Structured Sparse Representation Based Compressive Video Sampling

Sampling and reconstruction are two basic and core tasks in signal processing.Based on the theories of Shannon et al,traditional signal processing follows a procedure from sampling,then transformation,compression,coding to transmission,decoding and final reconstruction.However,the exact reconstruction can be guaranteed if the necessary sampling frequency is more than twice of signal's bandwidth according to the Nyquist sampling theory,which brings massive redundancy into the measurements of signals.In the subsequent compression,most of the transformation coefficients are abandoned,which is really a huge waste of computational and storage resources,but also an enormous challenge to hardware cost,transmission bandwidth and so on.As an application of sparsity,compressive sensing(CS)is a desirable framework for signal acquisition and reconstruction.CS attempts to acquire the sparse representation for unknown signals by randomly projecting them onto a space(observation)with much lower dimension.It fuses the sampling and compression into one step and the perfect reconstruction can be guaranteed with a high probability.Therefore,CS reduces the resource requirement and shifts the burden of encoder to the decoder by reducing the number of measurements to be sampled,thus the sampling rate is much lower than the Nyquist frequency.In view of its good prospects for the application,CS has been widely adopted to image and video processing,sensor network,channel coding and various imaging techniques such as holographic imaging,medical imaging,satellite multispectral imaging,radar imaging and so on.However,traditional CS theory assumes that signals are based on simple sparse model,which ignores the structures within the sparse coefficients for high-dimensional signals.Thus,it is critical to acquire the structural sparsity and the intrinsic structured information for the sampling and reconstruction of highdimensional signals.The main research topic of this dissertation focuses on compressive video sensing based on structured sparse representation.This dissertation proposes the union of data-driven subspace model,which is based on the spatial and temporal structures in the video signal for structured sparse representation,to achieve efficient compressive sampling.The proposed model is generalizable and scalable,which supports linear and multi-linear subspace learning,as well as the progressive representation of signals.The main contributions of this dissertation includes:This dissertation proposes a generalized model which adaptively decomposes signals into a union of data-driven subspaces(UoDS)for structured sparse representation.The proposed UoDS model leverages subspace clustering to derive the optimal structures and bases for the subspaces conditioned on the sample signals.For multidimensional signals with various statistics,it supports linear and multi-linear subspace learning for compressive sampling.As an improvement for generic CS model,the basis which represents the sparsity of sample signals is adaptively generated via linear subspace learning(LSL)method.Furthermore,a generalized model with multi-linear subspace learning is considered for CS to avoid vectorization of highdimensional signals.In comparison to UoS,the UoDS model requires fewer degrees of freedom for a desirable recovery quality.Experimental results demonstrate that the proposed model for video sampling is promising and applicable.This dissertation develops a block sparse subspace learning framework to leverage structured sparsity for generalized block sparse representation in compressive video sampling.The proposed framework can overcome the problem that the union of subspaces based models would obscure the block sparsity with correlated subspaces.The sparse representation based on a union of subspaces is improved by eliminating the intersection of subspaces with block coherence minimization.Regularized learning constrained by block coherence is developed to derive a class of independent bases for the union of subspaces.Under the assumption of block restricted isometric property,it is demonstrated that optimal sparse representation can be achieved for mutually orthogonal subspaces with a guarantee of stable recovery.Furthermore,the proposed framework can be generalized to sample signals that can be decomposed in a Kronecker product,especially multi-dimensional signals with varying non-stationary statistics.Experimental results demonstrate that the proposed framework achieves improved recovery stability and efficiency for compressive video sampling.This dissertation proposes a novel quality scalable structured compressive video sampling(SS-CVS)framework with hierarchical subspace learning to support video transmission over heterogeneous network conditions.The proposed framework incorporates the union of datadriven subspaces(UoDS)model to introduce structured sparsity into sensing matrix for progressive acquisition of measurements.Hierarchical subspace learning is developed to generate the subspaces with their bases based on adaptive subspace clustering in a progressive fashion.Consequently,two hierarchical structures are derived to enable progressive mapping of subspaces and bases on the structured sensing matrices to support quality scalability.To guarantee the convergence of hierarchical subspace learning,the training set is updated with the adaptive group set from the reconstructed reference frames.It is demonstrated that SS-CVS can guarantee stable recovery for each quality layer under the constraints of block restricted isometric property(RIP).Furthermore,the proposed SS-CVS model is generalized to tensor subspaces for scalable compressive sampling of high-dimensional signals.Experimental results demonstrate that the proposed algorithm can achieve quality scalabilities with an improved reconstructed performance in comparison to the state-of-the-art scalable compressive video sampling methods.This dissertation proposes a decomposable iterative algorithm for large-scale optimization problems.By decomposing the high-dimensional optimization problem into multiple subproblems solved iteratively,the distributed and accelerated computing of the optimization algorithm are realized.First,we consider the dual optimization algorithm for large-scale optimization.With Legendre transformation,the primal problem is transformed into its corresponding dual problem which can be iteratively solved.Thus,we developed a VERTIcal Grid based Newton-Raphson iterative algorithm for lOgistic regression(VERTIGO).After performing vertical distributed partitioning of data,the proposed algorithm transforms the primal problem into dual problem which can be solved iteratively with kernel trick and Newton-Raphson method,thereby not only reducing the complexity of training but also being applicable to privacypreserving federated data analysis.Considering the above Newton-Raphson iterative algorithm based on dual decomposition,the existence of the Legendre condition has been satisfied for the optimization function.Thus,we further propose a decomposable optimization algorithm based on the alternating direction method of multipliers,which can be applied to the constrained optimization problems based on structured sparsity for the performance improvement of the recovery of the sparse tensor representation over adaptive Kronecker basis.The experimental results show that the proposed method is superior to the state-of-the-art methods.