Method for recovering quaternion field color image in low sampling frequency

Abstract

The invention discloses a method for recovering a quaternion field color image in a low sampling frequency, and belongs to the technical field of digital picture processing. Firstly, a color image is expressed in a quaternion field, namely, values of an R component, a G component and a B component of the color image are respectively placed in three imaginary parts of a quaternion; and then downsampling is conducted to an original whole color image by utilizing an even stochastic matrix, and part of the sampled color image is obtained; furthermore, part of the color image is stored or conveyed; and finally the original color image is recovered through the part of the sampled color image by utilizing a real number expression form of the quaternion and quaternion matrix filling theory. The method for recovering the quaternion field color image in the low sampling frequency improves precision of recovering of the color image in the low sampling frequency and meanwhile simplifies complexity of sampling and storage content of data by utilizing a characteristic that a quaternion algorithm is good in binding force.

Description

technical field

[0001] The invention relates to a method for restoring a color image in a quaternion domain at a low sampling rate, and belongs to the technical field of digital image processing. Background technique

[0002] Quaternion q is a special hypercomplex number, which is an extended form of complex numbers. The quaternion q consists of 1 real part and 3 imaginary parts:

[0003] q=R(q)+I(q)i+J(q)j+K(q)k(1)

[0004] Among them, R(q), I(q), J(q), Indicates the field of real numbers, i, j, k are three imaginary units, satisfying the following properties:

[0005] i 2 = j 2 =k 2 =ijk=-1(2)

[0006] ij=-ji=k, jk=-kj=i, ki=-ik=j (3)

[0007] The conjugate and modulus of a quaternion are defined as:

[0008] q ‾ = R ( q ) - I ( q ) i - J ( ...

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