Abstract

This paper introduces a novel design for the dictionary learning algorithm, intended for scalable sparse representation of high motion video sequences and natural images. The proposed algorithm is built upon the foundation of the K-SVD framework originally designed to learn non-scalable dictionaries for natural images. Proposed design is mainly motivated by the main perception characteristic of the Human Visual System (HVS) mechanism. Specifically, its core structure relies on the exploitation of the high-frequency image components and contrast variations in order to achieve visual scene objects identification at all scalable levels. Proposed design is implemented by introducing a semi-random Morphological Component Analysis (MCA) based initialization of the K-SVD dictionary and the regularization of its atom’s update mechanism. In general, dictionary learning for sparse representations leads to state-of-the-art image restoration results for several different problems in the field of image processing. In experimental section we show that these are equally achievable by accommodating all dictionary elements to tailor the scalable data representation and reconstruction, hence modeling data that admit sparse representation in a novel manner. Performed simulations include scalable sparse recovery for representation of static and dynamic data changing over time (e.g., video) together with application to denoising and compressive sensing.

Highlights

  • Over the past couple of decades, image processing applications have undergone significant improvements

  • A recent critical factor in this growth is the sparse coding paradigm introduced firstly by [1], based on the assumption that signals admit a sparse decomposition over a learned representational basis i.e., dictionary. This so-called sparseland model [2, 3, 4] has led to numerous state-of-the-art algorithms for several image processing problems [3] in the context of dictionary D ∈ Rn×K learning for any image signal class

  • The applications of dictionary learning [10, 11] include areas such as classification [12, 13], efficient face recognition [14], inpainiting [15], denoising [16, 17], super-resolution [18, 19], Morphological Component Analysis (MCA) [20, 21] and those designed for sparse color image processing [22, 23]

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Summary

Introduction

Over the past couple of decades, image processing applications have undergone significant improvements. To the best of our knowledge existing literature just provides the dictionary learning algorithms such as K-SVD [3, 10] that only assume fine resolution as the representational output This is not sufficient nor tailored to provide the progressive image recovery over its trained sparse representation. Proposed implementation is carried out by introducing regularization of the K-SVD atoms update stage aiming for scalable sparse image reconstruction which would improve gradually as we take more and more entries per each coefficient xi ∈ X to restore {yi}Ni=1 patches. As a solution to the scalable image restoration problem, this paper provides an extension and upgrade of the K-SVD dictionary learning concept from nonscalable to scalable adaptive image reconstruction by introducing semi-random dictionary initialization based on the MCA activity norm [3] and by regularizing the learning process of dictionary elements overall promoting the HVS perceptual mechanism features; 4. Given the CS results in [43, 44] we test the performance of proposed scalable dictionary learning method in one of the CS sampling scenarios

Problem statement and proposed approach
Dictionary initialization
Sparse coding
Regularized dictionary update stage
Computational Complexity
Simulation results
Scalability Performance
Application to image processing 1: denoising
Application to image processing 2: compressive sensing
Discussion
Spatial frequencies distribution
Contrast variation
Findings
Noise distortion of the smooth and texture image patches
Conclusion
Full Text
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