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Compressed Sensing (CS) can be used to reconstruct sparse vector from less number of measurements, provided the signal can be represented in sparse domain. Sparse domain is a domain in which only a few measurements have non-zero values. Suppose a signal coefficients out of (where ) are non zero, then the signal is said to be sparse in that domain. This reconstructed sparse vector can be used to construct back the original signal if the sparse domain of signal is known. CS can be applied to speech signal only if sparse domain of speech signal is known. Consider a speech signal , which can be represented in a domain such that , where speech signal and the sparse coefficient vector , if number of significant (non zero) coefficients in sparse vector are . The observed signal is of dimension using CS speech signal is observed using a measurement matrix such that where such that minimization as }=\mbox\;\Vert \mathbf \Vert_1 \;\;\;\;\mbox\;\;\;\; \mathbf=\mathbf=\mathbf \mathbf = \mathbf, \;\mbox \;\;\mathbf=\mathbf}|}} If measurement matrix satisfies the restricted isometric property (RIP) and is incoherent with dictionary matrix . then the reconstructed signal is much closer to the original speech signal. Different types of measurement matrices like random matrices can be used for speech signals. Estimating the sparsity of speech signal is a problem since speech signal highly varies over time and thus sparsity of speech signal also varies highly over time. If sparsity of speech signal can be calculated over time without much complexity that will be best. If this is not possible then worst-case scenario for sparsity can be considered for a given speech signal. Sparse vector () using minimization.〔 Then original speech signal is reconstructed form the calculated sparse vector as ) to do some application-based processing like speaker recognition, speech enhancement, etc. == References == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Compressed sensing in speech signals」の詳細全文を読む スポンサード リンク
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