Method and device for digital image interpolation

Abstract

The invention discloses a digital image interpolation method and a device which is used for carrying out interpolation treatment for digital image signals, wherein, the method comprises the following steps: obtaining a digital image signal and generating a matrix equation set; carrying out filtering for the matrix equation set in a FIR filtering mode based on linear system decomposition algorithm and Demko lemma to obtain an interpolation, and inserting the obtained interpolation into the corresponding digital image signal. Thus, the digital image interpolation method and the device provided by the embodiment of the invention does not need carrying out complex inverse transformation computation for the matrix equation set obtained according to the digital image signal, thereby realizing rapid digital image interpolation, reducing amount of calculation and improving the efficiency of interpolation.

Description

technical field [0001] The invention relates to a technology for correcting digital images, in particular to a method and device for interpolating digital images. Background technique [0002] A digital signal is a discrete representation of a continuous signal. For example, a digital image is the brightness and chrominance digital information formed by sampling and quantizing the continuous image information in nature. This process turns a continuous signal into a finite and definite discrete The application of this digital technology to images facilitates the storage and transmission of images. For digital images, the size of the image is different from the continuous signal, which is measured in the unit of pixel number, that is, in the unit of image resolution. For example, 1024*768 usually means that the image has a width of 1024 pixels and a height of 768 Pixels, if an image with this resolution is displayed on the display, each pixel corresponds to a display element ...

AI Technical Summary

Problems solved by technology

If a polynomial is determined based on all the signals on the digital image, the calculation process is very huge. For example, for a signal with 720 sampling points, it is necessary to perform a multiplication operation with a scale of 720×720, and it is also necessary to reread all the signal points, which requires a large amount of calculation; In addition, polynomial interpolation also has essential defects: Oscillating Runge phenomenon, high-order interpolation polynomials do not converge to the interpolated function

This interpolation method also has some inherent defects: first, its overall piecewise polynomial can only guarantee continuity, and the derivative of the function may be discontinuous, which means that the obtained function may even be non-smooth, that is, a polynomial higher than 3 degrees It is also impossible to avoid this defect; secondly, the function in each segment of the interpolation is uniquely determined by many surrounding points, especially at high order, the function can guarantee a good overall characteristic, but when the signal is not stable, it is different from the front and back Combining many related signals into a function is actually meaningless, and it cannot guarantee the local characteristics of the signal; finally, there is also an oscillation phenomenon in high-order Lagrange interpolation, which is called the Runge phenomenon. The reason is still that an N-order polynomial can be completely determined by N+1 points

[0157] It can be seen from the above description that the existing third-order spline interpolation catch-up method and B-spline interpolation filter have advantages and disadvantages in realization

[0158] For tridiagonal matrices formed by third-order spline interpolation, the catch-up method can be used for fast calculation, but the catch-up method itself can only be applied to tridiagonal matrices, and it is not practical for matrices generated by other high-order interpolation, so It limits its scope of application. In addition, the catch-up method still needs to read and store a large amount of data before it can get the calculation results, and the resource (especially memory) consumption is still relatively large.

[0159] For B-spline interpolation, using the traditional method of solving linear equations requires a lot of calculation; while using the filter method to realize B-spline interpolation calculation, IIR filtering is used, although the calculation is relatively simple, but As far as the nature of filtering is concerned, it cannot achieve linear phase

In addition, in the process of B-spline fitting interpolation calculation, since the key is to solve the equation of ΦA=BF, the key in the third-order spline fitting is to solve the linear equation, which requires matrix inversion operation, using the current Whether it is a direct solution, LU decomposition, or iterative method, the amount of calculation is very large

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