Abstract
The L1 norm regularized least squares method is often used for finding sparse approximate solutions and is widely used in 1-D signal restoration. Basis pursuit denoising (BPD) performs noise reduction in this way. However, the shortcoming of using L1 norm regularization is the underestimation of the true solution. Recently, a class of non-convex penalties have been proposed to improve this situation. This kind of penalty function is non-convex itself, but preserves the convexity property of the whole cost function. This approach has been confirmed to offer good performance in 1-D signal denoising. This paper demonstrates the aforementioned method to 2-D signals (images) and applies it to multisensor image fusion. The problem is posed as an inverse one and a corresponding cost function is judiciously designed to include two data attachment terms. The whole cost function is proved to be convex upon suitably choosing the non-convex penalty, so that the cost function minimization can be tackled by convex optimization approaches, which comprise simple computations. The performance of the proposed method is benchmarked against a number of state-of-the-art image fusion techniques and superior performance is demonstrated both visually and in terms of various assessment measures.
Abstract (translated)
L1范数正则化最小二乘法常用于寻找稀疏近似解，在一维信号恢复中有着广泛的应用。基跟踪去噪（BPD）就是用这种方法来降低噪声的。然而，使用l1范数正则化的缺点是对真实解的低估。近年来，人们提出了一类非凸惩罚来改善这一状况。这种罚函数本身是非凸的，但保留了整个代价函数的凸性。该方法在一维信号去噪中具有良好的性能。本文将上述方法应用于二维信号（图像）的融合，并将其应用于多传感器图像融合。提出了一个反问题，并合理地设计了一个相应的成本函数，将两个数据附件项结合起来。通过适当选择非凸惩罚，证明了整个成本函数是凸的，从而可以用凸优化方法来解决成本函数的最小化问题，其中包括简单的计算。提出的方法的性能是以许多最先进的图像融合技术为基准的，并通过视觉和各种评估措施证明了其优越的性能。
URL
https://arxiv.org/abs/1905.09645
