RU61440U1 - DEVICE FOR CALCULATING A TWO-DIMENSIONAL WAVELET TRANSFORM - Google Patents

Abstract

The device relates to automation and computer technology and can be used in digital processing systems of two-dimensional signals, for example, for image analysis, identifying features, periodic dependencies and local inhomogeneities. The utility model is aimed at obtaining the frequency-spatial representation of a two-dimensional signal using wavelet transform. The specified technical result is achieved through the consistent application of the one-dimensional wavelet transform to the rows and columns of the matrix describing the two-dimensional signal. For this, three devices for the quick calculation of a discrete wavelet transform of a signal with an arbitrary step of discretization of scale coefficients implementing the method of calculating a continuous wavelet transform by means of the scalar product of the signal under study and basis functions are added to the proposed device. The inputs of the first two devices for calculating the wavelet transform receive discrete samples of one-dimensional signals, which are the rows and columns of the signal under study, received in the first random access memory from the output of the analog-to-digital converter. The third wavelet transform computation device receives discrete samples of one-dimensional signals, which are columns of the matrix of “horizontal” wavelet coefficients obtained at the output of the first wavelet transform computation device and stored in the second random access memory. At the second inputs of the wavelet transform calculation devices, a discrete sample of the "mother" wavelet is received from the read-only memory. At the outputs of the wavelet transform calculation devices, discrete samples of the converted signal corresponding to the "horizontal", "vertical" and "diagonal" wavelet transform coefficients are generated.

Description

The device relates to automation and computer engineering and can be used in digital processing systems of two-dimensional signals.

In particular, the proposed device can be used to analyze images, identify features, periodic dependencies and local heterogeneities.

A known method of series-parallel wavelet transform [Copyright certificate RU No. 22489850, IPC 7 G 06 F 17/14, BI No. 10, 2005], which consists in using a pair of filters for wavelet decomposition of the original signal specified in discrete time samples (Mall scheme) .

The disadvantage of this method is the need for a pair of filters ψ _ατ (t) and φ _ατ (t) to implement the wavelet transform, while the scaling function φ is inherent, as a rule, only to orthogonal wavelets. Bases based on continuous wavelets, as a rule, are not strictly orthonormal, and bases with only stability and “approximate” orthogonality properties are often used [1].

A device for the quick calculation of a discrete wavelet transform of a signal with an arbitrary step of discretization of scale factors [Copyright certificate RU No. 2246132, IPC 7 G 06 F 17/14, BI No. 4, 2005], based on the method of calculating a continuous wavelet transform by means of the scalar product of the signal under study s (t) and basis functions ψ _ατ (t):

This device is selected as a prototype.

The technical result of the proposed device that implements a method for quickly calculating a discrete wavelet transform with an arbitrary step of sampling scale factors is to expand the capabilities of the device to the possibility of obtaining wavelet transform coefficients of two-dimensional signals.

The specified technical result is achieved through the consistent application of the one-dimensional wavelet transform to rows and columns

matrix describing a two-dimensional signal.

Images belong to the class of non-stationary signals and often some of their features are not noticeable in the spatial representation. Wavelet transform allows you to get the frequency-spatial representation of the image, in which information about the features of the signal appears [5].

When analyzing two-dimensional signals, identifying features, periodic dependencies, local disturbances, it is only necessary to obtain a wavelet image; the reverse wavelet transform is not required. For these purposes, the most suitable is the use of a continuous wavelet transform with an arbitrary choice of the scale factor [4]. A continuous wavelet transform should be understood as an analogue of this transform for discrete signals, since it is assumed that a two-dimensional signal is specified using a matrix of its instantaneous values.

A wavelet transform of a two-dimensional signal can be performed along the rows and columns of a two-dimensional array, corresponding, for example, to the horizontal and vertical directions in the image, while the horizontal and vertical edges of the image objects will appear in the corresponding sets of wavelet coefficients [2]. In this case, it is possible to use a one-dimensional wavelet, used sequentially for convolution with the rows and columns of a two-dimensional signal, in order to obtain the "horizontal" and "vertical" coefficients of the two-dimensional wavelet transform. "Diagonal" wavelet coefficients are formed as a result of sequential convolution of the columns of the matrix of "horizontal" wavelet coefficients with the same wavelet [3].

The figure shows a diagram of the proposed device. The device consists of an analog-to-digital converter (ADC) - block 1, two random-access memory (RAM) - blocks 2 and 3, read-only memory (ROM) - block 4 and three devices for quickly calculating a discrete wavelet signal conversion with an arbitrary large-scale sampling step coefficients (UVP) - blocks 5-7.

The principle of operation of the proposed device is as follows. The analyzed two-dimensional signal s (t ₁ , t ₂ ) is fed to the ADC input (block 1), from the output of which a discrete sample s (n ₁ , n ₂ ) of size N ₁ × N ₂ samples goes to RAM 1 (block 2).

From the ROM (block 4), a discrete sample of the “mother” wavelet ψ (k) arrives

to the first inputs of the UVP (blocks 5-7). The second inputs of the first and second UVP (blocks 5 and 6) from the outputs of RAM 1 receive one-dimensional signals, which are, respectively, rows s (n _i , j) and columns s (i, n _j ) of the two-dimensional signal s (n ₁ , n ₂ ) At the outputs of these devices, discrete samples of the converted signal s (n ₁ , n ₂ ) are formed, which are, respectively, “horizontal” s ' _h (n ₁ , n ₂ ) and “vertical” s' _v (n ₁ , n ₂ ) wavelet coefficients .

From the output of the first UVP (block 5), discrete samples of the converted signal are fed to the input of RAM 2 (block 3), from the output of which, one-dimensional signals, which are columns of the matrix of "horizontal" wavelet coefficients s' _h (i, n _j ), are fed to the second the input of the third UVP (block 7), at the output of which discrete samples of the converted signal s (n ₁ , n ₂ ) are formed, which are the "diagonal"s' _d (n ₁ , n ₂ ) wavelet coefficients.

Information sources

1. Vorobiev V.I., Gribunin V.G. Theory and practice of wavelet transform. - S.-Pb .: VUS, 1999 .-- 204 p.

2. Finish I. Ten lectures on wavelets. - Izhevsk: Research Center "Regular and chaotic dynamics", 2001. - 464 p.

3. Malla S. Wavelets in signal processing: Trans. from English - M .: Mir, 2005 .-- 671 p., Ill.

4. Pereberin A.V. On the systematization of wavelet transforms // Computational methods and programming. 2001 - T.2. - S.15-40

5. Polikar R. Introduction to wavelet transform: Trans. from English Gribunin V.G. - S.-Pb .: AVTEX, 2002 .-- 59 p.

Claims (1)

A two-dimensional wavelet transform device that implements a method for quickly calculating a discrete wavelet transform with an arbitrary step of discretization of scale coefficients, containing blocks that implement a method for calculating a continuous one-dimensional wavelet transform by calculating cross-correlation functions for a pre-digitized analyzed signal and pre-compressed copies of the "mother" wavelet, characterized in that it contains three devices for the rapid calculation of a discrete one-dimensional wave et transforms (CWP) with an arbitrary step of discretization of scale factors, the first inputs of which from the ROM receive a discrete sample of the "mother" wavelet, and the second inputs of the first two CWP from the outputs of the first RAM containing the matrix of two-dimensional signal values received in this RAM with ADC output, discrete samples of one-dimensional signals corresponding to rows and columns of the matrix of values of the analyzed signal supplied to the ADC input are received, discrete samples of one-dimensional signals are formed at the outputs of the first two UVP of the waves, which are, respectively, “horizontal” and “vertical” wavelet coefficients, the output of the first UVP connected to the input of the second RAM, the output of which discrete samples of one-dimensional signals corresponding to the columns of the matrix of “horizontal” wavelet coefficients, are fed to the second input of the third UVP at the output of which discrete samples of one-dimensional signals are generated corresponding to the "diagonal" wavelet coefficients, which, like the "horizontal" and "vertical" wavelet coefficients, are represented in de matrix values of size equal to the size of the matrix of values of the discrete two-dimensional signal sample analyte.