You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Conventional deep neural network (DNN)-based speech enhancement (SE) approaches aim to minimize the mean square error (MSE) between enhanced speech and clean reference. The MSE-optimized model may not directly improve the performance of an automatic speech recognition (ASR) system. If the target is to minimize the recognition error, the recognition results should be used to design the objective function for optimizing the SE model. However, the structure of an ASR system, which consists of multiple units, such as acoustic and language models, is usually complex and not differentiable. In this study, we proposed to adopt the reinforcement learning algorithm to optimize the SE model based on the recognition results. We evaluated the propsoed SE system on the Mandarin Chinese broadcast news corpus (MATBN). Experimental results demonstrate that the proposed method can effectively improve the ASR results with a notable 12.40 and 19.23 error rate reductions for signal to noise ratio at 0 dB and 5 dB conditions, respectively.

Cited Abstract(s):
[1]: Abstract Automatic speech recognition in everyday environments must be robust to significant levels of reverberation and noise. One strategy to achieve such robustness is multi-microphone speech enhancement. In this study, we present results of an evaluation of different speech enhancement pipelines using a state-of-the-art ASR system for a wide range of reverberation and noise conditions. The evaluation exploits the recently released ACE Challenge database which includes measured multichannel acoustic impulse responses from 7 different rooms with reverberation times ranging from 0.33 to 1.34 s. The reverberant speech is mixed with ambient, fan and babble noise recordings made with the same microphone setups in each of the rooms. In the first experiment, performance of the ASR without speech processing is evaluated. Results clearly indicate the deleterious effect of both noise and reverberation. In the second experiment, different speech enhancement pipelines are evaluated with relative word error rate reductions of up to 82 . Finally, the ability of selected instrumental metrics to predict ASR performance improvement is assessed. The best performing metric, Short-Time Objective Intelligibility Measure, is shown to have a Pearson correlation coefficient of 0.79, suggesting that it is a useful predictor of algorithm performance in these tests.
It has been reported that when the goal is to improve the ASR performance, ideal binary mask (IBM) is more suitable than ideal ratio mask (IRM) or directly mapping [1] to be used to design the SE system. Therefore, we implement an IBM-based SE system in this study. For the IBM-based SE system, the input @math was filtered by IBM to obtain the enhanced output @math : where @math '' represents an element-wise multiplier, and @math is the IBM matrix, which is defined as: where @math is the unit step function applied to each element of @math .