Image coding apparatus and method utilizing separable transformations

Claim 3

The apparatus of claim 1 wherein said column processing means further comprises means for causing said linear filtering means to process each said column in said high-frequency row arrays to generate a high-frequency column array representing the high spatial frequency information in said image.

Claim 4

The apparatus of claim 1 wherein said filter coefficients further satisfy the condition ##EQU2## wherein q is any positive integer and (*) denotes complex conjugation.

Claim 5

The apparatus of claim 1 wherein said filter coefficients further satisfy the condition ##EQU3## wherein said condition is satisfied for all i >0 and any positive integer value q less than some predetermined value.

Claim 8

The apparatus of claim 5, wherein said filter coefficients further satisfy the condition ##EQU5## wherein q is any positive integer and (*) denotes complex conjugation.

Claim 9

The apparatus of claim 5 wherein said filter coefficients further satisfy the condition ##EQU6## wherein said condition is satisfied for all i>0 and any positive integer value q less than some predetermined value.

Claim 10

In an apparatus including a linear filter for filtering a one-dimensional sequence of digital values to generate a low frequency array representing the low-frequency components of said one-dimensional sequence and two or more high-frequency arrays representing high-frequency components of said one-dimensional sequence, said linear filter comprising means for convolving said one-dimensional signal with three or more sequences of filter coefficients i a p wherein ##EQU7## M is an integer greater than 2, i runs from 0 to the total number of high-frequency arrays so generated, and said low-frequency array is generated by convolving said one-dimensional sequence with the sequence 0 a p , a method for compressing an image comprising a two-dimensional array of pixel intensity values, said method comprising the step of: storing said array of pixel intensity values as a plurality of rows and columns; filtering a one-dimensional sequence of digital values to generate a low-frequency array representing the low-frequency components of said one-dimensional sequence and two or more high-frequency arrays representing high-frequency components of said one-dimensional sequence, said filtering step comprising convolving said one-dimensional signal with three or more sequences of filter coefficients i a p wherein ##EQU8## M is an integer greater than 2, i runs from 0 to the total number of high-frequency arrays so generated, and said low-frequency array is generated by convolving said one-dimensional sequence with the sequence 0 a p ; causing said linear filter to process each said row in said image storage means to generate a low-frequency row array comprising a two-dimensional array of digital values comprising a two-dimensional array of digital values organized as a plurality of rows and columns and a plurality of high-frequency row arrays, each said high-frequency row array comprising a two-dimensional array of digital values organized as a plurality of rows and columns; and causing said linear filter to process each said column in said low-frequency row array to generate a low-frequency column array representing the low spatial frequency information in said image.

Claim 11

In an apparatus including a linear filter for filtering a one-dimensional sequence of digital values to generate a low frequency array representing the low-frequency components of said one-dimensional sequence and two or more high-frequency arrays representing high-frequency components of said one-dimensional sequence, said linear filter comprising means for convolving said one-dimensional signal with three or more sequences of filter coefficients i a p wherein ##EQU7## M is an integer greater than 2, i runs from 0 to the total number of high-frequency arrays so generated, and said low-frequency array is generated by convolving said one-dimensional sequence with the sequence 0 a p , a method for compressing an image comprising a two-dimensional array of pixel intensity values, said method comprising the step of: storing said array of pixel intensity values as a plurality of rows and columns; filtering a one-dimensional sequence of digital values to generate a low-frequency array representing the low-frequency components of said one-dimensional sequence and two or more high-frequency arrays representing high-frequency components of said one-dimensional sequence, said filtering step comprising convolving said one-dimensional signal with three or more sequences of filter coefficients i a p wherein ##EQU8## M is an integer greater than 2, i runs from 0 to the total number of high-frequency arrays so generated, and said low-frequency array is generated by convolving said one-dimensional sequence with the sequence 0 a p ; causing said linear filter to process each said row in said image storage means to generate a low-frequency row array comprising a two-dimensional array of digital values comprising a two-dimensional array of digital values organized as a plurality of rows and columns and a plurality of high-frequency row arrays, each said high-frequency row array comprising a two-dimensional array of digital values organized as a plurality of rows and columns; and causing said linear filter to process each said column in said low-frequency row array to generate a low-frequency column array representing the low spatial frequency information in said image.

Claim 12

The method of claim 8 further comprising the step of causing said linear filter to process each said column in said high-frequency row arrays to generate a high-frequency column of arrays representing the high spatial frequency information in said image.

Claim 13

The method of claim 8 wherein said filter coefficients further satisfy the condition ##EQU9## wherein q is any positive integer and (*) denotes complex conjugation.

Claim 14

The method of claim 8 wherein said filter coefficients further satisfy the condition ##EQU10## wherein said condition is satisfied for all i>0 and any positive integer value q less than some predetermined value.

Claim 15

In an apparatus including a linear synthesizing means for combining M one-dimensional input sequences of digital values to generate an output numerical sequence, wherein each of said one-dimensional sequences may be obtained by filtering said output numerical sequence through a finite impulse response filter having a set of filter coefficients i a p corresponding to each said input sequence, wherein ##EQU11## for i from 0 to M-1, a method for synthesizing an image comprising a two-dimensional array of pixel intensity values organized as a plurality of rows and columns from M two-dimensional sets of image coefficients, each said set of image coefficients being organized as a plurality of rows and columns, wherein M is greater than two, said method comprising: storing said two-dimensional sets of image coefficients; causing said linear synthesizing means to combine corresponding columns of said sets of image coefficients to generate M column arrays, each said column array comprising a two-dimensional array of numerical values organized as a plurality of rows and columns; and causing said linear synthesizing means to combine corresponding rows of said column arrays to generate a row of said reconstructed image.

Claim 16

In an apparatus including a linear synthesizing means for combining M one-dimensional input sequences of digital values to generate an output numerical sequence, wherein each of said one-dimensional sequences may be obtained by filtering said output numerical sequence through a finite impulse response filter having a set of filter coefficients i a p corresponding to each said input sequence, wherein ##EQU11## for i from 0 to M-1, a method for synthesizing an image comprising a two-dimensional array of pixel intensity values organized as a plurality of rows and columns from M two-dimensional sets of image coefficients, each said set of image coefficients being organized as a plurality of rows and columns, wherein M is greater than two, said method comprising: storing said two-dimensional sets of image coefficients; causing said linear synthesizing means to combine corresponding columns of said sets of image coefficients to generate M column arrays, each said column array comprising a two-dimensional array of numerical values organized as a plurality of rows and columns; and causing said linear synthesizing means to combine corresponding rows of said column arrays to generate a row of said reconstructed image.

Claim 17

The method of claim 12 wherein said filter coefficients further satisfy the condition ##EQU12## wherein q is any positive integer and (*) denotes complex conjugation.

Claim 18

The method of claim 12 wherein said filter coefficients further satisfy the condition ##EQU13## wherein said condition is satisfied for all i>0 and any positive integer value q less than some predetermined value.