Denoising and Compression

Wavelet shrinkage, nonparametric regression, block thresholding, multisignal thresholding

Wavelet and wavelet packet denoising allow you to retain features in your data that are often removed or smoothed out by other denoising techniques. You can compress data by setting perceptually unimportant wavelet and wavelet packet coefficients to zero and reconstructing the data. Noise in a signal is not always uniform in time, so you can apply interval-dependent thresholds to denoise data with nonconstant variance.

Use Wavelet Toolbox™ functions to denoise and obtain compressed signals and images. You can select from many thresholding strategies and explore denoising signals and images by using Wavelet Signal Denoiser.

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Featured Examples

Signal Deconvolution and Impulse Denoising Using Pursuit Methods

Learn how to remove impulsive noise from signals using pursuit methods.

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Denoise a Signal with the Wavelet Signal Denoiser

Learn how to denoise a signal and reproduce the results in your workspace.

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Wavelet Denoising

Use wavelets to denoise signals and images. Because wavelets localize features in your data to different scales, you can preserve important signal or image features while removing noise. The basic idea behind wavelet denoising, or wavelet thresholding, is that the wavelet transform leads to a sparse representation for many real-world signals and images. What this means is that the wavelet transform concentrates signal and image features in a few large-magnitude wavelet coefficients. Wavelet coefficients which are small in value are typically noise and you can "shrink" those coefficients or remove them without affecting the signal or image quality. After you threshold the coefficients, you reconstruct the data using the inverse wavelet transform.

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Wavelet Interval-Dependent Denoising

The example shows how to denoise a signal using interval-dependent thresholds.

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Two-Dimensional True Compression

Starting from a given image, the goal of true compression is to minimize the number of bits needed to represent it, while storing information of acceptable quality. Wavelets contribute to effective solutions for this problem. The complete chain of compression includes iterative phases of quantization, coding, and decoding, in addition to the wavelet processing itself.

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