One-dimensional Hartley transform and match tracing based image sparse decomposition fast algorithm

Abstract

The invention discloses a one-dimensional Hartley transform and match tracing based image sparse decomposition fast algorithm. The algorithm comprises the following steps of: constructing a core atomic library, converting an original two-dimensional image into a one-dimensional real signal, sparsely decomposing the atoms in the atomic library into one-dimensional atoms, adopting the one-dimensional fast Hartley transform to realize the cross correlation operation of the image or image residual and the atoms, finding the best atom, and finally realizing the decomposition of the image. The algorithm has the advantages of realizing the fast sparse decomposition of the image and having good visual effect of the reconstructed image.

Description

technical field [0001] The invention relates to a fast algorithm for sparse decomposition of matching and tracking images used in still image denoising, image recognition, image compression and the like. Background technique [0002] In the actual engineering application of digital image processing, the expression or decomposition of digital image is a key link. In 1994, Mallat et al proposed a matching pursuit (Matching Pursuit, matching pursuit) method for image sparse decomposition (BERGEAU F, MALLAT S.Matching pursuit of images.Proceedings ofIEEE-SP.Piladel-phia, PA, USA, 1994.330-333 ). Since then, the application of sparse decomposition in the field of image processing has been continuously developed. In image sparse decomposition, the key to realize time-frequency search is to select which type of atoms to construct over-complete atomic library. For the over-complete atomic library, in order to better represent the image content, the researchers proposed the asymme...

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Problems solved by technology

For this reason, researchers proposed to use genetic algorithm (Li Hengjian, Yin Zhongke, Wang Jianying. Image sparse decomposition based on quantum genetic algorithm [J]. Southwest Jiaotong University Journal. 2007, 42(1): 19-23) to improve its calculation speed , however, since the genetic algorithm is an optimization algorithm for local search, it is difficult to find the optimal time-frequency atom among all the atoms, resulting in a poor reconstructed image; other similar methods based on intelligent computing have similar problems (Li Hengjian , Yin Zhongke, Zhang Jiashu, Wang Jianying. Image sparse decomposition based on chaotic mutation particle swarm optimization algorithm [J]. Southwest Jiaotong University Journal. 2008, 43(4)509-513); A Fast Algorithm for Generating Atoms According to the Classification Properties of Atomic Structures (Hua Zexi, Yin Zhongke, Huang Xionghua. A Fast Algorithm for Atom Formation in Signal Decomposition on Overcomplete Library[J]. Journal of Southwest Jiaotong University, 2005, 40(3): 402 -405.), this method improves the calculation speed to a certain extent, but still requires a large number of high-dimensional inner product operations.; In order to find the best atom in the whole world, some scholars propose to use the Fast Fourier Transform (FFT) , FFT) to achieve cross-correlation operations to find the best atom, but the fast Fourier transform involves complex operations, and the real signal needs to be artificially added with imaginary variables, which increases the complexity of the calculation, and the calculation speed is limited; in the fast Fourier transform On the basis of the leaf transform algorithm, for one-dimensional real signals, Liu Hao et al. proposed a fast algorithm using Fast Hartley Transform (FHT) to realize matching pursuit (Liu Hao, Pan Wei. Fast Algorithm for Sparse Decomposition of Real Signals Based on FHT [J]. Journal of Southwest Jiaotong University. 2009, 44 (1)), this algorithm is superior to the matching pursuit fast algorithm based on fast Fourier transform in terms of calculation speed, and it is also a global search algorithm, which avoids the genetic algorithm It can only achieve the limitation of local optimal search, but it can only achieve one-dimensional real signal decomposition

[0004] In a word, image sparse decomposition using matching pursuit method has achieved success in denoising of still images, image recognition and image compression, but it is still difficult to be promoted and industrialized at present, the main reason is that the matching of image sparse decomposition The amount of tracking calculation is huge, and the calculation time is unbearable under the existing conditions

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