Noise filtering is a common step in image processing, and is particularly effective in improving the subjective quality of images. A large number of techniques have been developed, many of which concentrate on the problem of removing noise without damaging small structures such as edges. One recent approach that demonstrates empirical merit is the non-local means (NLM) algorithm. However, in or...

The seismic reflection method is one of the most important methods in geophysical exploration. There are three stages a exploration survey: acquisition, processing, and interpretation. This paper focuses on pre-processing tool, Non-Local Means (NLM) filter algorithm, which powerful technique that can significantly suppress noise data. However, domain NLM algorithm whole dataset 3D data being ve...

Partial Differential equations (PDE), wavelets-based methods and neighborhood filters were proposed as locally adaptive machines for noise removal. Recently, Buades, Coll and Morel proposed the Non-Local (NL-) means filter for image denoising. This method replaces a noisy pixel by the weighted average of other image pixels with weights reflecting the similarity between local neighborhoods of th...

In this paper we make a novel use of the Johnson-Lindenstrauss Lemma. The Lemma has an existential form saying that there exists a JL transformation f of the data points into lower dimensional space such that all of them fall into predefined error range δ. We formulate in this paper a theorem stating that we can choose the target dimensionality in a random projection type JL linear transformati...