Universal Multi-Sensor Data Compression

A method for compression of a signal x of length N1 comprising data, the method comprising:

• at least for a first level of decomposition, transforming the signal based on a first sparse matrix A1, of size N1×N1 formed by an invertible matrix Φd1 of size d1×di, wherein di is a divisor of N1, representing a divisor-based signal decomposition for a first divisor d1 to obtain a first decomposed vector s1 of transformation coefficients, wherein s1=A1x, and wherein the first decomposed vector s1 comprises an initial component v1 and detail components
• w
• 1
• 1
• ,
• w
• 2
• 1
• ,
• …
• ,
• w
• d
• 1
• -
• 1
• 1
• ,
• and wherein each of one or more row vectors of Φd1 is extended up to a signal length N1 by appending N1−d1 zeros and wherein the one or more row vectors of Φd1 are shifted by kd1 for each row, wherein k=0, 1, 2, . . . , N1/d1−1;
• at least for a second level of decomposition, transforming the initial component based on a second sparse matrix A2, of size N2×N2, where
• N
• 2
• =
• N
• 1
• d
• 1
• ,
• formed by an invertible matrix Φd2, of size d2×d2, wherein d2 is a divisor of N2,, representing a divisor-based signal decomposition for a second divisor d2, to obtain a second decomposed vector s2 of transformation coefficients wherein s2=A2v1, and wherein the second decomposed vector s2 comprises an initial component v2 and detail components
• w
• 1
• 2
• ,
• w
• 2
• 2
• ,
• …
• ,
• w
• d
• 2
• -
• 1
• 2
• ,
• and wherein each of one or more row vectors of Φd2 is extended up to a signal length N2 by appending N2−d2 zeros and wherein the one or more row vectors of Φd2 are shifted by kd2 for each row, wherein k=0, 1, 2, . . . , N2/d2−1;
• quantizing the transformation coefficients of the second decomposed vector of transformation coefficients
• v
• 2
• ,
• w
• 1
• 2
• ,
• w
• 2
• 2
• ,
• …
• ,
• w
• d
• 2
• -
• 1
• 2
• and detail components of the first decomposed vector
• w
• 1
• 1
• ,
• w
• 2
• 1
• ,
• …
• ,
• w
• d
• 2
• -
• 1
• 1
• ,
• to obtain a quantized transformation vector;
• and
• compressing the signal based on the quantized transformation vector.

An IoT (Internet of Things) device comprising:

• a plurality of sensors;
• and
• processing circuitry configured to:
• at least for a first level of decomposition, transform the signal based on a first sparse matrix A1, of size N1×N1 formed by an invertible matrix Φd1 of size d1×di, wherein d1 is a divisor of N1, representing a divisor-based signal decomposition for a first divisor d1 to obtain a first decomposed vector s1 of transformation coefficients, wherein s1=A1x, and wherein the first decomposed vector s1 comprises an initial component v1 and detail components
• w
• 1
• 1
• ,
• w
• 2
• 1
• ,
• …
• ,
• w
• d
• 1
• -
• 1
• 1
• ,
• and wherein each of one or more row vectors of Φd1 is extended up to a signal length N1 by appending N1−d1 zeros and wherein the one or more row vectors of Φd1 are shifted by kd1 for each row, wherein k=0, 1, 2, . . . , N1/d1−1;
• at least for a second level of decomposition, transform the initial component based on a second sparse matrix A2, of size N2×N2, where
• N
• 2
• =
• N
• 1
• d
• 1
• ,
• formed by an invertible matrix Φd2 of size d2×d2, wherein d2 is a divisor of N2,, representing a divisor-based signal decomposition for a second divisor d2, to obtain a second decomposed vector s2 of transformation coefficients wherein s2=A2v1, and wherein the second decomposed vector s2 comprises an initial component v2 and detail components
• w
• 1
• 2
• ,
• w
• 2
• 2
• ,
• …
• ,
• w
• d
• 2
• -
• 1
• 2
• ,
• and wherein each of one or more row vectors of Φd2 is extended up to a signal length N2 by appending N2−d2 zeros and wherein the one or more row vectors of Φd, are shifted by kd2 for each row, wherein k=0, 1, 2, . . . , N2/d2−1;
• quantize the transformation coefficients of the second decomposed vector of transformation coefficients
• v
• 2
• ,
• w
• 1
• 2
• ,
• w
• 2
• 2
• ,
• …
• ,
• w
• d
• 2
• -
• 1
• 2
• and detail components of the first decomposed vector
• w
• 1
• 1
• ,
• w
• 2
• 1
• ,
• …
• ,
• w
• d
• 1
• -
• 1
• 1
• ,
• to obtain a quantized transformation vector;
• and
• compress the signal based on the quantized transformation vector.

A signal compression system comprising:

• a memory device;
• and
• compression circuitry;
• and
• wherein the signal compression system is configured to:
• at least for a first level of decomposition, transform the signal based on a first sparse matrix A1, of size N1×N1 formed by an invertible matrix Φd1 of size d1×d1, wherein d1 is a divisor of N1, representing a divisor-based signal decomposition for a first divisor d1 to obtain a first decomposed vector s1 of transformation coefficients, wherein s1=A1x, and wherein the first decomposed vector s1 comprises an initial component v1 and detail components
• w
• 1
• 1
• ,
• w
• 2
• 1
• ,
• …
• ,
• w
• d
• 1
• -
• 1
• 1
• ,
• and wherein each of one or more row vectors of Φd1 is extended up to a signal length N1 by appending N1−d1 zeros and wherein the one or more row vectors of Φd1 are shifted by kd1 for each row, wherein k=0, 1, 2, . . . , N1/d1−1;
• at least for a second level of decomposition, transform the initial component based on a second sparse matrix A2, of size N2×N2, where
• N
• 2
• =
• N
• 1
• d
• 1
• ,
• formed by an invertible matrix Φd2 of size d2×d2, wherein d2 is a divisor of N2,, representing a divisor-based signal decomposition for a second divisor d2, to obtain a second decomposed vector s2 of transformation coefficients wherein s2=A2v1, and wherein the second decomposed vector s2 comprises an initial component v2 and detail components
• w
• 1
• 2
• ,
• w
• 2
• 2
• ,
• …
• ,
• w
• d
• 2
• -
• 1
• 2
• ,
• and wherein each of one or more row vectors of Φd2 is extended up to a signal length N2 by appending N2−d2 zeros and wherein the one or more row vectors of Φd2 are shifted by kd2 for each row, wherein k=0, 1, 2, . . . , N2/d2−1;
• quantize the transformation coefficients of the second decomposed vector of transformation coefficients
• v
• 2
• ,
• w
• 1
• 2
• ,
• w
• 2
• 2
• ,
• …
• ,
• w
• d
• 2
• -
• 1
• 2
• and detail components of the first decomposed vector
• w
• 1
• 1
• ,
• w
• 2
• 1
• ,
• …
• ,
• w
• d
• 1
• -
• 1
• 1
• ,
• to obtain a quantized transformation vector;
• and
• compress the signal based on the quantized transformation vector.