Wavelet denoising using signal location windowing

A method of denoising a signal comprising:

• transforming a signal using an undecimated discrete wavelet transformation into at least a first wavelet component, the first wavelet component having a plurality of coefficients, the first wavelet component having a plurality of decomposition level, where a number of the plurality of coefficients in each level are the same;
• positioning one or more windows on the first wavelet component for a highest decomposition level determined for thresholding;
• for the highest decomposition level determined for thresholding, comparing each coefficient outside the one or more windows with a threshold, and selectively changing a value of the coefficient based on the comparison thereby generating a first modified first wavelet component having changed coefficients and unchanged coefficients for the highest decomposition level determined for thresholding;
• positioning the one or more windows on the first wavelet component for a subset of other decomposition levels of the plurality of decomposition levels at the same positions;
• for the subset of other decomposition levels, comparing each coefficient of the plurality of coefficients outside the one or more windows with a threshold, and selectively changing a value of the coefficient based on the comparison thereby generating a second modified first wavelet component having changed coefficients and unchanged coefficients, respectively for each decomposition level of the subset of other decomposition levels;
• for the remaining decomposition levels of the plurality of decomposition levels lower than the highest decomposition level determined for thresholding, comparing each coefficient of the plurality of coefficients with a threshold and selectively changing a value of the coefficient based on the comparison thereby generating a third modified first wavelet component having changed coefficients and unchanged coefficients, respectively for each decomposition level of the remaining decomposition levels;
• and
• transforming, using an inverse undecimated discrete wavelet transformation, the first modified first wavelet component for the highest decomposition level, the second modified first wavelet component for each decomposition level of the subset of other decomposition levels, respectively and the third modified first wavelet component for the remaining decomposition levels lower than the highest decomposition level determined for thresholding, respectively, into a denoised signal.

A method of denoising a signal comprising:

• reversing in time, a signal;
• transforming the time reversed signal using an undecimated discrete wavelet transformation into at least a first wavelet component, the first wavelet component having a plurality of coefficients, the first wavelet component having a plurality of decomposition level, where a number of the plurality of coefficients in each level are the same;
• for each decomposition level, dividing coefficients for the first wavelet component into a first-subset of coefficients and a second-subset of coefficients based on a determined signal to noise ratio of the signal;
• for each decomposition level determined for thresholding for the first-subset of coefficients and the second-subset of coefficients,
• comparing each coefficient in the first-subset of coefficients with a first threshold, and selectively changing a value of the coefficient in the first-subset of coefficients based on the comparison thereby generating a first modified first subset of coefficients having changed coefficients and unchanged coefficients;
• and
• comparing each coefficient in the second-subset of coefficients with a second threshold, and selectively changing a value of the coefficient in the second-subset of coefficients based on the comparison thereby generating a first modified second subset of coefficients having changed coefficients and unchanged coefficients;
• positioning one or more windows on the first modified first subset of coefficients and the first modified second subset of coefficients for a highest decomposition level determined for thresholding, by evaluating the changed coefficients and unchanged coefficients in the first modified first subset of coefficients and the first modified second subset of coefficients, respectively, for the highest decomposition level, respectively;
• changing coefficients in the first modified first subset of coefficients and the first modified second subset of coefficients for the highest decomposition level, respectively, to its original value when the coefficients are within the one or more windows while keeping the coefficients outside the one or more windows the same as in the first modified first subset of coefficients and the first modified second subset of coefficients, respectively, to generate a second modified first subset of coefficients and a second modified second subset of coefficients, respectively, for the respective highest decomposition level;
• positioning the one or more windows on the first modified first subset of coefficients and the first modified second subset of coefficients for a subset of other decomposition levels of the plurality of decomposition levels at the same positions;
• changing coefficients in the first modified first subset of coefficients and the first modified second subset of coefficients for each of the subset of other decomposition levels to its original value when the coefficients are within the one or more windows while keeping the coefficients outside the one or more windows the same as the first modified first subset of coefficients and the first modified second subset of coefficients, respectively, to generate a third modified first subset of coefficients and a third modified second subset of coefficients, respectively, for a decomposition level of the subset of other decomposition levels;
• transforming, using an inverse undecimated discrete wavelet transformation, the first modified first subset of coefficients and the first modified second subset of coefficients for decomposition levels other than the subset of other decomposition levels and the highest decomposition level, respectively, the second modified first subset of coefficients and the second modified second subset of coefficients for the highest decomposition level and the third modified first subset of coefficients and the third modified second subset of coefficients for the subset of other decomposition levels, respectively, into a reversed in time denoised signal;
• and
• reversing in time the reversed in time denoised signal to generate a denoised signal.

A method of denoising a signal comprising:

• reversing in time, a signal;
• transforming the time reversed signal using an undecimated discrete wavelet transformation into at least a first wavelet component, the first wavelet component having a plurality of coefficients, the first wavelet component having a plurality of decomposition level, where a number of the plurality of coefficients in each level are the same;
• for each decomposition level, dividing coefficients for the first wavelet component into a first-subset of coefficients and a second-subset of coefficients based on a determined signal to noise ratio of the signal;
• positioning one or more windows on the first-subset of coefficients and the second-subset of coefficients for a highest decomposition level determined for thresholding for the first-subset of coefficients and the second-subset of coefficients;
• for the highest decomposition level determined for thresholding for the first-subset of coefficients and the second-subset of coefficients, comparing each coefficient outside the one or more windows in the first-subset of coefficients with a threshold, and selectively changing a value of the coefficient based on the comparison thereby generating a first modified first wavelet coefficients having changed coefficients and unchanged coefficients for the highest decomposition level and comparing each coefficient outside the one or more windows in the second-subset of coefficients with a second threshold and selectively changing a value of the coefficient based on the comparison thereby generating a first modified second wavelet component having changed coefficients and unchanged coefficients for the highest decomposition level determined for thresholding, respectively;
• positioning the one or more windows on the first subset of coefficients for a subset of other decomposition levels of the plurality of decomposition levels at the same positions;
• changing coefficients in the first-subset of coefficients for each of the subset of other decomposition levels when the coefficients are outside the windows and based on a comparison with a threshold, respectively, to generate a second modified first subset of coefficients having changed coefficients and unchanged coefficients, respectively, for a decomposition level of the subset of other decomposition levels;
• for the remaining decomposition levels of the plurality of decomposition levels lower than the highest decomposition level determined for thresholding, comparing each coefficient in the first-subset of coefficients with a threshold and selectively changing a value of the coefficient based on the comparison thereby generating a third modified first wavelet coefficients having changed coefficients and unchanged coefficients, respectively for each decomposition level of the remaining decomposition levels;
• and
• transforming, using an inverse undecimated discrete wavelet transformation, a first modified first wavelet coefficients and first modified second wavelet coefficients for the highest decomposition level, a second modified first subset of coefficients, respectively, and the third modified first wavelet coefficients, respectively, into a reversed in time denoised signal;
• and
• reversing in time the reversed in time denoised signal to generate a denoised signal.