Objective Hyperspectral images(HSIs)are contaminated by noises due to the imaging mechanism,equipment errors,and imaging environment.Because of the diverse sensitivity of sensors at different wavelengths,the noise intensi-ties among bands are always dissimilar,that is,spectrally non-independent and identically distributed noises exist.Noise interference greatly limits the interpretation and application of HSIs.Therefore,HSI denoising is an indispensable prepro-cessing step to improve the utility of HSIs.Sparse-representation(SR)-based methods assume clean HSIs are structural and can be linearly represented by a few atoms in the dictionary,while structureless random noise cannot be represented.However,most SR-based methods follow the pipeline to break the compete HSIs into many overlapped,small local patches,sparsely representing each small patch independently,and average overlapped pixels between each patch to recover HSIs globally.Such a"local-global"denoising mechanism ignores dependencies between overlapping patches,pro-ducing lower denoising effectiveness and visual defects.Differently,convolutional sparse coding(CSC)employs convolu-tion kernels as atoms and can represent the image without patch division thanks to the shift-invariant property of the convo-lution operators.In this way,the spatial relationships between different patches are naturally retained.Inspired by this,this paper introduces a multitask convolutional sparse coding network(MTCSC-Net)for HIS denoising.Method In this paper,the denoising problem of an individual band is regarded as a single task and the CSC model is used to describe the local spatial structure correlation within each band.The denoising of all the bands is regarded as a multitask problem.All the bands are connected by sharing the sparse coding coefficients to depict the global spectral correlation between different bands,forming a multitask convolutional sparse coding(MTCSC)model.The MTCSC model can realize joint spatial-spectral relationship modeling of HSIs.Moreover,the MTCSC model takes the HSIs as whole and can naturally remain the spatial relationship between pixels;thus,it has a strong denoising ability.Drawing on the powerful learning ability of deep learning,this paper transforms the iterative optimization of the MTCSC model into an end-to-end learnable deep neural net-work by the deep unfolding technique,that is,MTCSC-Net,to improve the model denoising ability and efficiency further.Result In this paper,our method is evaluated on the ICVL and CAVE datasets.In both experiments,different levels of Gaussian noises are added to clean HSI to produce noise-clean pairs.Besides the synthetic experiment,MTCSC-Net is tested on the real-world HYDICE Urban Dataset(Urban)dataset.Eight methods are selected for comparison to prove the effectiveness of the proposed denoising method.Experimental results show peak signal-to-noise ratio(PSNR)is improved by 1.38 dB on the CAVE dataset and 0.64 dB on the ICVL dataset,compared with the traditional patch-based SR method.The visual results show MTCSC-Net can produce cleaner spatial images and more accurate spectral reflectance with a better match with the reference ones.Conclusion The MTCSC-Net proposed in this paper can effectively utilize the spatial-spectral correlation information of HSIs and has a strong denoising ability.
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