Compressive sensing method based on principal component analysis

Abstract

The invention discloses a compressive sensing method based on principal component analysis and mainly solves the problem of low sampling efficiency in the prior art. The method comprises the following steps of: (1) taking z images from a gray natural image library, taking a 32*32 sub-block from each image which is taken at intervals of three pixels along the horizontal and vertical directions to form a training sample set x1, x2, ..., and xm, and training a full-rank observation matrix Phi(f) for the training sample set x1, x2, ..., and xm by using a principal component analysis method, wherein z is not less than 15 and not more than 25, and m is the quantity of training samples; (2) dividing an image which is required to be sampled into n 32*32 sub-blocks x1, x2, ..., and xn, acquiring an observation matrix Phi according to sampling rate s and the full-rank observation matrix Phi(f), sampling each image sub-block by using the observation matrix Phi, and thus obtaining an observation vector y; (3) acquiring an initial solution x0 of the image according to the observation vector y; and (4) iterating according to the initial solution x0 until iteration is in accordance with end conditions, and thus obtaining a reconstructed image x'. The compressive sensing method has the advantages of high sampling efficiency, high image reconstruction quality and clear principle, and is easy to operate and applicable to sampling and reconstruction of a natural image.

Description

technical field [0001] The invention belongs to the field of digital image processing, and in particular relates to a method of using principal component analysis to train a sampling matrix, which can be used for sampling and reconstructing natural images. Background technique [0002] Today's society is an information society. People's pursuit of information not only stays in the quantity, but also has requirements for the speed of signal acquisition, that is, how to obtain the required information quickly and accurately, while avoiding the failure of redundant information as much as possible. Acquisition and processing. Compressed sensing theory is an emerging signal sampling strategy, which successfully integrates the signal sampling process and compression process. The premise of this theory is to collect, encode and decode data under the condition that the signal is known to be sparse or compressible. Its core is mainly to reduce the cost of measuring the signal. In t...

AI Technical Summary

Problems solved by technology

In fact, the wavelet transform has weak sparsity, that is to say, the sparse representation of the signal x under the wavelet basis Ψ represents the l of α 0 The norm is not very small. In a sense, the l of α 0 The norm is a very large value, because the wavelet transform has the nature of "high spikes and long tails", so although there are many relatively small coefficients in α, there are not many coefficients that are actually zero

Therefore, the sparse coefficients reconstructed using the zero-norm minimum prior Usually with a high error, the discarding of many small coefficients will cause some details of the image to be lost, greatly affecting the reconstruction quality of the image

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