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Average reconstruction error ESNR in sparse representation using dictionary learnt by K-SVD (non-solid lines) and R-SVD (solid lines), for L = 10000 synthetic vectors varying the additive noise power (in the legend) Averages are calculated over 100 trials and plotted versus update iteration count. Left: D ∈ R 50 × 100 with sparsity k = 5, Right: D ∈ R 100 × 200 with sparsity k = 10.
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In the sparse representation model, the design of overcomplete dictionaries plays a key role for the effectiveness and applicability in different domains. Recent research has produced several dictionary learning approaches, being proven that dictionaries learnt by data examples significantly outperform structured ones, e.g. wavelet transforms. In t...
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... Recently, Sulam et al. [87] introduced OSDL, an hybrid version of dictionary design, which builds dictionaries, fast to apply, by imposing a structure based on a multiplication of two matrices, one of which is fully-separable cropped Wavelets and the other is sparse, bringing to a double-sparsity format. Another method maintaining the alternating scheme is the R-SVD [53], an algorithm for dictionary learning in the sparsity model, inspired by a type of statistical shape analysis, called Procrustes method 10 [48], which has applications also in other fields such as psychometrics [83] and crystallography [61]. In fact, it consists in applying Euclidean transformations to a set of vectors (atoms in our case) to yield a new set with the goal of optimizing the model fitting measure. ...
... The Procrustes analysis is the technique applied in R-SVD algorithm [53]: it consists in applying affine transformations (shifting, stretching and rotating) to a given geometrical object in order to best fit the shape of another target object. When the admissible transformations are restricted to orthogonal ones, it is referred to as Orthogonal Procrustes analysis [48]. ...
The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In statistics the many applications of sparse modeling span regression, classification tasks, graphical model selection, sparse M-estimators and sparse dimensionality reduction. It is also particularly effective in many statistical and machine learning areas where the primary goal is to discover predictive patterns from data which would enhance our understanding and control of underlying physical, biological, and other natural processes, beyond just building accurate outcome black-box predictors. Common examples include selecting biomarkers in biological procedures, finding relevant brain activity locations which are predictive about brain states and processes based on fMRI data, and identifying network bottlenecks best explaining end-to-end performance. Moreover, the research and applications of efficient recovery of high-dimensional sparse signals from a relatively small number of observations, which is the main focus of compressed sensing or compressive sensing, have rapidly grown and became an extremely intense area of study beyond classical signal processing. Likewise interestingly, sparse modeling is directly related to various artificial vision tasks, such as image denoising, segmentation, restoration and superresolution, object or face detection and recognition in visual scenes, and action recognition. In this manuscript, we provide a brief introduction of the basic theory underlying sparse representation and compressive sensing, and then discuss some methods for recovering sparse solutions to optimization problems in effective way, together with some applications of sparse recovery in a machine learning problem known as sparse dictionary learning.
... The update of the sparsifying transform in problem (3) can be achieved using a closed form solution [19,23]. The problem (3) can be considered as an orthogonal Procrustes problem [7,9,27]. The objective (3) can be rewritten in terms of the trace of the matrix as ...
The reconstruction of signals from their blind compressed measurements is a highly ill-posed problem because the representing basis is unknown. This paper proposes an alternating optimization method to estimate the signal from a given set of blind compressive measurement vectors. The representing coefficients, representing basis (sparsifying basis), and the updated estimate of the signals are identified iteratively. The representing basis is identified using the orthogonal Procrustes method. The signal estimate is updated using -trend filtering. The high computational intensity of the proposed method compared to other existing methods limits its application to non-real-time signal estimation. The proposed method reconstructs the signal uniquely up to a lower error bound.
... The processing effects of the three algorithms were compared when the noise ρ was 10, 30, 50, and 70, respectively. The results showed that the PSNR and SSIM values of N-KSVD dictionary after denoising were both greater Computational and Mathematical Methods in Medicine than those of DCT dictionary, and the differences were statistically significant, which indicated that N-KSVD dictionary had the best denoising effect, in line with the research results of Grossi et al. [30]. Subsequently, N-KSVD dictionary was used in the diagnosis of patients, and the test group and the control group were compared for basic information. ...
The study is aimed at evaluating the application value of ultrasound combined with gastroscopy in diagnosing gastrointestinal bleeding (GIB) caused by Helicobacter pylori (HP). An ultrasound combined with a gastroscopy diagnostic model based on improved K-means Singular Value Decomposition (N-KSVD) was proposed first. 86 patients with Peptic ulcer (PU) and GIB admitted to our Hospital were selected and defined as the test group, and 86 PU patients free of GIB during the same period were selected as the control group. The two groups were observed for clinical manifestations and HP detection results. The results showed that when the noise ρ was 10, 30, 50, and 70, the Peak Signal to Noise Ratio (PSNR) values of N-KSVD dictionary after denoising were 35.55, 30.47, 27.91, and 26.08, respectively, and the structure similarity index measure (SSIM) values were 0.91, 0.827, 0.763, and 0.709, respectively. Those were greater than those of DCT dictionary and Global dictionary and showed statistically significant differences versus the DCT dictionary (P<0.05). In the test group, there were 60 HP-positives and 26 HP-negatives, and there was significant difference in the numbers of HP-positives and HP-negatives (P<0.05), but no significant difference in gender and age (P>0.05). Of the subjects with abdominal pain, HP-positives accounted for 59.02% and HP-negatives accounted for 37.67%, showing significant differences (P<0.05). Finally, the size of the ulcer lesion in HP-positives and HP-negatives was compared. It was found that 71.57% of HP-positives had ulcers with a diameter of 0-1 cm, and 28.43% had ulcers with a diameter of ≥1 cm. Compared with HP-negatives, the difference was statistically significant (P<0.05). In conclusion, N-KSVD-based ultrasound combined with gastroscopy demonstrated good denoising effects and was effective in the diagnosis of GIB caused by HP.
... At the very first step, the dictionary D may be initialized by randomly selecting training feature vectors; the sparse coding step can then be solved resorting to standard sparse approximation algorithms like [1] or [14] as well as for the dictionary update rule that can be casted into different forms (e.g. [3,9,8]). ...
In this work we address the problem of gender recognition from facial images acquired in the wild. This problem is particularly difficult due to the presence of variations in pose, ethnicity, age and image quality. Moreover, we consider the special case in which only a small sample size is available for the training phase. We rely on a feature representation obtained from the well known VGG-Face Deep Convolutional Neural Network (DCNN) and exploit the effectiveness of a sparse-driven sub-dictionary learning strategy which has proven to be able to represent both local and global characteristics of the train and probe faces. Results on the publicly available LFW dataset are provided in order to demonstrate the effectiveness of the proposed method.
... Nonetheless, there are several heuristics to tackle this problem, including some of those reviewed above, such as Lasso, [7], Orthogonal Matching Pursuit [8], Limaps [24]. For the following empirical assessment sections we choose the implementation of the greedy algorithm Orthogonal Matching Pursuit provided by the dictionary learning [25] oriented package OMP-Box v10 [26] since it is rather efficient and well-established. This package as well as the code of our method are tested in a Matlab R2014b environment on a standard Intel Core i7 desktop platform. ...
Optimal well-being is a new multi-dimensional construct, which incorporates the well-known preexisting notions of subjective and psychological well-being. Classical models for describing the predictors of optimal well-being binary response variable are generalized linear models (GLM), such as logistic regression model. Since the number of predictors might be relatively large in these models, we devise a sparse optimization method for the regression problem based on subsequent iterations of a suitable sparse quadratic approximant problem, so that the resulting parameter vector estimate is sparse and indicates few significant predictors. We conduct empirical assessments using data of the European Social Survey, in order to identify the set of determinants which better predict optimal well-being by means of the proposed sparse regression method. ESS data analysis confirms that few selected predictors provide good data interpretation and no loss of information in the frequency of correct classification for people meeting the criteria of optimal well-being. Moreover, simulations with different structural parameter values indicate that sparse logistic model performs better in terms of the estimation of the true vector of parameters in a more parsimonious setting compared to classical logistic regression. The benefits increase as the structural sparsity of the optimization problem becomes stronger.
... Recently, sparse representation has been extensively used for applications such as compressed sensing, reconstruction, and de-noising of medical images [46]. However, there are limited studies for sparse bio-signals de-noising [47]. These methods assume that the natural signal are sparse on to either a fixed dictionary like the Fourier and wavelet transform or a learned dictionary [48]. ...
There has been growing interest in low-cost light sources such as light-emitting diodes (LEDs) as an excitation source in photoacoustic imaging. However, LED-based photoacoustic imaging is limited by low signal due to low energy per pulse—the signal is easily buried in noise leading to low quality images. Here, we describe a signal de-noising approach for LED-based photoacoustic signals based on dictionary learning with an alternating direction method of multipliers. This signal enhancement method is then followed by a simple reconstruction approach delay and sum. This approach leads to sparse representation of the main components of the signal. The main improvements of this approach are a 38% higher contrast ratio and a 43% higher axial resolution versus the averaging method but with only 4% of the frames and consequently 49.5% less computational time. This makes it an appropriate option for real-time LED-based photoacoustic imaging.
... At the very first step, the dictionary D may be initialized by randomly selecting training feature vectors; the sparse coding step can then be solved resorting to standard sparse approximation algorithms like [1] or [14] as well as for the dictionary update rule that can be casted into different forms (e.g. [3,9,8]). ...
In this work we address the problem of gender recognition from facial images acquired in the wild. This problem is particularly difficult due to the presence of variations in pose, ethnicity, age and image quality. Moreover, we consider the special case in which only a small sample size is available for the training phase. We rely on a feature representation obtained from the well known VGG-Face Deep Convolutional Neural Network (DCNN) and exploit the effectiveness of a sparse-driven sub-dictionary learning strategy which has proven to be able to represent both local and global characteristics of the train and probe faces. Results on the publicly available LFW dataset are provided in order to demonstrate the effectiveness of the proposed method.
... In particular, the set of semantic elements assumed by w t is determined from low level spatial features f spatial t adopting either clustering, learning sparse dictionaries [12] or other ensemble techniques as discussed in Sec. 3.1. ...
Computational visual attention is a hot topic in computer vision. However, most efforts are devoted to model saliency, whilst the actual eye guidance problem, which brings into play the sequence of gaze shifts characterising overt attention, is overlooked. Further, in those cases where the generation of gaze behaviour is considered, stimuli of interest are by and large static (still images) rather than dynamic ones (videos). Under such circumstances, the work described in this note has a twofold aim: (i) addressing the problem of estimating and generating visual scan paths, that is the sequences of gaze shifts over videos; (ii) investigating the effectiveness in scan path generation offered by features dynamically learned on the base of human observers attention dynamics as opposed to bottom-up derived features. To such end a probabilistic model is proposed. By using a publicly available dataset, our approach is compared against a model of scan path simulation that does not rely on a learning step.
... In particular, the set of semantic elements assumed by w t is determined from low level spatial features f spatial t adopting either clustering, learning sparse dictionaries [12] or other ensemble techniques as discussed in Sec. 3.1. ...
Computational visual attention is a hot topic in computer vision. However, most efforts are devoted to model saliency, whilst the actual eye guidance problem, which brings into play the sequence of gaze shifts characterising overt attention, is overlooked. Further, in those cases where the generation of gaze behaviour is considered, stimuli of interest are by and large static (still images) rather than dynamic ones (videos). Under such circumstances, the work described in this note has a twofold aim: i) addressing the problem of estimating and generating visual scan paths, that is the sequences of gaze shifts over videos; ii) investigating the effectiveness in scan path generation offered by features dynamically learned on the base of human observers attention dynamics as opposed to bottom-up derived features. To such end a probabilistic model is proposed. By using a publicly available dataset, our approach is compared against a model of scan path simulation that does not rely on a learning step.
... The feature space is obtained employing deep features coupled with the linear discriminant analysis, while the concise model is derived adopting the method of optimal directions (MOD) [13], which has proved to be very efficient for low-dimensional input data. The benefits of this approach is that, contrarily to generic learning algorithms [14], the label consistency between dictionary atoms and training data is maintained, allowing the direct application of the classification stage based on majority voting (a demo code is available on the website: https://github.com/phuselab/SSLD-face_recognition). ...
Face recognition using a single reference image per subject is challenging, above all when referring to a large gallery of subjects. Furthermore, the problem hardness seriously increases when the images are acquired in unconstrained conditions. In this paper we address the challenging Single Sample Per Person (SSPP) problem considering large datasets of images acquired in the wild, thus possibly featuring illumination, pose, face expression, partial occlusions, and low-resolution hurdles. The proposed technique alternates a sparse dictionary learning technique based on the method of optimal direction and the iterative ℓ 0 -norm minimization algorithm called k-LiMapS. It works on robust deep-learned features, provided that the image variability is extended by standard augmentation techniques. Experiments show the effectiveness of our method against the hardness introduced above: first, we report extensive experiments on the unconstrained LFW dataset when referring to large galleries up to 1680 subjects; second, we present experiments on very low-resolution test images up to 8 × 8 pixels; third, tests on the AR dataset are analyzed against specific disguises such as partial occlusions, facial expressions, and illumination problems. In all the three scenarios our method outperforms the state-of-the-art approaches adopting similar configurations.
