Autoregressive (AR) modeling is invaluable in signal processing, in particular in speech and audio fields. Attempts in the literature can be found that regularize or constrain either the time-domain signal values or the AR coefficients, which is done for various reasons, including the incorporation of prior information or numerical stabilization. Although these attempts are appealing, an encompassing and generic modeling framework is still missing. We propose such a framework and the related optimization problem and algorithm. We discuss the computational demands of the algorithm and explore the effects of various improvements on its convergence speed. In the experimental part, we demonstrate the usefulness of our approach on the audio declipping and dequantization problems. We compare its performance against state-of-the-art methods and demonstrate the competitiveness of the proposed method in declipping musical signals, and its superiority in declipping speech. The evaluation includes a heuristic algorithm of generalized linear prediction (GLP), a strong competitor which has only been presented as a patent and is new in the scientific community.

翻译：自回归（AR）建模在信号处理领域，尤其是在语音和音频领域，具有重要价值。文献中已有尝试对时域信号值或AR系数进行正则化或约束，这出于多种原因，包括融入先验信息或实现数值稳定。尽管这些尝试颇具吸引力，但仍缺乏一个全面且通用的建模框架。本文提出了这样一个框架，以及相关的优化问题和算法。我们讨论了算法的计算需求，并探讨了各种改进对其收敛速度的影响。在实验部分，我们通过音频削波修复和去量化问题展示了所提方法的实用性。我们将其性能与先进方法进行了比较，结果表明所提方法在修复音乐信号削波方面具有竞争力，在修复语音削波方面则更具优势。评估对象包括广义线性预测（GLP）的启发式算法，这是一种强有力的竞争者，此前仅以专利形式公开，在科学界尚属新颖。