| Summary: | Three-dimensional (3D) synthetic aperture radar (SAR) imaging provides complete 3D spatial information, which has been used in environmental monitoring in recent years. Compared with matched filtering (MF) algorithms, the regularization technique can improve image quality. However, due to the substantial computational cost, the existing observation-matrix-based sparse imaging algorithm is difficult to apply to large-scene and 3D reconstructions. Therefore, in this paper, novel 3D sparse reconstruction algorithms with generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>q</mi></msub></semantics></math></inline-formula>-regularization are proposed. First, we combine majorization–minimization (MM) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>1</mn></msub></semantics></math></inline-formula> regularization (MM-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>1</mn></msub></semantics></math></inline-formula>) to improve SAR image quality. Next, we combine MM and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></semantics></math></inline-formula> regularization (MM-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></semantics></math></inline-formula>) to achieve high-quality 3D images. Then, we present the algorithm which combines MM and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>0</mn></msub></semantics></math></inline-formula> regularization (MM-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>0</mn></msub></semantics></math></inline-formula>) to obtain 3D images. Finally, we present a generalized MM-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>q</mi></msub></semantics></math></inline-formula> algorithm (GMM-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>q</mi></msub></semantics></math></inline-formula>) for sparse SAR imaging problems with arbitrary <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mspace width="0.166667em"></mspace><mfenced separators="" open="(" close=")"><mrow><mn>0</mn><mo>≤</mo><mi>q</mi><mo>≤</mo><mn>1</mn></mrow></mfenced></mrow></semantics></math></inline-formula> values. The proposed algorithm can improve the performance of 3D SAR images, compared with existing regularization techniques, and effectively reduce the amount of calculation needed. Additionally, the reconstructed complex image retains the phase information, which makes the reconstructed SAR image still suitable for interferometry applications. Simulation and experimental results verify the effectiveness of the algorithms.
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