[Paper Review] Compressed Sensing SAR Imaging with Multilook Processing

Jian Fang, Zongben Xu+3 more|arXiv (Cornell University)|Oct 27, 2013

Sparse and Compressive Sensing Techniques18 references3 citations

TL;DR

This paper proposes a compressed sensing SAR imaging method that integrates multilook processing into the reconstruction phase to reduce speckle noise while operating below the Nyquist rate. By inverting the multilook procedure and combining it with random sampling, the method formulates a joint sparse regularization model that recovers multiple subimages simultaneously, achieving effective speckle suppression and high-quality image reconstruction with sub-Nyquist measurements.

ABSTRACT

Multilook processing is a widely used speckle reduction approach in synthetic aperture radar (SAR) imaging. Conventionally, it is achieved by incoherently summing of some independent low-resolution images formulated from overlapping subbands of the SAR signal. However, in the context of compressive sensing (CS) SAR imaging, where the samples are collected at sub-Nyquist rate, the data spectrum is highly aliased that hinders the direct application of the existing multilook techniques. In this letter, we propose a new CS-SAR imaging method that can realize multilook processing simultaneously during image reconstruction. The main idea is to replace the SAR observation matrix by the inverse of multilook procedures, which is then combined with random sampling matrix to yield a multilook CS-SAR observation model. Then a joint sparse regularization model, considering pixel dependency of subimages, is derived to form multilook images. The suggested SAR imaging method can not only reconstruct sparse scene efficiently below Nyquist rate, but is also able to achieve a comparable reduction of speckles during reconstruction. Simulation results are finally provided to demonstrate the effectiveness of the proposed method.

Motivation & Objective

• Address the challenge of integrating multilook speckle reduction into compressed sensing SAR (CS-SAR) imaging, where conventional frequency-domain multilooking is incompatible with time-domain CS models.
• Overcome the issue of signal aliasing in sub-Nyquist CS-SAR, which hinders direct application of standard multilook techniques.
• Develop a unified CS-SAR observation model that embeds multilook processing during image reconstruction to simultaneously achieve sparse scene recovery and speckle reduction.
• Preserve the benefits of CS-SAR—reduced sampling rates—while improving image quality through in-process speckle suppression to avoid target truncation during reconstruction.

Proposed method

• Replace the standard SAR observation matrix in CS-SAR with the inverse of the multilooking procedure, enabling frequency-domain multilooking to be integrated into the compressed sensing framework.
• Construct a new observation model by combining the inverse multilook matrix with the random sampling matrix, forming a modified sensing matrix that supports multilook CS-SAR reconstruction.
• Formulate a joint sparse regularization model that exploits the group sparsity of multilook subimages, enforcing shared support across all looks to improve reconstruction accuracy.
• Use block sparse optimization (e.g., $L_q$ minimization with $0 < q \leq 1$) to recover individual subimages from compressed measurements, followed by incoherent averaging to produce the final low-speckle image.
• Leverage time-frequency transformations to bridge the gap between time-domain CS sampling and frequency-domain multilook operations, enabling faster computation.
• Apply thresholding and iterative reweighting to enhance sparsity and suppress aliasing effects in the reconstructed subimages.

Experimental results

Research questions

• RQ1 Can multilook processing be effectively integrated into the compressed sensing framework for SAR imaging without requiring full-bandwidth sampling?
• RQ2 How can the inverse of the multilooking process be mathematically modeled to enable joint reconstruction of multiple subimages in a CS-SAR context?
• RQ3 To what extent does the proposed method reduce speckle noise while maintaining high reconstruction fidelity at sub-Nyquist sampling rates?
• RQ4 How does the performance of the proposed method compare to conventional RDA and multilook RDA in terms of ENL and image quality under varying sampling rates and look numbers?

Key findings

• The proposed method successfully reconstructs sparse SAR scenes using only 20% of the Nyquist rate, achieving artifact-free images comparable to full-sampled RDA results.
• The equivalent look number (ENL) increases with the number of looks, demonstrating effective speckle reduction—ENL improves significantly with higher look counts, especially at full sampling rates.
• At 20% sampling rate, the ENL of the proposed method shows a slight decline compared to full-sampling performance, indicating a minor trade-off between sampling reduction and speckle suppression quality.
• The method achieves a balance between low sampling complexity and speckle reduction, with reconstructed images showing reduced sidelobes and preserved target strength compared to standard CS-SAR.
• Simulation results confirm that the joint sparse regularization model effectively captures pixel dependencies across multilook subimages, enhancing reconstruction fidelity.
• The proposed method maintains comparable image quality to multilook RDA when using full data, and outperforms standard CS-SAR in speckle suppression while operating at sub-Nyquist rates.