Adaptive StructureConstrained Robust Latent LowRank Coding for Image Recovery In this paper, we propose a robust representation learning model called Adaptive Structureconstrained LowRank Coding (ASLRC) for the latent representation of data. To recover the underlying subspaces more accurately, ASLRC seamlessly integrates an adaptive weighting based blockdiagonal structureconstrained lowrank representation and the group sparse salient feature extraction into a unified framework. Specifically, ASLRC performs the latent decomposition of given data into a lowrank reconstruction by a blockdiagonal codes matrix, a group sparse localityadaptive salient feature part and a sparse error part. To enforce the blockdiagonal structures adaptive to different real datasets for the lowrank recovery, ASLRC clearly computes an autoweighting matrix based on the localityadaptive features and multiplies by the lowrank coefficients for direct minimization at the same time. This encourages the codes to be blockdiagonal and can avoid the tricky issue of choosing optimal neighborhood size or kernel width for the weight assignment, suffered in most local geometrical structurespreserving lowrank coding methods. In addition, our ASLRC selects the L2, 1norm on the projection for extracting group sparse features rather than learning lowrank features by Nuclearnorm regularization, which can make learnt features robust to noise and outliers in samples, and can also make the feature coding process efficient. Extensive visualizations and numerical results demonstrate the effectiveness of our ASLRC for image representation and recovery.

Variations on the Convolutional Sparse Coding Model Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding (CSC), has been recently reintroduced and extensively studied. CSC brings a natural remedy to the limitation of typical sparse enforcing approaches of handling global and highdimensional signals by local, patchbased, processing. While the classic field of sparse representations has been able to cater for the diverse challenges of different signal processing tasks by considering a wide range of problem formulations, almost all available algorithms that deploy the CSC model consider the same   ell _1  ell _2   problem form. As we argue in this paper, this CSC pursuit formulation is also too restrictive as it fails to explicitly exploit some local characteristics of the signal. This work expands the range of formulations for the CSC model by proposing two convex alternatives that merge global norms with local penalties and constraints. The main contribution of this work is the derivation of efficient and provably converging algorithms to solve these new sparse coding formulations.