Image Restoring And Classification Based On Incoherent Dictionary Learning And Sparse Representation

Dictionary learning plays an important role for sparse representation and compressed sensing.By giving the training samples,dictionary learning can adaptively learn the optimal atoms set,which is called as dictionary.A learned dictionary allows these training samples to be represented as linear combination with relatively few atoms,and the representation coefficients are as sparse as possible.Many studies of compressed sensing focus on the mutual coherence of dictionary,which is a key factor in controlling the support of solutions of the least-squares with l₁penalized and greedy problems.Furthermore,highly incoherent dictionaries can improve the generalization of learned dictionary,and tend to avoid the over-fitting of training samples to training samples and atoms degeneracy?two atoms are failed to be same?when sparse coding is enforced.Incoherent dictionary learning have been widely applied in many areas,such as signal and image recovery,classification,decomposition,and compressed sensing,et al.In recent years,incoherent dictionary learning have attracted a lot of attentions by researchers both at home and abroad,since it is the hotspot and key problem of dictionary learning,sparse representation and compressed sensing.In this paper,we focus on the incoherent dictionary learning algorithm and its application.Our contributions are presented as?1?Incoherent dictionary learningIn the process of dictionary learning,the coherence of dictionary plays an important role of sparse recovery of signal.In this paper,we propose two novel incoherent dictionary learning algorithms,denoted as UNTF-INKSVD and UNTF-IP.The two algorithms distin-guishes themselves from traditional dictionary learning approaches by explicitly taking into account the border condition.In particular,the learned dictionary approximates the equian-gular tight frame via matrix polar decomposition,the incoherence of dictionary have been improved.Unlike INK-SVD algorithm,the proposed UNTF-INKSVD algorithm minimizes the sum of squared inner product of all atom pairs between the dictionary and reference unit norm tight frame,and the new objective function of dictionary learning is developed.We translate it into low rank correlation coefficient optimization problem,which can be solved by using majorized penalty approach.Meanwhile,the novel incoherent dictionary learn-ing model is designed in the proposed UNTF-IP algorithm,in which tight frame,structure and spectrum constraint set are optimized alternatively.It encourage the learned dictionary to be incoherent.In order to trade-off the sparse representation performance and incoher-ence of learned dictionary,we propose Manifold Optimization to further optimize the sparse representation performance of incoherent dictionary.Experiments on synthetic data and re-al audio data show that the proposed algorithms can achieve considerable improvements in terms of approximating equiangular tight frame?ETF?and implementing the maximal sparse coding,and can effective control the trade-off between low sparse representation errors and dictionary coherence in comparison to other algorithms.?2?Incoherent dictionary learning and sparse representation for single-image rain re-movalWe present the incoherent dictionary learning for single-image rain removal.First,rainy image can be decomposed into high frequency image and low frequency image based on bilateral filter.Then,the incoherence of the dictionary is introduced to reduce the simi-larity between rain atoms and non-rain atoms,and a new objective function is designed to ensure the separability of rain dictionary and non-rain dictionary in the dictionary learning,thus the learned dictionary has similar properties to the tight frame and approximates the equiangular tight frame.Furthermore,the high frequency in the rain image can be decom-posed into a rain component and a non-rain component by performing sparse coding via the learned incoherent dictionary.Finally,the non-rain component in the high frequency and the low frequency are fused to remove rain.Experimental results demonstrate that our learned incoherent dictionary has better performance of sparse representation.The recovered rain-free image has the less residual rain,and preserves effectively the edges and details.So the visual effect of recovered image is more sharpness and natural.?3?Novel discriminative feature-oriented dictionary learning algorithm with Fisher criterion?FCDFDL?for histopathological image classificationHistopathological images present some discriminative features about the tissue archi-tecture such as the spatial geometric structure,various cell categories,diverse morphologies of the similar cells and smaller inter-class variation.How to extract accurately discrimi-native features becomes a key problem for histopathological image classification.In or-der to effectively improve the discriminative ability of learned sparse representation for histopathological image classification,we propose a novel discriminative dictionary learn-ing algorithm with Fisher criterion?FCDFDL?in this paper,First,we construct two special regularization terms based on Fisher criterion that aims to encourage the clustering within each intra-class dictionary and large diversity between inter-class dictionaries,and the regu-larization terms are embedded into the objective function to learn the discriminative healthy and diseased dictionaries directly.Simultaneously,the sparse representation can be obtained via the learned healthy and diseased dictionaries,in which the sparse reconstruction errors of the intra-sample and inter-sample are simultaneously optimized to trade-off the reconstruc-tion and discrimination of learned dictionaries.Finally,based on the sparse reconstruction error vector via the learned dictionaries,we construct the classifier for histopathological image classification.The experimental results obtained on ADL datasets show that the pro-posed FCDDL can promote the discriminative power of learned dictionaries and lead to the improved classification accuracy for the histopathological image.?4?Discriminative dictionary learning with two categories coherence constrained?C-CDDL?for histopathological image classificationAlthough the improved classification performance has been reported in the FCDFDL,there still remains one critical issue,i.e.Optimizing the Euclidean distance of intra-class scatter and inter-scatter cannot encourage intra-class atoms have the similar characteristic-s and inter-class atoms have the dissimilar characteristics.This causes the overlapping of sparse coding in the reduced space when inter-class sample have the small diversity.There-fore,it is necessary to improve the robustness of classification.In this section,we present a novel discriminative dictionary learning with two categories of coherence constrained?C-CDDL?for histopathological image classification.Compared with FCDFDL method,the coherence of intra-class atoms within each dictionary and inter-class atoms between dictio-naries are incorporated into the dictionary learning objective function.Since the proposed algorithm can encourage the similar intra-class atoms and discourage the similar inter-class atoms,the learned healthy dictionary and diseased dictionary have the better reconstruction and robustness to the intra-class samples and the discrimination to the inter-class samples.Experimental results show that the proposed algorithm can enforce the discrimination and robust of learned dictionaries.And the improved classification performance can be achieved with compared to the other previous discriminative dictionary learning algorithms.