A lossless image compression algorithm using wavelets and fractional Fourier transform

Abstract

The necessity of data transfer at a high speed, in fast-growing information technology, depends on compression algorithms. Maintaining quality of data reconstructed at high compression rate is a very difficult part of the data compression technique. In this paper, a new lossless image compression algorithm is proposed, which uses both wavelet and fractional transforms for image compression. Even though wavelets are the best choice for feature extraction from the source image at different frequency resolutions, the low-frequency sub-bands of wavelet decomposition are the untouched part in compression method in most of the existing methods. On the other hand, fractional Fourier transform is a convenient form of generalized Fourier transform that helps in the compact lossless coding of the source image with optimal fractional orders. Hence, we have used discrete fractional Fourier transform to compress those sensitive sub-bands of the wavelet transform, carefully. In this method, an image is split into low-and high-frequency sub-bands by using Daubechies wavelet filter and level 1 quantization is applied for both low-frequency and high-frequency subbands. The low-frequency sub-bands are compressed by using fractional Fourier transform with optimal fractional orders, and at the same time, high-frequency sub-bands are compressed by eliminating zeroes and storing only nonzero blocks and its position. The compressed wavelet coefficients are further compressed by the application of level 2 quantization and stored as a reduced array. This reduced array is encoded by using arithmetic encoder followed by run-length coding. The experimental results of the proposed algorithm with a different set of test images are compared with some of the existing image compression algorithms. The results show that the proposed method has significant improvement in image reconstruction quality.

Bilateral anisotropic Gabor wavelet transformation based deep stacked auto encoding for lossesless image compression

“…The performance metrics, such as MSE, PSNR, compression ratio, computation time are analyzed. The performance of the proposed method is compared with three existing methods, like wavelet and fractional transforms based lossless image compression in aerial image (WFT‐LIC‐AI), 27 convolutional neural network with Lempel Ziv Markov chain algorithm based lossless image compression in aerial image (CNN‐LMCA‐LIC‐AI) 28 and high‐resolution quantization scheme with exp‐Golomb code based lossless image compression in aerial image (HSQ‐EXGC‐LIC‐AI) 29 respectively.…”

“…In this section performance of digital image dataset are analyzed. In this the proposed BAGWT‐DSAE‐LIC method is analyzed with existing WFT‐LIC, 27 CNN‐LMCA‐LIC, 28 and HSQ‐EXGC‐LIC methods 29 . The following Table 2 shows the performance analysis of digital image dataset.…”

“…Naveen Kumar et al, 27 have presented an innovative lossless image compression model. The presented model utilized wavelet and fractional transforms for image compression.…”

“…In DSAE, the decoder of the auto encoder achieves a better quality decompressed image. By creating the latent space representations, the encoder compresses the image, whereas the decoder converts the latent space into image space. The proposed method is implemented in MATLAB simulations run in PC through Intel Core, 8 GB of RAM, 2.50 GHz CPU and Windows 8. The simulation performance of the proposed method is estimated under certain performances metrics, like root mean square error (RMSE), peak signal to noise ratio (PSNR), mean square error (MSE), compression ratio and computation time, compression factor (CF), bit rate and space saving are analyzed The performance of the proposed method is compared with three existing methods: wavelet and fractional transforms based lossless image compression (WFT‐LIC), 27 Convolutional neural network with Lempel Ziv Markov chain algorithm based lossless image compression (CNN‐LMCA‐LIC) 28 and high‐resolution quantization scheme with exp‐Golomb code based lossless image compression (HSQ‐EXGC‐LIC) 29 …”

Deep Learning on Airborne Radar Echograms for Tracing Snow Accumulation Layers of the Greenland Ice Sheet

“…They also have localization properties, in both the spatial and frequency domains, which can be combined with CNNs to simultaneously learn and remove noise from the input image [10], [14]. These variety of properties have resulted in their applications in image denoising [10], [15], [16], image compression [17], [18], and image restoration [11], [16], [19]. Each level, or scale, of these wavelet transforms is at a downsampled resolution of the previous scale, where the lower scale highlights intricate features and the higher scale emphasizes more global features.…”