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How is the sparse signal of M defined?
A random M sparse signal F is defined with M nonzero coefficient positions that are randomly distributed in {0,…, N – 1} with amplitudes that are independent Gaussian random variables of unit variance. For realizations f of F, a basis pursuit approximation f ˜ is computed from the Q measurements Y = Uf with no noise.
How is sparse signal approximation used in science?
Sparse signal approximation has gained popularity over the last decade. The sparse approximation model suggests that a natural signal could be compactly approximated by only a few atoms out of a properly given dictionary, where the weights associated with the dictionary atoms are called the sparse codes.
How is the basis pursuit of a sparse signal computed?
For realizations f of F, a basis pursuit approximation f ˜ is computed from the Q measurements Y = Uf with no noise. The ratio of perfect recovery is the probability that an M sparse signal f drawn from this distribution is exactly recovered by the basis pursuit.
How to find the probabilities of a random variable?
For any normal random variable, if you find the Z-score for a value (i.e standardize the value), the random variable is transformed into a standard normal and you can find probabilities using the standard normal table. For instance, assume U.S. adult heights and weights are both normally distributed.
How are sparse codes used in signal processing?
Proven to be both robust to noise and scalable to high-dimensional data, sparse codes are known as powerful features, and benefit a wide range of signal processing applications, such as source coding [1], denoising [2], source separation [3], pattern classification [4], and clustering [5].
What is the ratio of perfect recovery in sparse signal?
The ratio of perfect recovery is the probability that an M sparse signal f drawn from this distribution is exactly recovered by the basis pursuit. It is evaluated numerically by Monte-Carlo sampling. Figure 13.10 shows the recovery performance of basis pursuit for Q = 100 and for several values of N.