Learning sparse representations for adaptive compressive sensing

Sparse representation and dictionary learning have been successfully applied to encode dense data and facilitate image classification. Though existing dictionary learning methods achieve better performance than their counterparts, the class discriminative ability of learned dictionary is still limited. This paper proposes a novel supervised dictionary learning method based on the prior of the block diagonal phenomenon, i.e., each sample should be well reconstructed by the samples in the same class while poorly reconstructed by the samples in other class. Specifically, a block diagonal regularizer is imposed on the affinity matrix to enforce the sparse representation matrix to have an approximately block diagonal structure, which makes the learned dictionary more discriminative and suitable for classification tasks. Furthermore, we present an effective optimization strategy by combining the alternating minimization with the alternating direction method of multipliers (ADMM) for the proposed framework. Experimental results on six real-world datasets show that the proposed method is more effective than state-of-the-art dictionary learning methods.

This paper describes how to construct a probability map using sparse representation and dictionary learning to indicate the probability of each optic disk pixel of belonging to the optic cup. This probability map will be used in the future as input to a method for automatically detecting glaucoma from color fundus images. The probability map was obtained constructing a model (using the Bayes classifier) which takes into account texture information, by means of sparse representation and RLS-DLA dictionary learning technique, and intensity information. Several experiments on a private database are presented in this work. The results are compared with the segmentation made by specialists, highlighting the promising performance of this technique in difficult cases where the optic cup is barely visible.

[1] Sparse geologic dictionaries provide a novel approach for subsurface flow model representation and calibration. Learning sparse dictionaries from prior training data sets is an effective approach to describe complex geologic connectivity patterns in subsurface imaging applications. However, the computational cost of sparse learning algorithms becomes prohibitive for large models. Performing the sparse dictionary learning process on smaller image patches (segments) provides a simple approach to address this problem in image processing applications. However, in underdetermined subsurface flow model calibration inverse problems, reconstruction of a segmented image can introduce significant structural distortion and discontinuity at the boundaries of the segments. This paper proposes an alternative sparse learning approach where the sparse dictionaries are learned from low-rank representations of the large-scale training data set in spectral domains (e.g., frequency domain). The objective is to develop a computationally efficient dictionary learning approach that emphasizes large-scale spatial connectivity patterns. This is achieved by removing the strong spatial correlations in the training data, thereby eliminating a large number of insignificant components from the sparse learning computation. In addition to improving the computational complexity, sparse learning from low-rank training data sets suppresses the small-scale details from entering the reconstruction of large-scale connectivity patterns, thereby providing a regularization effect in solving the resulting ill-posed inverse problems. We apply the proposed approach to travel-time tomography inversion and nonlinear subsurface flow model calibration inverse problems to demonstrate its effectiveness and practicality.

Sparse representation matrix is of great significance for Compressed Sensing (CS) reconstruction accuracy. Contourlet Transform (CT) offer a much richer set of directions and shapes, and it is more effective in capturing smooth contours and geometric structures in images. While dictionaries learned by machine learning methods can represent images more effectively. In this paper, we propose a multi-level adaptive dictionary learning (DL) strategy which combines both of the above advantages. We learn sub-dictionaries of high frequency of CT by an improved K-SVD algorithm, and moreover, the stopping criteria of sparse representation stage is associated with the iteratively updated dictionaries to get an adaptive sparse constraint, which gets more effective sparse representation coefficients and then improves the dictionary updating. This approach achieves a good reconstruction accuracy of the high frequency with less CS measurement. Experiment results demonstrate that the reconstructed images using dictionaries learned by the proposed algorithm in CS have better effect.

Sparse representation is efficient to approximately recover signals by a linear composition of a few bases from an over-complete dictionary. However, in the scenario of data compression, its efficiency and popularity are hindered due to the extra overhead for encoding the sparse coefficients. Therefore, how to establish an accurate rate model in sparse coding and dictionary learning becomes meaningful, which has been not fully exploited in the context of sparse representation. According to the Shannon entropy inequality, the variance of data source can bound its entropy, thus can reflect the actual coding bits. Therefore, a Globally Variance-Constrained Sparse Representation (GVCSR) model is proposed, where a variance-constrained rate term is introduced to the conventional sparse representation. To solve the non-convex optimization problem, we employ the Alternating Direction Method of Multipliers (ADMM) for sparse coding and dictionary learning, both of which have shown state-of-the-art rate-distortion performance in image representation.

In this paper, we present an automated system for robust biometric recognition based upon sparse representation and dictionary learning. In sparse representation, extracted features from the training data are used to develop a dictionary. Training data of real world applications are likely to be exposed to geometric transformations, which is a big challenge for designing of discriminative dictionaries. Classification is achieved by representing the extracted features of the test data as a linear combination of entries in the dictionary. We propose joint weighted dictionary learning and classifier training (JWDL-CT) approach which simultaneously learns from a set of training samples along with weight vectors that correspond to the atoms in the learnt dictionary. The components of the weight vector associated with an atom represent the relationship between the atom and each of the classes. The weight vectors and atoms are jointly obtained during the dictionary learning. In the proposed method, a constraint is imposed on the correlation between the atoms to decrease the similarity between these atoms. The proposed dictionary learning objective function enhances the class-discrimination capabilities of individual atoms that renders the designed dictionaries especially suitable for classification of query images with very sparse representation. Experiments conducted on the West Virginia University (WVU) and the University of Notre Dame (UND) datasets for ear recognition show that the proposed method outperforms other state-of-the-art classifiers.

An automatic segmentation method of hippo-campus for volume measurement in MR brain images by using sparse patch representation and discriminative dictionary learning is proposed in this paper, which can overcome the limitation of multi-atlas approaches that mostly rely on similarity between target image and atlases for more accurate segmentation. In the proposed method, atlases are registered to a target image, then patch-based features including intensity and gradient are extracted from registered atlases for a dictionary learning model, from which dictionaries and classifiers are learned simultaneously. The label for voxels in the target image is determined via solving sparse representation of target patch over learned dictionary. Performance of the proposed method is evaluated on 30 subjects from the public dataset CIND by cross validation. Qualitative and quantitative comparisons illustrate that the proposed method is competitive compared with state-of-the-art approaches based on multi-atlas.

This paper proposes an adaptive image representation learning method for cervix cancer tumor detection. The method learns the representation in two stages, a local feature description using a sparse dictionary learning and a global image representation using a bag-of-features (BOF) approach. The resultant representation is thus a BOF histogram, learned from a sparse local patch representation. The parameters of the sparse learning representation algorithm are tuned up by searching dictionaries with low coherence and high sparsity. The proposed method was evaluated in a dataset of 394 cervical histology images with tumoral and non-tumoral pathologies acquired at a 10X magnification and a resolution of 3800 × 3000 pixels in RGB color. A conventional BOF image representation, using a linearized raw-block patch descriptor, was selected as the baseline. The preliminary results show that our proposed method improves the baseline for all different BOF dictionary sizes (125, 250, 500, 1000 and 2000). Under a 10 cross-validation test and a 2000 BOF dictionary, the best performance was 0:77±0:04 in average accuracy, improving in 2:5% the baseline. These results suggest that a learning-from-data approach could be used in different stages of an image classifier construction pipeline, in particular for the image representation stage.

Automatic prostate segmentation from MR images is an important task in various clinical applications such as prostate cancer staging and MR-guided radiotherapy planning. However, the large appearance and shape variations of the prostate in MR images make the segmentation problem difficult to solve. Traditional Active Shape/Appearance Model (ASM/AAM) has limited accuracy on this problem, since its basic assumption, i.e., both shape and appearance of the targeted organ follow Gaussian distributions, is invalid in prostate MR images. To this end, the authors propose a sparse dictionary learning method to model the image appearance in a nonparametric fashion and further integrate the appearance model into a deformable segmentation framework for prostate MR segmentation. To drive the deformable model for prostate segmentation, the authors propose nonparametric appearance and shape models. The nonparametric appearance model is based on a novel dictionary learning method, namely distributed discriminative dictionary (DDD) learning, which is able to capture fine distinctions in image appearance. To increase the differential power of traditional dictionary-based classification methods, the authors' DDD learning approach takes three strategies. First, two dictionaries for prostate and nonprostate tissues are built, respectively, using the discriminative features obtained from minimum redundancy maximum relevance feature selection. Second, linear discriminant analysis is employed as a linear classifier to boost the optimal separation between prostate and nonprostate tissues, based on the representation residuals from sparse representation. Third, to enhance the robustness of the authors' classification method, multiple local dictionaries are learned for local regions along the prostate boundary (each with small appearance variations), instead of learning one global classifier for the entire prostate. These discriminative dictionaries are located on different patches of the prostate surface and trained to adaptively capture the appearance in different prostate zones, thus achieving better local tissue differentiation. For each local region, multiple classifiers are trained based on the randomly selected samples and finally assembled by a specific fusion method. In addition to this nonparametric appearance model, a prostate shape model is learned from the shape statistics using a novel approach, sparse shape composition, which can model nonGaussian distributions of shape variation and regularize the 3D mesh deformation by constraining it within the observed shape subspace. The proposed method has been evaluated on two datasets consisting of T2-weighted MR prostate images. For the first (internal) dataset, the classification effectiveness of the authors' improved dictionary learning has been validated by comparing it with three other variants of traditional dictionary learning methods. The experimental results show that the authors' method yields a Dice Ratio of 89.1% compared to the manual segmentation, which is more accurate than the three state-of-the-art MR prostate segmentation methods under comparison. For the second dataset, the MICCAI 2012 challenge dataset, the authors' proposed method yields a Dice Ratio of 87.4%, which also achieves better segmentation accuracy than other methods under comparison. A new magnetic resonance image prostate segmentation method is proposed based on the combination of deformable model and dictionary learning methods, which achieves more accurate segmentation performance on prostate T2 MR images.

Compressive sensing (CS) is widely being used in recent times for image compression and transmission. The major challenge in CS is perfect reconstruction of the original image from fewest samples with fast convergence. Dictionary learning and the wide-ranging optimization problem give rise to high computation complexity. Group sparse representation (GSR)-based approach is one of the fast and efficient methods of CS image recovery. However, it may tend to oversmoothen the recovered image. This research work focuses on enhancing the performance of GSR-based methods. In this research work, both local and non-local image patches are exploited in two phases of reconstruction. In the initialization phase, adaptive sparsifying l0 optimization model is utilized for local overlapping patches. Further, constrained GSR is applied on the outcome. The split Bregman iteration is harnessed to solve the resultant patch-group model. The execution time, PSNR and FSIM are employed as the evaluation parameters for evaluating the CS performance. The parametric performance is tested over a set of standard images. The experimental results show the competence of the proposed patch-group method over the existing ALSB, GSR and GSR-NCR (GSR with non-convex regularization) methods. The proposed model offers 1.3, 0.32 and 0.51 dB average PSNR gain over ALSB, GSR and GSR-NCR methods, respectively. The average execution time taken by the proposed work is 29% less than the traditional GSR method.

This work presents a video compression method based on sparse representation and dictionary learning algorithms. The proposed scheme achieves superb rate-distortion performance and decent subjective quality, compared to modern standards, especially at low bit-rates. Different from similar works, sparse representation is employed here for both intra-frame and block matching inter-frame motion information. Dividing video frames to reference and current frames, motion vectors and motion compensation residuals of current frames are estimated in regard to reference frames. The sparse codes of reference frames and motion compensation residuals are obtained using learned dictionaries, entropy-coded, and stored or sent to the receiver along with the coded motion field. In the receiver, after decoding the sparse codes and motion vectors, the reference frames and residuals are reconstructed employing the same learned dictionary and the current frames are recovered using the reference frames and motion fields. In the proposed scheme, the Iterative Least Square Dictionary Learning Algorithm (ILS-DLA) and K-SVD dictionary building methods are employed in the DCT domain. The compression rate and quality of the method based on the two dictionary learning algorithms are compared to each other and to H.264/AVC and HEVC modern standards. The results based on PSNR and SSIM criteria show that the proposed approach presents superior performance respect to H.264/AVC and even HEVC for higher bit-rates of QCIF video format, and the K-SVD learning algorithm performs slightly better than the ILS-DLA for the purpose.

This work presents the use of Dictionary Learning methods for a sparse representation of 4D seismic data in history matching. We consider a trade-off between the number of coefficients retained in the sparse data representation, the computational cost, and how well we can capture the main features of the 4D seismic signal. K-SVD is an iterative algorithm used in Dictionary Learning problems that alternates between the calculation of the sparse representation vector and dictionary update. For the definition of the sparse representation vector, one can constrain the problem into two distinct approaches: (1) sparsity-constrained; and (2) error-constrained. We evaluated the two methods and the influence of critical parameters of the algorithm (dictionary size, number of iterations, patch size, and training dataset size) using a synthetic reservoir model. Results showed that regardless of which of the constrained approaches we used, the dictionary learning method can capture the main features of the 4D seismic signal with a sparse representation. However, the number of nonzero coefficients is highly dependent on the approach. Besides, dictionary size, number of iterations, patch size, and training dataset size, also have a significant impact on the number of coefficients and the computational cost. Consequently, the selection of these variables is crucial as it might affect the history-matching process. In a permanent-reservoir-monitoring (big data) scenario, the use of sparse representation allows us to retain the main features of the reservoir in a reasonably sized data representation that can be directly used in a history matching method, leading to improved reservoir characterization and a better understanding of the reservoir properties. This paper gives a practical implementation of a technique already used in other areas (image denoising, processing of raw seismic data, and facies representation) applied to 4D seismic data.

This work develops a structured dictionary learning (SDL) for industrial process monitoring. The proposed SDL is based on the incorporation of full graph Laplacian (FGL) and manifold graph Laplacian (MGL). In order to enhance the monitoring performance of dictionary learning, SDL integrates the fault information into the latent-variable residuals using the augmented dictionary and FGL regularization. While the local geometry structure is preserved in the representation coefficients by combining with MGL regularization. To better isolate faulty variables, this article further constructs a fault isolation model by imposing $l_{1}/l_{2,1}$-norm on the representation coefficients and designing a structured regularization term (SRT), including additional $l_{2,1}$- and Frobenius-norms. The row- and subgraphsparsity of SRT ensures that faulty variables can be isolated by a two-stage isolation strategy. It is proved that the proposed strategy is suitable for fault isolation. The better performance of SDL is illustrated by the application to a boiler process.

The importance of sparse signal structures has been recognized in a plethora of applications ranging from medical imaging to group disease testing to radar technology. It has been shown in practice that various signals of interest may be (approximately) sparsely modeled, and that sparse modeling is often beneficial, or even indispensable to signal recovery. Alongside an increase in applications, a rich theory of sparse and compressible signal recovery has recently been developed under the names compressed sensing (CS) and sparse approximation (SA). This revolutionary research has demonstrated that many signals can be recovered from severely undersampled measurements by taking advantage of their inherent low-dimensional structure. More recently, an offshoot of CS and SA has been a focus of research on other low-dimensional signal structures such as matrices of low rank. Low-rank matrix recovery (LRMR) is demonstrating a rapidly growing array of important applications such as quantum state tomography, triangulation from incomplete distance measurements, recommender systems (e.g., the Netflix problem), and system identification and control. In this dissertation, we examine CS, SA, and LRMR from a theoretical perspective. We consider a variety of different measurement and signal models, both random and deterministic, and mainly ask two questions. How many measurements are necessary? How large is the recovery error? We give theoretical lower bounds for both of these questions, including oracle and minimax lower bounds for the error. However, the main emphasis of the thesis is to demonstrate the efficacy of convex optimization---in particular l1 and nuclear-norm minimization based programs---in CS, SA, and LRMR. We derive upper bounds for the number of measurements required and the error derived by convex optimization, which in many cases match the lower bounds up to constant or logarithmic factors. The majority of these results do not require the restricted isometry property (RIP), a ubiquitous condition in the literature.

The compressive sensing (CS) framework states that a signal that has a sparse representation in a known basis may be reconstructed from samples obtained at a sub-Nyquist sampling rate. The Fourier domain is widely used in CS applications due to its inherent properties. Sparse signal recovery applications using a small number of Fourier transform coefficients have made solutions to large-scale data recovery problems, including image recovery problems, more practical. The sparse reconstruction of 2D images is performed using the sampling patterns generated by taking the general frequency characteristics of the images into account. In this work, instead of forming a general sampling pattern for infrared (IR) images, a special sampling pattern is obtained by gathering a database to extract the frequency characteristics of IR sea-surveillance images. Experimental results show that the proposed sampling pattern provides better sparse recovery results compared to the widely used patterns proposed in the literature. It is also shown that, together with a certain image dataset, the sampling pattern generated by the proposed scheme can be generalized for various image sparse recovery applications.