Image Compressive Sensing Recovery Using Adaptively Learned Sparsifying Basis via L0 Minimization (1404.7566v1)

Abstract: From many fewer acquired measurements than suggested by the Nyquist sampling theory, compressive sensing (CS) theory demonstrates that, a signal can be reconstructed with high probability when it exhibits sparsity in some domain. Most of the conventional CS recovery approaches, however, exploited a set of fixed bases (e.g. DCT, wavelet and gradient domain) for the entirety of a signal, which are irrespective of the non-stationarity of natural signals and cannot achieve high enough degree of sparsity, thus resulting in poor CS recovery performance. In this paper, we propose a new framework for image compressive sensing recovery using adaptively learned sparsifying basis via L0 minimization. The intrinsic sparsity of natural images is enforced substantially by sparsely representing overlapped image patches using the adaptively learned sparsifying basis in the form of L0 norm, greatly reducing blocking artifacts and confining the CS solution space. To make our proposed scheme tractable and robust, a split Bregman iteration based technique is developed to solve the non-convex L0 minimization problem efficiently. Experimental results on a wide range of natural images for CS recovery have shown that our proposed algorithm achieves significant performance improvements over many current state-of-the-art schemes and exhibits good convergence property.

• The paper introduces a novel image compressive sensing recovery framework that adaptively learns sparsifying bases from image patches using an efficient L0 minimization technique to enhance reconstruction quality.
• Experimental results demonstrate that this method achieves significantly higher PSNR and FSIM values, surpassing state-of-the-art methods by 2-6 dB depending on the benchmark.
• This research highlights the effectiveness of adaptive basis learning in compressive sensing and offers practical improvements for applications like medical imaging and remote sensing where data acquisition is limited.

Compressive Sensing Recovery via Adaptive Sparsifying Basis

The paper "Image Compressive Sensing Recovery Using Adaptively Learned Sparsifying Basis via $L_0$ Minimization" offers significant advancements in the domain of image compressive sensing (CS). The authors introduce a novel framework that leverages adaptively learned sparsifying bases to address challenges associated with traditional CS recovery methods. This framework improves the quality of image reconstruction from a limited number of measurements, surpassing many state-of-the-art methodologies.

Key Contributions

The paper focuses on enhancing CS recovery by embracing two critical properties of natural images: sparsity and nonlocal self-similarity. Unlike traditional methods that utilize fixed basis functions like DCT or wavelets, this work employs a basis that is adaptively learned to better capture the sparsity inherent in image patches. This adaptive learning is realized via $L_0$ minimization, directly addressing limitations posed by non-convex optimization.

1. Adaptive Sparsifying Basis: By learning sparsifying bases from the image at each iteration, the approach accounts for the non-stationary characteristics of natural images, facilitating better sparsity and, thus, more effective reconstruction.
2. $L_0$ Minimization Framework: The paper opts for a non-convex $L_0$ minimization technique, addressing the inherent NP-hard nature efficiently through a split Bregman iteration method. This choice significantly confines the solution space and improves convergence.
3. Split Bregman Iteration: This established optimization technique is adapted to solve the $L_0$ framework effectively. It enhances computational feasibility, boosting convergence without compromising performance.

Results and Performance

The experimental results are robust, demonstrating superior recovery performance across a range of test images. The method consistently yields higher PSNR and FSIM values compared to existing CS approaches such as wavelet-based methods, total variation techniques, and multi-hypothesis algorithms.

• Overlapped Patch Strategy: The use of overlapping patches is emphasized in the experimental section, showing its efficacy in reducing artifacts and maintaining high recovery quality.
• Comparison with Other Methods: Against benchmarks, the proposed algorithm improves PSNR by over 6 dB when compared with basic DWT methods, and enhancements of around 2 to 3 dB over more advanced algorithms like CoS and MH.
• Computation Time: While the adaptive basis learning and $L_0$ minimization add to computational complexity, the paper details an acceptable trade-off between quality and processing time. The approach takes approximately 9 minutes for a $256 \times 256$ image in standard computational environments, which is competitive given the quality improvements.

Theoretical and Practical Implications

This research carries both significant theoretical and practical implications. Theoretically, it underscores the efficacy of adaptive basis learning in CS, prompting a shift away from static domains. Practically, the improvement in image recovery opens avenues in applications where high-quality imaging is critical yet constrained by stringent measurement capabilities, such as medical imaging and remote sensing.

Future Directions

Looking forward, the framework could further benefit from integration with deep learning methodologies to automate and potentially enhance the learning of sparsifying bases. Additionally, exploring real-time performance optimizations could broaden its applicability in dynamic settings where computational resources are limited.

In summary, this paper presents a compelling enhancement in image compressive sensing recovery, attributing its success to the adaptive learning of sparsifying bases and efficient handling of non-convex $L_0$ minimization challenges. Its contribution is poised to influence future research and application development in efficient data acquisition and reconstruction methods.