Low-complexity inverse transform and sub-sampling

A method of inverse transform and sub-sampling having low computational complexity, comprising:

• separating input signals into high-frequency signals and low-frequency signals;
• expressing said high-frequency signals as a high frequency matrix in spatial domain, and expressing said low-frequency signals as a low frequency matrix in spatial domain;
• performing compensation computations according to H1−1×H2×Y3+Y2×K2×K1−1×H1−1×H2×Y4×K2×K1−1, wherein
• H1−1 is the inversed first portion of the combined matrix from the down-scale matrix and the transposed inverse transform matrix,
• H2 is the second portion of the combined matrix from the down-scale matrix and the transposed inverse transform matrix,
• Y3 is the left-bottom portion of the frequency-domain coefficient matrix,
• Y2 is the right-top portion of the frequency-domain coefficient matrix,
• Y4 is the right-bottom portion of the frequency-domain coefficient matrix,
• K2 is the second portion of the combined matrix from the inverse transform matrix and the transposed down-scale matrix,
• K1−1 is the inversed first portion of the combined matrix from the inverse transform matrix and the transposed down-scale matrix;
• obtaining compensation values for non-zero high-frequency signals;
• adding separated low-frequency signals with said compensation values;
• selecting a dimension of an inverse transform matrix depending on actual sub-sampling requirements for said inverse transform and said sub-sampling;
• said dimension of said inverse transform matrix being less than that of an original inverse transform matrix;
• integrating a matrix of said inverse transform with said matrix of said sub-sampling in cooperation with compensated frequency-domain coefficients, in proceeding with said inverse transform and said sub-sampling of said matrix;
• separating said input signals into said high-frequency signals and said low-frequency signals being based on ways of sub-sampling;
• determining the dimension of the inverse transform matrix according to reduction ratios of a frame length and width;
• utilizing an original frame size L1×W1 in reducing a frame size into L2×W2;
• reducing said dimension of said inverse transform matrix through reduction ratios of L2/L1 and W2/W1;
• realizing a frame-size reduction transform, and determining a plurality of said low-frequency signals;
• and
• performing an inverse transform and a sub-sampling for a result of additions.