Quaternion field colored image compressed sensing recovery method based on Quasi Newton algorithm

Abstract

The invention discloses a quaternion field colored image compressed sensing recovery method based on a Quasi Newton algorithm. The quaternion field colored image compressed sensing recovery method comprises the following steps of: converting a colored image two-dimensional matrix to a two-dimensional matrix of the quaternion field; and carrying out compressed sensing on the two-dimensional matrix of the quaternion field once to recover the original colored image, so that the operation time is saved in comparison with a conventional method of carrying out compressed sensing on the three vectors, i.e. RGB (Red, Green, Blue) of the colored image respectively. According to the quaternion field colored image compressed sensing recovery method based on the Quasi Newton algorithm disclosed by the invention, a quaternion matrix signal is written into an Euler form of a quaternion, the amplitude and the phase are adopted as novel bound terms of compressed sensing optimization problems, therefore, the recovery effect is better in comparison with the conventional method which converts the data of the three channels, i.e. RGB of the colored image into three real-number two-dimensional matrixes for being processed respectively. According to the quaternion field colored image compressed sensing recovery method based on the Quasi Newton algorithm disclosed by the invention, the result image is a mean value of an image obtained by carrying out compressed sensing decoding in rows and an image obtained by carrying out compressed sensing decoding in columns, therefore, the obtained image is smoother than the image which is recovered by being processed only in rows or in columns.

Description

technical field [0001] The invention relates to a quaternion domain color image compression sensing restoration method based on a pseudo-Newton method, belonging to the technical field of digital image processing. Background technique [0002] The theory of Compressed Sensing (CS) points out that as long as the signal is compressible or sparse in a certain transform domain, an observation matrix unrelated to the transform base can be used to project the transformed high-dimensional signal to a low-dimensional signal. dimensional space, and then the original signal can be reconstructed with high probability from these few projections by solving an optimization problem. Its theoretical framework is as figure 1 As shown, the CS information matrix A=ΦΨ* in the figure, where Φ is the measurement matrix, Ψ is the sparse matrix, and the superscript "*" indicates the conjugate transpose. The figure shows: [0003] (1) The ultimate goal of CS is to recover the original signal with...

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Problems solved by technology

[0027] At present, the processing of color images by compressed sensing adopts the traditional way of processing the three components of RGB separately, without considering the correlation between the three channel data, which makes the constraint information of the restoration algorithm not perfect enough, and the restored image effect is not satisfactory. ideal effect

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