KR102252359B1 - Method and apparatus for restoring signal by using compressive sensing - Google Patents

Abstract

A signal restoration method using compression sensing and a device thereof are disclosed. The signal restoration method using compression sensing comprises the following steps of: receiving a measurement signal; reconstructing the measurement signal according to a magnitude order; and calculating an optimal solution for a linear measurement equation of the reconstructed measurement signal in a frequency domain.

Description

Signal restoration method and apparatus using compression sensing {METHOD AND APPARATUS FOR RESTORING SIGNAL BY USING COMPRESSIVE SENSING}

The present invention relates to a method and apparatus for reconstructing an original signal for a measurement signal, and more particularly, to a method and apparatus for reconstructing a signal using compression sensing.

Existing information/communication systems have been developed mainly on digital systems designed based on Sampling Theorem by Shannon and Nyquist. It is Shannon-Nyquist's sampling theory that if you sample at least twice the highest frequency of the signal, the signal can be accurately restored to an analog signal. Until today, this theory has been faithfully used as a basic theory for building a digital system. Has been used.

However, recently, a compression sensing theory capable of completely recovering a signal without sampling a signal above the Nyquist rate is receiving a lot of interest.

Compression sensing theory notes that most commonly handled signals are so-called sparse signals whose most values are zero when they are transformed into a certain signal space. Signals transformed into the frequency domain through Fourier transform are mostly sparse signals with a magnitude F of 0 at frequency x and a non-zeor value of magnitude F at a relatively small number of x. .

According to compression sensing theory, these sparse signals can be almost completely restored to the original signal with very few linear measurements.

The essence of compression sensing theory can be summarized as finding the optimal solution of the linear equation y=Ax. Here, y is a measurement signal, A is a linear measurement matrix, and x is an original signal for the measurement signal. That is, this linear measurement equation is defined as a linearly measured signal y obtained by multiplying the original signal x by a certain matrix.

Since this linear equation is an under-determined system, there are many solutions for the original signal x, and among these solutions, the optimal solution can be calculated through _{L 0} -optimization (Optimization or minimization), L ₁ -optimization, or L _{2 -optimization techniques.} I can.

As related prior documents, Korean Patent Nos. 10-1526774, 10-1580532, Korean Patent Publication No. 2019-0042982, which are patent documents, non-patent documents, "Introduction to Compression Sensing, Heung-no Lee, Sang-jun Park, Soon-cheol Park, 2011 Monthly Journal of Electronics Engineers Vol. 38, No. 1, is available.

An object of the present invention is to provide a signal restoration method capable of further increasing the accuracy of signal restoration using compression sensing.

According to an embodiment of the present invention for achieving the above object, receiving a measurement signal; Reconstructing the measurement signal according to the order of magnitude; And calculating an optimal solution to the linear measurement equation of the reconstructed measurement signal in a frequency domain.

In addition, according to another embodiment of the present invention for achieving the above object, according to the order of magnitude, the reconstruction unit for reconstructing the measurement signal; An optimum solution calculator for calculating an optimum solution for the linear measurement equation of the reconstructed measurement signal in a frequency domain; And an inverse transform unit for inversely transforming the optimal solution into a time domain value.

According to an embodiment of the present invention, the leanness of the measurement signal is increased, so that the accuracy of the optimal solution to the original signal may be improved.

In addition, according to an embodiment of the present invention, even when some data of the measurement signal is lost, the original signal can be accurately restored.

1 is a diagram illustrating a signal recovery apparatus using compression sensing according to an embodiment of the present invention.
2 is a diagram for explaining a signal recovery method using compression sensing according to an embodiment of the present invention.
3 to 5 are diagrams for explaining a restoration result of a signal restoration method according to an embodiment of the present invention.

In the present invention, various modifications may be made and various embodiments may be provided, and specific embodiments will be illustrated in the drawings and described in detail in the detailed description. However, this is not intended to limit the present invention to a specific embodiment, it should be understood to include all changes, equivalents, and substitutes included in the spirit and scope of the present invention. In describing each drawing, similar reference numerals have been used for similar elements.

As described above, compression sensing is a theory of restoring a signal based on sparsity of a measured signal, and an optimal solution to the original signal can be more accurately calculated as the slackness increases.

In view of this, the present invention restores the original signal from the measurement signal by calculating an optimal solution to the original signal by increasing the leanness of the measurement signal. According to an embodiment of the present invention, in order to increase the leanness of the measurement signal, after reconstructing the measurement signal according to the order of magnitude, an optimal solution to the original signal is calculated from a linear conversion equation of the reconstructed measurement signal. In this way, the linearity of the reconstructed measurement signal increases, and since the period in which the data rapidly changes decreases, a high frequency component of the reconstructed measurement signal decreases, and the leanness of the measurement signal may increase.

The signal restoration method according to an embodiment of the present invention can be applied to all technical fields of receiving and restoring a measurement signal based on compression sensing, such as a communication system, an image processing device, and a power system.

The signal restoration method according to an exemplary embodiment of the present invention may be performed in a computing device including a processor, and as an exemplary embodiment, it may be performed in a desktop, a laptop computer, a server, or a separate signal restoration apparatus.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

1 is a diagram illustrating a signal recovery apparatus using compression sensing according to an embodiment of the present invention.

Referring to FIG. 1, a signal restoration apparatus according to an embodiment of the present invention includes a reconstruction unit 110, an optimum solution calculation unit 120, and an inverse transform unit 130.

The reconstruction unit 110 reconstructs the measurement signal according to the order of magnitude. The reconfiguration unit 110 may reconstruct the measurement signal by rearranging the sampling data for the measurement signal in the time domain in an ascending or descending order according to an embodiment.

The measurement signal may vary according to an embodiment in which the signal recovery device is used. For example, in a communication system, a measurement signal may be a reception signal from a receiving device, and a measurement signal from an image processing device may be an image signal. Alternatively, in the power system, measurement data on the amount of power consumption or generation may correspond to the measurement signal.

In addition, the sampling data is data in which a continuous measurement signal in the time domain is sampled according to a sampling frequency according to compression sensing. The measurement signal can be sampled according to this sampling frequency.

The optimum solution calculator 120 calculates an optimum solution for the linear measurement equation of the reconstructed measurement signal in the frequency domain.

The optimal solution calculator 120 performs Fourier transform on the reconstructed measurement signal, converts the reconstructed measurement signal into a frequency domain signal, and then, as an embodiment, may calculate an optimum solution using _{L 1 -optimization.} . And for L ₁ -optimization, an optimal solution calculation algorithm such as Operator Splitting QP Solver can be used.

The inverse transform unit 130 inversely transforms the optimal solution calculated in the frequency domain into a time domain value, and may calculate a time domain value through an inverse Fourier transform. At this time, since the optimal solution calculated in the frequency domain is an optimal solution calculated from the reconstructed measurement signal, the inverse transform unit 130 uses an index for the sampled data before reconstruction to obtain the time domain value of the optimum solution for the measurement signal before reconstruction. I can.

According to an embodiment of the present invention, the leanness of the measurement signal is increased, so that the accuracy of the optimal solution to the original signal may be improved.

FIG. 2 is a diagram for explaining a signal restoration method using compression sensing according to an embodiment of the present invention. In FIG. 2, a signal restoration method of the above-described signal restoration apparatus is described as an embodiment.

The signal recovery apparatus according to an embodiment of the present invention receives a measurement signal (S210). As an example, the measurement signal may be input in the form of an analog signal or may be input in the form of pre-sampled data according to a sampling frequency according to compression sensing. When input in the form of an analog signal, the signal recovery device may sample the measurement signal according to a preset sampling frequency.

Then, the signal recovery apparatus reconstructs the measurement signal according to the order of magnitude of the measurement signal (S220). The signal recovery apparatus may reconstruct the measurement signal by rearranging the sampled data for the measurement signal in an ascending or descending order according to an exemplary embodiment. When the input measurement signal is y, _{the relationship between the reconstructed measurement signal y s} and the input measurement signal may be expressed as [Equation 1].

는, 벡터 형태의 측정 신호 y를 크기 순서에 따라서 재구성하는 재구성 오퍼레이터를 나타낸다.here,

Denotes a reconstruction operator that reconstructs the vector-shaped measurement signal y in order of magnitude.

In addition, the signal recovery apparatus calculates an optimal solution to the linear measurement equation of the reconstructed measurement signal in the frequency domain (S230). The linear measurement equation for the reconstructed measurement signal may be expressed as [Equation 2], and the signal recovery apparatus may calculate an optimal solution for [Equation 2] through _{L 1 -optimization.}

는 재구성된 측정 신호에 대한 원신호를 나타내며, 벡터 형태로 표현될 수 있다.Where G denotes a linear measurement matrix,

Denotes the original signal for the reconstructed measurement signal, and may be expressed in a vector form.

The optimal solution in the frequency domain may be transformed into an optimal solution in the time domain through an inverse Fourier transform. At this time, since the optimum solution in the frequency domain is calculated from the reconstructed measurement signal, and the optimum solution to be finally obtained is the optimum solution to the original signal of the measurement signal before reconstruction, the signal recovery apparatus according to an embodiment of the present invention , The time domain value is restored according to the index for the sampling data of the input measurement signal.

That is, the signal recovery apparatus according to an embodiment of the present invention generates the time domain value of the optimal solution calculated in the frequency domain, and then, according to the index for the sampling data, the time domain value of the original signal for the input measurement signal. To restore. Since the index allocated to the reconstructed sampled data indicates an order before reconstruction of the sampled data, the time domain value of the original signal for the measured signal input through the index may be restored.

The signal recovery apparatus may convert the sorting order of the reconstructed sampling data to the sorting order before reconstruction, using the index for the sampling data of the input measurement signal, and as the sorting order of the reconstructed sampling data is converted, The order of each element of the time domain value vector is also rearranged, and as a result, the time domain value of the original signal for the input measurement signal can be restored. This can be expressed in Equation 3 as shown in [Equation 3].

는 재구성 오퍼레이터

에 대한 역변환 오퍼레이터로서, 재구성된 샘플링 데이터를 재구성전의 순서로 변환하는 오퍼레이터이다.here,

The reconfiguration operator

It is an operator that converts reconstructed sampled data in the order before reconstruction.

On the other hand, when loss data is included in the measurement signal, reconstruction is not necessary for the loss data, so the signal recovery apparatus according to an embodiment of the present invention generates a lossless data vector and a loss data vector from the sampling data of the input measurement signal. And, the lossless data vector can be reconstructed in ascending or descending order. The lossless data is data in which a measurement value exists, the loss data is data in which a measurement value does not exist, and the loss data vector may be composed of a preset null value.

으로 표현될 수 있으며, 이 경우, 무손실 데이터 벡터 및 손실 데이터 벡터에 대한 선형 측정식은 [수학식 4]와 같이 표현될 수 있다.If the reconstructed lossless data vector with measurement values is expressed as m and the lossy data vector without measurement values is expressed as u, the reconstructed measurement signal is

In this case, the lossless data vector and the linear measurement equation for the lossy data vector can be expressed as [Equation 4].

와 같은 관계이며, 선형 측정 행렬 C는 선형 측정 행렬 G의 영공간(null space)에 대한 벡터를 나타낸다.Here, the linear measurement matrix G and the linear measurement matrices B and C are

The relationship is the same as, and the linear measurement matrix C represents a vector for the null space of the linear measurement matrix G.

Since [Equation 4] has the same form as [Equation 2], the signal recovery apparatus may calculate an optimal solution for [Equation 4] through _{L 1 -optimization as described above.}

3 to 5 are diagrams for explaining a restoration result of a signal restoration method according to an embodiment of the present invention, and are diagrams for explaining a restoration result when loss data is included in a measurement signal.

3 is a diagram showing a measurement signal as in [Equation 5], and a red point in FIG. 3 indicates sampled data.

When data of a certain section 310 is lost among these sampling data, a result of restoring the measurement signal according to the linear measurement equation without reconstructing the measurement signal is shown in FIG. 4. In FIG. 4, a red point (measured) represents the original signal as well as the measurement signal, and the solid line (reconstructed) represents the reconstruction result of the original signal. It can be seen that there is a considerable error between the original signal and the reconstruction result.

On the other hand, FIG. 5(b) is a diagram showing the result of reconstructing the lossless data of the measurement signal in ascending order as shown in FIG. 5(a), and it can be seen that the original signal and the restoration result are substantially the same.

As described above, according to an embodiment of the present invention, even when some data of the measurement signal is lost, the original signal can be accurately restored.

The above-described technical contents may be implemented in the form of program instructions that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, etc. alone or in combination. The program instructions recorded on the medium may be specially designed and configured for the embodiments, or may be known and usable to those skilled in computer software. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tapes, optical media such as CD-ROMs and DVDs, and magnetic media such as floptical disks. -A hardware device specially configured to store and execute program instructions such as magneto-optical media, and ROM, RAM, flash memory, and the like. Examples of program instructions include not only machine language codes such as those produced by a compiler, but also high-level language codes that can be executed by a computer using an interpreter or the like. The hardware device may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

As described above, in the present invention, specific matters such as specific components, etc., and limited embodiments and drawings have been described, but this is provided only to help a more general understanding of the present invention, and the present invention is not limited to the above embodiments. , If a person of ordinary skill in the field to which the present invention belongs, various modifications and variations are possible from these descriptions. Accordingly, the spirit of the present invention is limited to the described embodiments and should not be defined, and all things that are equivalent or equivalent to the claims as well as the claims to be described later fall within the scope of the inventive concept. .

Claims (9)

Receiving a measurement signal;
Reconstructing the measurement signal according to the order of magnitude; And
Computing an optimal solution to the linear measurement equation of the reconstructed measurement signal in a frequency domain,
Reconstructing the measurement signal comprises:
Generating a lossless data vector and a lossy data vector from the sampled data of the measurement signal; And
Reconstructing the lossless data vector in ascending or descending order,
The linear measurement equation is
The following equation
Signal recovery method using compression sensing.
[Equation]

Here, the reconstructed measurement signal y _s is

And the linear transformation vector G is

Is,

Is the original signal for the reconstructed measurement signal,

And m is the reconstructed lossless data vector, and u is the lossy data vector.
delete delete delete The method of claim 1,
The sampled data is
Data sampled according to the sampling frequency according to compression sensing
Signal recovery method using compression sensing.
The method of claim 1,
Generating a time domain value of the optimal solution calculated in the frequency domain; And
Restoring the time domain value according to the index allocated to the sampling data
Signal restoration method using compression sensing further comprising a.
A reconstruction unit for reconstructing the measurement signal according to the order of magnitude;
An optimum solution calculator for calculating an optimum solution for the linear measurement equation of the reconstructed measurement signal in a frequency domain; And
And an inverse transform unit for inversely transforming the optimal solution into a time domain value,
The reconfiguration unit
From the sampling data of the measurement signal, a lossless data vector and a lossy data vector are generated, and the lossless data vector is reconstructed in ascending or descending order,
The linear measurement equation is
The following equation
Signal recovery device using compression sensing.
[Equation]

Here, the reconstructed measurement signal y _s is

And the linear transformation vector G is

Is,

Is the original signal for the reconstructed measurement signal,

And m is the reconstructed lossless data vector, and u is the lossy data vector.
delete The method of claim 7,
The inverse transform unit
Restoring the time domain value according to the index assigned to the sampling data
Signal recovery device using compression sensing.

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