction technology improves the noise reduction effect of complex phases, thereby laying the foundation for phase noise reduction in synthetic aperture radar interferometry and phase noise reduction in magnetic resonance images. In this patent, a two-dimensional wavelet transform method is used to obtain the complex multi-resolution form of the phase image to be denoised, and the obtained multi-resolution images are divided into image blocks to obtain an image block set. Then, the complex coding dictionary is obtained by using the online training method corresponding to the complex image blocks of the original phase image, and the sparse coding coefficients are obtained by encoding the multi-resolution image block set using the dictionary obtained by training. The denoised image block is obtained by multiplying the coding dictionary and the coding coefficients. The image block sets are assembled according to the inverse operation of the segmentation method to obtain the noise reduction results under different resolutions, the noise reduction results of different resolutions are fused to obtain the final complex noise reduction effect, and the complex number is obtained by taking the phase operation to obtain the final phase. Noise reduction results.

本发明另一实施例提供了一种计算机可读存储介质,所述计算机可读存储介质存储有信号映射的计算机程序,所述计算机程序被至少一个处理器执行时,以实现上述实施例中任一种所述的多分辨率稀疏编码的相位信息降噪算法。相关内容可参见方法实施例部分进行理解,在此不做详细论述。Another embodiment of the present invention provides a computer-readable storage medium, where the computer-readable storage medium stores a computer program for signal mapping, and when the computer program is executed by at least one processor, implements any of the foregoing embodiments. A phase information noise reduction algorithm of the multi-resolution sparse coding. The related content can be understood by referring to the method embodiment section, and will not be discussed in detail here.

尽管为示例目的,已经公开了本发明的优选实施例,本领域的技术人员将意识到各种改进、增加和取代也是可能的,因此,本发明的范围应当不限于上述实施例。Although the preferred embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, and therefore, the scope of the present invention should not be limited to the above-described embodiments.

Claims (10)

1. A multi-resolution sparsely encoded phase information noise reduction algorithm, comprising:
acquiring a plurality of multi-resolution images corresponding to the phase image to be denoised, and respectively carrying out image block segmentation on each resolution image to obtain an image block set, wherein the image block set is multiple and is respectively and uniquely corresponding to the resolution images;
respectively executing the following steps to any image block set: obtaining a coding dictionary from the image blocks in the image block set through online training, coding the image block set through the coding dictionary to obtain sparse coding coefficients corresponding to the image block set, multiplying the coding dictionary by the sparse coding coefficients to obtain noise-reduced image blocks, and splicing the image block set according to the inverse operation of segmentation to obtain noise-reduced images;
and fusing the noise-reduced images with different resolutions to obtain a final phase image with a plurality of noise-reduced images, and performing phase operation on the complex number to obtain a final phase noise reduction result.
2. The method according to claim 1, wherein the obtaining of the multi-resolution image corresponding to the complex number of the phase image to be noise-reduced comprises:
passing the phase image to be denoised by z ═ eConverting the image into a corresponding complex resolution image, wherein phi is a phase image to be denoised, e is a natural base number, and j is an imaginary unit;
according to the number of layers of the multi-resolution to be acquired, a two-dimensional Harr wavelet transformation mode is applied to acquire complex images z to be denoised with different resolutions(1),z(2),…z(R)And R is the resolution layer number.
3. The method according to claim 2, wherein the separately performing image block segmentation on each resolution image to obtain an image block set comprises:
the complex image z to be denoised(1),z(2),…z(R)Converting the image blocks into column vectors in a column-by-column splicing mode, segmenting the image blocks of the corresponding vectors of the original image according to the sizes of the segmented image blocks, and defining a selection matrix MiSo that z isi=Miz, matrix MiEach row has only one non-zero element and has a value of 1, where ziIs the ith image block; define the following matrix
Figure FDA0002609121040000011
wherein ,NpThe number of image blocks which can be divided by the image z is T, and the T is transposition;
similarly, z for different resolutions(1),z(2),…z(R)Respectively define corresponding partition matrices M(1),M(2),…M(R)By selecting a matrix to segment the original image correspondence vector into sizes
Figure FDA0002609121040000021
M is an integer squared, i.e.:
Figure FDA0002609121040000022
Figure FDA0002609121040000023
4. the method according to claim 3, wherein the obtaining of the coding dictionary by online training of the image blocks of the plurality of phase images to be denoised comprises:
from the collection
Figure FDA0002609121040000024
In-between randomly acquired image block group zt,t=1,…,Ng,NgPerforming dictionary learning according to the image block groups according to a preset sequence for the number of the image blocks in the selected image block groups, wherein each training cycle adopts one of the image block groups to update dictionary elements, namely performing dictionary training by the following minimization formula:
Figure FDA0002609121040000025
5. the method according to claim 1, wherein the step of obtaining sparse coding coefficients corresponding to the set of image blocks comprises:
for the image block set under each resolution, carrying out sparse coding on the column vector corresponding to each image block in the image block set, and for the coding dictionary D obtained by training, if the column vector is matched
Figure FDA0002609121040000026
Each vector z ofiPerforming sparse coding is obtained by solving the following optimization problem
Figure FDA0002609121040000027
With respect to the resolution r of the image,by solving for
Figure FDA0002609121040000028
To obtain optimized sparse coding coefficients, where αiIs ziIn the encoding of the encoding dictionary D,
Figure FDA0002609121040000029
is that
Figure FDA00026091210400000210
Encoding in the encoding dictionary D.
6. The method according to claim 5, wherein said multiplying the coding dictionary by the sparse coding coefficients to obtain the noise-reduced image block comprises:
Figure FDA0002609121040000031
wherein ,NrIs the number of image blocks of the r-th resolution,
Figure FDA0002609121040000032
is ziThe image block after the noise reduction is performed,
Figure FDA0002609121040000033
is composed of
Figure FDA0002609121040000034
And (5) denoising the image block.
7. The method according to claim 5, wherein said stitching the set of image blocks according to an inverse operation of the segmentation to obtain the noise-reduced image comprises:
splicing image block sets under the same resolution according to the following formula to obtain noise-reduced images under different resolutions;
Figure FDA0002609121040000035
Figure FDA0002609121040000036
wherein ,
Figure FDA0002609121040000037
is the result of the noise reduction in z,
Figure FDA0002609121040000038
is z(r)The noise reduction result of (1).
8. The method according to claim 5, wherein the fusing the noise-reduced images with different resolutions to obtain a final complex noise reduction effect comprises:
obtaining a final fusion result by using a hypothesis test mode according to the sequence from high resolution to low resolution, wherein the fusion result of each step is used as the fusion input of the next resolution;
firstly, the first step is to
Figure FDA0002609121040000039
Performing upsampling, obtaining and
Figure FDA00026091210400000310
same size N1×N2Noise reduction result of (2), N1Is composed of
Figure FDA00026091210400000311
Length of (2), N2Is composed of
Figure FDA00026091210400000312
Is assumed to be as follows:
Figure FDA00026091210400000313
Figure FDA00026091210400000314
suppose that
Figure FDA00026091210400000315
Obeying to the zero mean gaussian distribution, where the standard deviation of the gaussian distribution is σ, and under the condition that the confidence coefficient is 0.95, the following condition should be satisfied for each pixel point in the image
Figure FDA00026091210400000316
If the above formula is satisfied, when the resolution is assumed to be r 1, the estimation is performed
Figure FDA0002609121040000041
Is available, otherwise, the estimate may be considered unavailable and will therefore be
Figure FDA0002609121040000042
And
Figure FDA0002609121040000043
the fusion result of (A) is
Figure FDA0002609121040000044
Wherein i is 1,2, …, N1,j=1,2,…,N2
Similarly, zr is added according to the above method1And
Figure FDA0002609121040000045
fusion to give zr2And obtaining a fusion result zr of the noise reduction result with the resolution R of the last stageR
9. The method according to any one of claims 1-8, wherein the phase-extracting the complex number to obtain a final phase noise reduction result comprises:
according to the final fusion result zr of the denoised complex imageRObtaining a complex number zrRPhase angle of (c) is the final phase estimate:
Figure FDA0002609121040000046
wherein imag (-) and real (-) compute the real and imaginary parts, respectively.
10. A computer-readable storage medium, characterized in that the computer-readable storage medium stores a signal mapped computer program which, when executed by at least one processor, implements the multi-resolution sparsely encoded phase information noise reduction algorithm of any one of claims 1-9.
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