WO2021145631A1

WO2021145631A1 - Method and device for restoring signal using compressive sensing

Info

Publication number: WO2021145631A1
Application number: PCT/KR2021/000363
Authority: WO
Inventors: 박문규
Original assignee: 세종대학교산학협력단
Priority date: 2020-01-15
Filing date: 2021-01-12
Publication date: 2021-07-22
Also published as: KR102252359B1

Abstract

Disclosed are a method and a device for restoring a signal using compressive sensing. The disclosed method for restoring a signal using compressive sensing comprises the steps of: receiving input of measurement signals; reconstructing the measurement signals in order of size; and calculating an optimal solution for a linear measurement equation of the reconstructed measurement signals in a frequency domain.

Description

Signal restoration method and apparatus using compression 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 for digital systems designed based on the Sampling Theorem by Shannon and Nyquist. Shannon-Nykist's sampling theory is that the signal can be accurately restored back to an analog signal by sampling at more than twice the maximum frequency of the signal. To this day, this theory has been faithfully maintained as a basic theory for building digital systems. has been used

However, recently, a compression sensing theory capable of reconstructing a complete signal without sampling the signal above the Nyquist rate has received much attention.

Compression sensing theory pays attention to the so-called sparse signals with most of the values of 0 when transformed into a specific signal space. Most of the signals transformed into the frequency domain through Fourier transform are sparse signals in which magnitude F is 0 at frequency x, and a relatively small number of x values in magnitude F represent non-zero values. .

According to the compressed sensing theory, such a sparse signal can be almost completely restored to the original signal with a very small number of linear measurements.

The core of compressive 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, in this linear measurement equation, y obtained by multiplying the original signal x by a certain matrix is defined as a linearly measured signal.

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.} can

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, the step of receiving a measurement signal; reconstructing the measurement signal according to the magnitude order; 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 calculation unit for calculating an optimum solution for the linear measurement equation of the reconstructed measurement signal in a frequency domain; and an inverse transform unit configured to inversely transform the optimal solution into a time domain value.

According to an embodiment of the present invention, the accuracy of the optimal solution for the original signal may be improved by increasing the sparseness of the measurement signal.

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 view for explaining a signal restoration apparatus using compression sensing according to an embodiment of the present invention.

2 is a diagram for explaining a signal restoration 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.

Since the present invention can have various changes and can have various embodiments, specific embodiments are illustrated in the drawings and described in detail in the detailed description. However, this is not intended to limit the present invention to specific embodiments, and it should be understood to include all modifications, equivalents and substitutes included in the spirit and scope of the present invention. In describing each figure, like reference numerals have been used for like elements.

As described above, compression sensing is a theory of reconstructing a signal based on the sparsity of the measurement signal, and as the sparsity increases, the optimal solution for the original signal can be more accurately calculated.

In view of this, the present invention restores the original signal from the measurement signal by increasing the sparseness of the measurement signal and calculating an optimal solution for the original signal. In one embodiment of the present invention, in order to increase the sparseness of the measurement signal, the measurement signal is reconstructed according to the magnitude order, and then an optimal solution to the original signal is calculated from the linear transformation equation of the reconstructed measurement signal. As described above, the linearity of the reconstructed measurement signal is increased, and the section in which data is rapidly changed is reduced, so that a high frequency component of the reconstructed measurement signal may decrease and the sparseness of the measurement signal may increase.

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

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

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

Referring to FIG. 1 , the signal restoration apparatus according to an embodiment of the present invention includes a reconstruction unit 110 , an optimal 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 reconstruction unit 110 may reconstruct the measurement signal by rearranging the sampling data for the measurement signal in the time domain in an ascending order or a descending order according to an embodiment.

The measurement signal may vary according to an embodiment in which the signal restoration apparatus is used. For example, in a communication system, a measurement signal may be a reception signal of a receiving device, and a measurement signal of 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 may be sampled according to this sampling frequency.

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

The optimal solution calculator 120 may perform a Fourier transform on the reconstructed measurement signal, convert the reconstructed measurement signal into a signal in the frequency domain, and, as an embodiment, calculate the optimal solution using _{L 1 -optimization.} . And for L ₁ -optimization, an optimal solution calculation algorithm such as Operator Splitting QP Solver may 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 the optimal solution calculated from the reconstructed measurement signal, in order to obtain the time domain value of the optimal solution for the measurement signal before reconstruction, the inverse transform unit 130 uses the index for the sampling data before reconstruction. can

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

The signal restoration 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 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 restoration apparatus may sample the measurement signal according to a preset sampling frequency.

And the signal restoration apparatus reconstructs the measurement signal according to the order of magnitude of the measurement signal (S220). The signal restoration apparatus may reconstruct the measurement signal by rearranging sampling data for the measurement signal in an ascending order or a descending order according to an 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 in [Equation 1].

here,

denotes a reconstruction operator that reconstructs the vector-shaped measurement signal y according to the magnitude order.

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

where G represents the linear measurement matrix,

represents 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 for the original signal of the measurement signal before reconstruction, the signal restoration apparatus according to an embodiment of the present invention is , restores the time domain value according to the index to the sampling data of the input measurement signal.

That is, the signal restoration 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 sampling data indicates the order before reconstruction of the sampling data, the time domain value of the original signal for the input measurement signal through the index can be restored.

The signal restoration apparatus may convert the sort order of the reconstructed sampling data to the sort order before the reconstruction by using an index for the sampling data of the input measurement signal, and as the sort order of the reconstructed sampling data is converted, The order of each element of the time domain value vector is also rearranged, and eventually, the time domain value of the original signal for the input measurement signal can be restored. Expressing this as an equation is [Equation 3].

here,

is the reconstruction operator

As an inverse transform operator for , it is an operator that transforms the reconstructed sampling data in the order before reconstruction.

On the other hand, when loss data is included in the measurement signal, since reconstruction is unnecessary for the lost data, the signal restoration apparatus according to an embodiment of the present invention generates a lossless data vector and a lossy data vector from sampling data of the input measurement signal. And, it is possible to reconstruct the lossless data vector in ascending or descending order. The lossless data is data in which a measured value exists, the loss data is data in which a measured value does not exist, and the lossy data vector may include a preset null value.

If the reconstructed lossless data vector with the measured value is expressed as m and the lossy data vector without the measured value as u, the reconstructed measurement signal is

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

Here, the linear measurement matrix G and the linear measurement matrices B and C are

, 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 restoration apparatus may calculate an optimal solution to [Equation 4] through _{L 1 -optimization, as described above.}

3 to 5 are views 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 illustrating a measurement signal as in [Equation 5], and black points shown in FIG. 3 indicate sampled data.

When the data of the predetermined section 310 of the sampling data is lost, the result of reconstructing the measurement signal according to the linear measurement equation without reconstructing the measurement signal is shown in FIG. 4 . The black point (measured) shown in FIG. 4 represents the original signal as well as the measured signal, and the solid line (reconstructed) represents the restoration result for the original signal. It can be seen that there is a significant error between the original signal and the restoration result. there is.

On the other hand, FIG. 5(b) is a diagram showing the restored result after 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 restored result are almost the same.

As such, 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 technical contents described above 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 available to those skilled in the art of computer software. Examples of the computer-readable recording medium include magnetic media such as hard disks, floppy disks and magnetic tapes, optical media such as CD-ROMs and DVDs, and magnetic such as floppy disks. - includes magneto-optical media, and hardware devices specially configured to store and carry out program instructions, such as ROM, RAM, flash memory, and the like. Examples of program instructions include not only machine language codes such as those generated by a compiler, but also high-level language codes that can be executed by a computer using an interpreter or the like. A 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, the present invention has been described with specific matters such as specific components and limited embodiments and drawings, but these are provided to help a more general understanding of the present invention, and the present invention is not limited to the above embodiments. , various modifications and variations are possible from these descriptions by those of ordinary skill in the art to which the present invention pertains. Therefore, the spirit of the present invention should not be limited to the described embodiments, and not only the claims to be described later, but also all those with equivalent or equivalent modifications to the claims will be said to belong to the scope of the spirit of the present invention. .

Claims

receiving a measurement signal;

reconstructing the measurement signal according to the magnitude order; and

calculating an optimal solution to the linear measurement equation of the reconstructed measurement signal in the frequency domain

A signal restoration method using compression sensing comprising a.
The method of claim 1,

The step of reconstructing the measurement signal is

Reconstructing the sampling data for the measurement signal in ascending or descending order

A signal reconstruction method using compressed sensing.
3. The method of claim 2,

The step of reconstructing the measurement signal is

generating a lossless data vector and a lossy data vector from the sampling data; and

reconstructing the lossless data vector in the ascending or descending order

A signal restoration method using compression sensing comprising a.
4. The method of claim 3,

The linear measurement formula

the formula below

A signal reconstruction method using compressed 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,
, where m is the reconstructed lossless data vector, and u is the lossy data vector.
3. The method of claim 2,

The sampling data is

Data sampled according to the sampling frequency according to compression sensing

A signal reconstruction method using compressed sensing.
3. The method of claim 2,

generating a time domain value of the optimal solution calculated in the frequency domain; and

Restoring the time domain value according to the index for the sampling data

A signal restoration method using compression sensing comprising a.
a reconstruction unit for reconstructing the measurement signal according to the order of magnitude;

an optimum solution calculation unit for calculating an optimum solution for the linear measurement equation of the reconstructed measurement signal in a frequency domain; and

An inverse transform unit that inversely transforms the optimal solution into a time domain value

A signal restoration apparatus using compression sensing comprising a.
8. The method of claim 7,

The reconstruction unit

Reconstructing the sampling data for the measurement signal in ascending or descending order

A signal restoration device using compression sensing.
9. The method of claim 8,

The inverse transform unit

Restoring the time domain value according to the index for the sampling data

A signal restoration device using compression sensing.