Abstract: Time series decomposition method and system are provided. Time series data including at least a seasonality component is received. A noise removal filter may be applied to the time series data. Furthermore, a trend component and the seasonality component are extracted from the time series data. A residual component may subsequently be extracted from the time series data based on the trend component and the seasonality component. Anomaly detection may then be performed on the trend component or the residual component to determine whether an anomaly exists in the time series data.

Abstract: Time series decomposition method and system are provided. Time series data including at least a seasonality component is received. A noise removal filter may be applied to the time series data. Furthermore, a trend component and the seasonality component are extracted from the time series data. A residual component may subsequently be extracted from the time series data based on the trend component and the seasonality component. Anomaly detection may then be performed on the trend component or the residual component to determine whether an anomaly exists in the time series data.

Abstract: A method of compressed sensing imaging includes acquiring a sparse digital image b, said image comprising a plurality of intensities corresponding to an I-dimensional grid of points, initializing points (x(k), y(k)), wherein x(k) is an element of a first expanded image x defined by b=R??1 x, wherein R is a Fourier transform matrix, ? is a wavelet transform matrix, y(k) is a point in ? ( ? i = 1 l ? ( ? i ? ? - 1 ? x ( k ) ) 2 ) 1 / 2 , ?i is a forward finite difference operator for a ith coordinate, and k is an iteration counter; calculating a first auxiliary variable s(k) from x ( k ) - ? 1 ( ?? ? ? n ? L n * ? y n ( k ) + ? ? ? R * ( R ? ? ? - 1 ? x ( k ) - b ) ) , wherein ?1,? are predetermined positive scalar constants, the sum is over all points n in x, and L* is an adjoint of operator L=(?1, . . .

Abstract: A method of compressed sensing imaging includes acquiring a sparse digital image b, said image comprising a plurality of intensities corresponding to an I-dimensional grid of points, initializing points (x(k), y(k)), wherein x(k) is an element of a first expanded image x defined by b=R??1 x, wherein R is a Fourier transform matrix, ? is a wavelet transform matrix, y(k) is a point in ? ( ? i = 1 l ? ( ? i ? ? - 1 ? x ( k ) ) 2 ) 1 / 2 , ?i is a forward finite difference operator for a ith coordinate, and k is an iteration counter; calculating a first auxiliary variable s(k) from x ( k ) - ? 1 ( ?? ? ? n ? L n * ? y n ( k ) + ? ? ? R * ( R ? ? ? - 1 ? x ( k ) - b ) ) , wherein ?1,? are predetermined positive scalar constants, the sum is over all points n in x, and L* is an adjoint of operator L=(?1, . . .