A Convolutional Dictionary Learning based l1 Norm Error with Smoothed l0 Norm Regression

2019 ◽  
Author(s):  
Kaede Kumamoto ◽  
Shinnosuke Matsuo ◽  
Yoshimitsu Kuroki
Keyword(s):  
Dictionary Learning ◽  
L1 Norm ◽  
Norm Error

scholarly journals Optimization for L1-Norm Error Fitting via Data Aggregation

2020 ◽  
Author(s):  
Young Woong Park
Keyword(s):  
Data Aggregation ◽  
State Of The Art ◽  
Subset Selection ◽  
Global Optimum ◽  
L1 Norm ◽  
Orthogonal Procrustes Problem ◽  
Monotonic Convergence ◽  
Procrustes Problem ◽  
Fitting Model ◽  
Norm Error

We propose a data aggregation-based algorithm with monotonic convergence to a global optimum for a generalized version of the L1-norm error fitting model with an assumption of the fitting function. The proposed algorithm generalizes the recent algorithm in the literature, aggregate and iterative disaggregate (AID), which selectively solves three specific L1-norm error fitting problems. With the proposed algorithm, any L1-norm error fitting model can be solved optimally if it follows the form of the L1-norm error fitting problem and if the fitting function satisfies the assumption. The proposed algorithm can also solve multidimensional fitting problems with arbitrary constraints on the fitting coefficients matrix. The generalized problem includes popular models, such as regression and the orthogonal Procrustes problem. The results of the computational experiment show that the proposed algorithms are faster than the state-of-the-art benchmarks for L1-norm regression subset selection and L1-norm regression over a sphere. Furthermore, the relative performance of the proposed algorithm improves as data size increases.

Sparse and limited-angle CT image reconstruction using dictionary learning constrained by L1 norm

2019 ◽  
Vol 61 (10) ◽  
pp. 584-590
Author(s):  
Jun-Nian Gou ◽  
Pan-Pan Zhai ◽  
Hai-Ying Dong
Keyword(s):  
Dictionary Learning ◽  
Absolute Error ◽  
Image Feature ◽  
Projection Data ◽  
Reconstruction Technique ◽  
L1 Norm ◽  
Noisy Projection ◽  
The Impact ◽  
Better Than ◽  
Limited Angle

Reconstructed images from computed tomography (CT) using the algebraic reconstruction technique (ART) and simultaneous ART (SART) algorithms often suffer from obvious artefacts when only sparse and limited-angle projection data are available. Using the ability of dictionary learning (DL) in image feature extraction and sparse signal representation, a new iterative reconstruction algorithm, ART-DL-L1, is proposed to overcome the aforementioned limitations. This new algorithm is based on DL and an L1 norm constraint, combined with ART. An alternate iterative solving strategy based on an approach of 'ART first, then adaptive dictionary learning' is suggested and is explicitly described in a flowchart depicting the ART-DL-L1 algorithm. For both a noisy projection of 360° sparse data and limitedangle data of 120°, simulation reconstruction results from the classic Shepp-Logan image obtained using ART-DL-L1 appear to be better than those obtained using SART and total variation (TV) algorithms and also better than the cutting-edge ART-DL-L2 algorithm. Five evaluation metrics corresponding to the root-mean-square error (RMSE), the mean absolute error (MAE), the peak signal-to-noise ratio (PSNR), the residuals and the structural similarity (SSIM) index are adopted to estimate the reconstruction effect. The results suggest that the five metrics obtained using ART-DL-L1 outperform those obtained using the other three algorithms. The impact of using patches of various sizes played by the DL part in ART-DL-L1 is considered in the simulations and the patch size achieving the best reconstructed image quality is identified in this case as 25 (5 × 5). Overall, the proposed ART-DL-L1 algorithm may reduce artefacts and suppress noise from incomplete noisy projection CT imaging to some degree.

scholarly journals Nonnegative Dictionary-Learning Algorithm Based on L1 Norm with the Sparse Analysis Model

2015 ◽  
Vol 1 (4) ◽  
pp. 1-10
Author(s):  
Yujie Li ◽  
Shuxue Ding ◽  
Zhenni Li ◽  
Wuhui Chen
Keyword(s):  
Dictionary Learning ◽  
Learning Algorithm ◽  
Analysis Model ◽  
L1 Norm

scholarly journals Inverse Synthetic Aperture Radar Sparse Imaging Exploiting the Group Dictionary Learning

2021 ◽  
Vol 13 (14) ◽  
pp. 2812
Author(s):  
Changyu Hu ◽  
Ling Wang ◽  
Daiyin Zhu ◽  
Otmar Loffeld
Keyword(s):  
Image Reconstruction ◽  
Dictionary Learning ◽  
Reconstruction Error ◽  
Imaging Method ◽  
L1 Norm ◽  
Norm Minimization ◽  
Imaging Results ◽  
Computational Speed ◽  
Feature Information ◽  
The Relationship

Sparse imaging relies on sparse representations of the target scenes to be imaged. Predefined dictionaries have long been used to transform radar target scenes into sparse domains, but the performance is limited by the artificially designed or existing transforms, e.g., Fourier transform and wavelet transform, which are not optimal for the target scenes to be sparsified. The dictionary learning (DL) technique has been exploited to obtain sparse transforms optimized jointly with the radar imaging problem. Nevertheless, the DL technique is usually implemented in a manner of patch processing, which ignores the relationship between patches, leading to the omission of some feature information during the learning of the sparse transforms. To capture the feature information of the target scenes more accurately, we adopt image patch group (IPG) instead of patch in DL. The IPG is constructed by the patches with similar structures. DL is performed with respect to each IPG, which is termed as group dictionary learning (GDL). The group oriented sparse representation (GOSR) and target image reconstruction are then jointly optimized by solving a l1 norm minimization problem exploiting GOSR, during which a generalized Gaussian distribution hypothesis of radar image reconstruction error is introduced to make the imaging problem tractable. The imaging results using the real ISAR data show that the GDL-based imaging method outperforms the original DL-based imaging method in both imaging quality and computational speed.

scholarly journals Scalable Block-Diagonal Locality-Constrained Projective Dictionary Learning

2019 ◽  
Author(s):  
Zhao Zhang ◽  
Weiming Jiang ◽  
Zheng Zhang ◽  
Sheng Li ◽  
Guangcan Liu ◽  
...  
Keyword(s):  
Dictionary Learning ◽  
Data Matrix ◽  
Testing Time ◽  
L1 Norm ◽  
Reconstruction Process ◽  
Label Information ◽  
Diagonal Representation ◽  
Efficient Representation ◽  
Multiclass Classifier ◽  
Block Diagonal

We propose a novel structured discriminative block- diagonal dictionary learning method, referred to as scalable Locality-Constrained Projective Dictionary Learning (LC-PDL), for efficient representation and classification. To improve the scalability by saving both training and testing time, our LC-PDL aims at learning a structured discriminative dictionary and a block-diagonal representation without using costly l0/l1-norm. Besides, it avoids extra time-consuming sparse reconstruction process with the well-trained dictionary for new sample as many existing models. More importantly, LC-PDL avoids using the com- plementary data matrix to learn the sub-dictionary over each class. To enhance the performance, we incorporate a locality constraint of atoms into the DL procedures to keep local information and obtain the codes of samples over each class separately. A block-diagonal discriminative approximation term is also derived to learn a discriminative projection to bridge data with their codes by extracting the special block-diagonal features from data, which can ensure the approximate coefficients to associate with its label information clearly. Then, a robust multiclass classifier is trained over extracted block-diagonal codes for accurate label predictions. Experimental results verify the effectiveness of our algorithm.

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