A white noise signal can access any possible configuration of values, though
statistically over many samples tends to a uniform spectral distribution, and
is highly unlikely to produce intelligible sound. But how unlikely? The
probability that white noise generates a music-like signal over different
durations is analyzed, based on some necessary features observed in real music
audio signals such as mostly proximate movement and zero crossing rate. Given
the mathematical results, the rarity of music as a signal is considered
overall. The applicability of this study is not just to show that music has a
precious rarity value, but that examination of the size of music relative to
the overall size of audio signal space provides information to inform new
generations of algorithmic music system (which are now often founded on audio
signal generation directly, and may relate to white noise via such machine
learning processes as diffusion). Estimated upper bounds on the rarity of music
to the size of various physical and musical spaces are compared, to better
understand the magnitude of the results (pun intended). Underlying the research
are the questions `how much music is still out there?' and `how much music
could a machine learning process actually reach?'.

白噪声能够生成类似音乐信号的概率以及音乐信号的稀有程度对音频信号空间的大小提供了信息，对算法音乐系统的新一代发展具有实际应用价值。

音乐音频信号在可能音频生成空间中的稀有性

The Rarity of Musical Audio Signals Within the Space of Possible Audio  Generation

Existing image complexity metrics cannot distinguish meaningful content from
noise. This means that white noise images, which contain no meaningful
information, are judged as highly complex. We present a new image complexity
metric through hierarchical clustering of patches. We use the minimum
description length principle to determine the number of clusters and designate
certain points as outliers and, hence, correctly assign white noise a low
score. The presented method has similarities to theoretical ideas for measuring
meaningful complexity. We conduct experiments on seven different sets of
images, which show that our method assigns the most accurate scores to all
images considered. Additionally, comparing the different levels of the
hierarchy of clusters can reveal how complexity manifests at different scales,
from local detail to global structure. We then present ablation studies showing
the contribution of the components of our method, and that it continues to
assign reasonable scores when the inputs are modified in certain ways,
including the addition of Gaussian noise and the lowering of the resolution.

提出了一种基于层次聚类和最小描述长度的图像复杂度衡量方法，可以正确识别出白噪声图像，并在多组实验中表现出最准确的衡量结果，同时还可以从不同层次的聚类中揭示出复杂度的局部和全局特征以及相关构成因素。

用最小描述长度聚类法度量有意义图片复杂度

Minimum Description Length Clustering to Measure Meaningful Image  Complexity

To denoise a reference patch, the Non-Local-Means denoising filter processes
a set of neighbor patches. Few Nearest Neighbors (NN) are used to limit the
computational burden of the algorithm. Here here we show analytically that the
NN approach introduces a bias in the denoised patch, and we propose a different
neighbors' collection criterion, named Statistical NN (SNN), to alleviate this
issue. Our approach outperforms the traditional one in case of both white and
colored noise: fewer SNNs generate images of higher quality, at a lower
computational cost.

通过分析研究表明，最近邻的方法引入了去噪补丁的偏差，并提出了一种名为 “统计最近邻（SNN）” 的不同邻居收集准则，以减轻此问题。我们的方法在白噪声和彩色噪声的情况下均优于传统方法：较少的 SNN 生成更高质量的图像，计算成本更低。