Adaptive Convolutional Sparse Coding with Weighted l1 Norm

Convolutional Sparse Coding computes a sparse representation for an entire image by modeling the signal as a sum of several convolutions of dictionary filters and sparse feature maps, instead of the linear combination of dictionary vectors in standard sparse coding. Most of the existing algorithms use a invariant regularization parameter, which can hardly deal well with varying local contrast. In this paper, we propose a new method Adaptive Convolutional Sparse Coding (ACSC) by introducing a set of weight vectors into the ℓ
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regularization term to set different penalty coefficients for different sparse feature maps, which can better adapt with the varying local sparse requirements of images. Experimental results show that the proposed ACSC is superior to the existing convolutional sparse coding algorithm in image reconstruction.