Image Convolutional Sparse Representation Algorithm

Sparse representation is a coding method that uses as few non-zero atomic coefficients as possible to represent signals,and it conforms to the mechanism of human visual perception.When sparse representation is applied to an image,in order to reduce the burden of modeling and calculation,the standard sparse representation method is to decompose the image into a set of overlapping image blocks and calculate the sparse representation of all blocks independently.The convolutional sparse representation treats the entire signal as a whole and models it as the sum of the convolution of the dictionary filter and the convolutional sparse feature map,which generates translation invariants and maintains the potential structure of the signal,thereby overcoming the sparse representation Block-based disadvantages.The convolutional sparse representation algorithm is usually decomposed into two convex subproblems,the convolutional sparse coding problem and the convolution dictionary update problem,which are solved alternately in an iterative manner.This article studies these two sub-problems separately,and finally conducts an experimental analysis of the combination of these two sub-problems.?1?The existing convolutional sparse coding algorithm basically uses the l₁ norm with fixed parameters as the regularization penalty term.In response to this situation,this article introduces the l₁ weight vector associated with the signal to assign different weights to different coefficients.This paper proposes convolutional sparse coding with weighted l₁ norm,and gives the definition of l₁ weight vector and the algorithm solution process.Experimental results show that this algorithm is superior to the traditional sparse coding algorithm and similar algorithms in image reconstruction accuracy.?2?The existing FISTA-based convolution dictionary learning algorithm uses a fixed step size,which limits search efficiency and stability.In response to this situation,we introduce a dynamic step size strategy with step size growth and backtracking.Increase the step size slightly at the beginning of each iteration and correct the excessive increase through the backtracking steps.This paper proposes a Convolutional Dictionary Learning With Dynamic Step FISTA and conducts a lot of experimental comparisons with mainstream algorithms.Experimental results show that the algorithm proposed in this paper improves the stability of convergence under the premise of achieving a good convergence speed.?3?The above two works were independently verified by experiments during the research.For the completeness of this article,we combine the above-mentioned convolutional sparse coding algorithm and convolution dictionary learning algorithm to conduct image coding reconstruction and degaussian noise comparison experiments.At the same time,since the standard convolutional sparse coding algorithm cannot effectively remove salt and pepper noise,we added a gradient term to the proposed convolutional sparse coding based on the weighted l₁ norm to improve the algorithm's ability to remove salt and pepper noise.Experimental data shows that the algorithm proposed in this paper has good effect in image reconstruction and denoising.