An NSST-Based Fusion Method for Airborne Dual-Frequency, High-Spatial-Resolution SAR Images | IEEE Journals & Magazine | IEEE Xplore

What is NSST ?

NSST is a discrete form of Shearlet transform, and it differs from other multi-scale transformations by avoiding up-down samplers. NSST consists of two main stages, multi-scale and multi-directional separations.

Multi-scale

• The Laplacian Pyramid (NSLP) without subsampling produces low and high frequency images whose size is the same as the size of the source image.

Multi-directional

• Versatility is achieved by using different "combinations of Shear Filters" in the so-called polar (pseude-polar) coordinate

NSST Steps

The process steps performed to obtain the NSST coefficients of an image of NxN size at a fixed resolution scale are as follows:

1. Laplacian pyramid is applied to the image. Low and High pass sub-images are obtained.
2. The fourier transformations of the high pass sub-images are calculated and transformed into the Polar coordinate system.
3. Bandpass filter is applied to Polar coordinate system transformations and Fourier transforms (FFT) of Shearlet coefficients are obtained.
4. The Inverse Fourier Transform (IFT) is applied to obtain the Shearlet coefficients and the transformation is performed to the Cartesian coordinate system.

Pipeline

1. Firstly, the input image must be converted to the Intensity channel. At this stage, only Y channel will be used for NSST. You can use ConvertBMPToIntensity() for this process. General formula :

1. Y = (0.11 * Red + 0.59 * Green + 0.3 * Blue)

2. Intensity image given to NSST function. Low (AFK) and High (YFK) Frequency coefficients are obtained at its output. You can use NsstDec1e() for this process.

You can get the input Intensity image using TNSST (Inverse NSST). You can use NsstRec1() for this process.

 

An NSST-Based Fusion Method for Airborne Dual-Frequency, High-Spatial-Resolution SAR Images | IEEE Journals & Magazine | IEEE Xplore

summary of "An NSST-Based Fusion Method for Airborne Dual-Frequency, High-Spatial-Resolution SAR Images" https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10109765

The paper titled "An NSST-Based Fusion Method for Airborne Dual-Frequency, High-Spatial-Resolution SAR Images" presents a fusion technique for enhancing the quality of airborne synthetic aperture radar (SAR) images. The method utilizes the Non-Subsampled Shearlet Transform (NSST) to combine images acquired at different frequencies and improve their spatial resolution.

The authors begin by explaining the limitations of traditional SAR imaging techniques, which often suffer from low spatial resolution due to the system constraints. To overcome this limitation, the proposed method exploits the complementary information provided by dual-frequency SAR images.

The fusion process consists of several steps. First, the dual-frequency SAR images are decomposed into different frequency subbands using the NSST. The NSST is chosen because it effectively captures the directional and scale information in images. This decomposition leads to a set of subband coefficients at multiple scales and orientations.

Next, a fusion rule is applied to the NSST coefficients to combine the information from both frequency bands. The fusion rule is based on the principle of selecting coefficients that possess high-energy content while preserving the fine details. This step ensures that the fused image maintains both the high-frequency information and the spatial details from the original images.

After the fusion step, the fused NSST coefficients are reconstructed to obtain the final fused SAR image. The reconstruction process involves inversely transforming the NSST coefficients in each subband to their corresponding spatial domain using the inverse NSST.

To evaluate the performance of the proposed fusion method, the authors conducted experiments using real airborne dual-frequency SAR data. They compared the fused images with the original dual-frequency images as well as other existing fusion techniques. The evaluation metrics included visual quality assessment and quantitative measures such as peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM).

The experimental results demonstrate that the NSST-based fusion method effectively enhances the spatial resolution of airborne dual-frequency SAR images while preserving important details. The fused images exhibit improved visual quality and outperform other fusion techniques in terms of PSNR and SSIM.

In conclusion, the paper presents a detailed description of an NSST-based fusion method for enhancing the spatial resolution of airborne dual-frequency SAR images. The method utilizes the NSST decomposition and fusion rules to effectively combine the complementary information from different frequency bands. The experimental results validate the effectiveness of the proposed method in improving the quality of SAR images for various applications.

The Non-Subsampled Shearlet Transform (NSST) is a mathematical tool used for image analysis and processing. It is an extension of the traditional Discrete Wavelet Transform (DWT) and provides a more flexible and directional representation of images.

The NSST is designed to capture the sparse and directional characteristics of images by using shearlets, which are specialized waveforms that are elongated and oriented in different directions. Shearlets are well-suited for representing edges, curves, and other geometric features in images.

Compared to the DWT, which only captures scale information, the NSST captures both scale and directional information. This makes it particularly useful for tasks such as image denoising, image fusion, and feature extraction.

The NSST operates in a multiscale and multidirectional manner. It decomposes an input image into a set of subbands at different scales and orientations. This decomposition is achieved by convolving the image with a set of shearlet filters. Each subband represents a specific range of frequencies and directions.

The NSST coefficients obtained from the decomposition can be used for various image processing tasks. For example, in image fusion, NSST coefficients from different images can be combined to create a fused image that contains the most salient information from each input image.

The NSST reconstruction process involves taking the inverse transform of the NSST coefficients to reconstruct the image in the spatial domain. This allows for the recovery of the original image from its shearlet representation.

Overall, the NSST provides a powerful tool for analyzing and processing images, especially in scenarios where capturing both scale and directional information is important. Its ability to represent image features in a sparse and localized manner makes it particularly useful for applications in image fusion, denoising, texture analysis, and other image processing tasks.

The non-subsampled shearlet transform (NSST) is a multiscale and directional transform that is well-suited for representing a wide variety of signals, including images, audio, and video. NSST is a discrete form of the shearlet transform, which is a continuous-time transform that was introduced by Mallat and Hwang in 1999.

NSST is a non-subsampled transform, which means that it does not involve any upsampling or downsampling of the input signal. This makes NSST more efficient than other multiscale transforms, such as the wavelet transform, which do involve upsampling and downsampling.

NSST is also a directional transform, which means that it can represent signals that have directional features. This makes NSST well-suited for representing images, which often have edges and other directional features.

NSST has been used for a variety of signal processing applications, including image denoising, image compression, and image segmentation. NSST has also been used for audio processing applications, such as audio denoising and audio compression.

Here are some of the advantages of using NSST:

• It is a non-subsampled transform, which makes it more efficient than other multiscale transforms.
• It is a directional transform, which makes it well-suited for representing signals that have directional features.
• It has been shown to be effective for a variety of signal processing applications.

Here are some of the disadvantages of using NSST:

• It is a relatively new transform, so there is less research on it than on other transforms, such as the wavelet transform.
• It can be computationally more expensive than other transforms, such as the wavelet transform.

Overall, NSST is a powerful and versatile transform that can be used for a variety of signal processing applications.

https://link.springer.com/article/10.1007/s00521-020-05173-2 

https://github.com/fbasatemur/Non-Subsampled_Shearlet_Transform