The wave packet transform in the framework of linear canonical transform

In this paper, we introduce the concept of linear canonical wave packet transform (LCWPT) based on the idea of linear canonical transform (LCT) and wave packet transform (WPT). Parseval’s identity and some properties of LCWPT are discussed. The inversion formula of LCWPT is formulated. Moreover, the composition of LCWPTs is defined and some properties are studied related to it. The LCWPTs of Mexican hat wavelet function are obtained.

The C-Band All-Sky Survey: total intensity point-source detection over the northern sky

ABSTRACT We present a point-source detection algorithm that employs the second-order Spherical Mexican Hat wavelet filter (SMHW2), and use it on C-Band All-Sky Survey (C-BASS) northern intensity data to produce a catalogue of point sources. This catalogue allows us to cross-check the C-BASS flux-density scale against existing source surveys, and provides the basis for a source mask that will be used in subsequent C-BASS and cosmic microwave background (CMB) analyses. The SMHW2 allows us to filter the entire sky at once, avoiding complications from edge effects arising when filtering small sky patches. The algorithm is validated against a set of Monte Carlo simulations, consisting of diffuse emission, instrumental noise, and various point-source populations. The simulated source populations are successfully recovered. The SMHW2 detection algorithm is used to produce a $4.76\, \mathrm{GHz}$ northern sky source catalogue in total intensity, containing 1784 sources and covering declinations δ ≥ −10°. The C-BASS catalogue is matched with the Green Bank 6 cm (GB6) and Parkes-MIT-NRAO (PMN) catalogues over their areas of common sky coverage. From this we estimate the 90 per cent completeness level to be approximately $610\, \mathrm{mJy}$, with a corresponding reliability of 98 per cent, when masking the brightest 30 per cent of the diffuse emission in the C-BASS northern sky map. We find the C-BASS and GB6 flux-density scales to be consistent with one another to within approximately 4 per cent.

A Relative Method of Video Coding using Different Wavelets with SPIHT

Lossy or lossless data compression is needed to Bring down the storage size and greater transmission rate. Wavelet transform is one of the ideal methods used for video compression. Different types of wavelet transforms are now available. In this paper, video is compressed by different wavelets and modified version of SPIHT. Totally seven types of wavelets are used here to compress the video, MSPIHT is used as encoding technique. They are (i) Video coding using duabechies wavelet and MSPIHT (VDM) (ii) Video coding using haar wavelet and MSPIHT (VHM) (iii) video coding using bi orthogonal wavelet and MSPIHT (VBM) (iv) video coding using symlet wavelet and MSPIHT (VSM) (v) video coding using coiflet wavelet and MSPIHT (VCM) (vi) video coding using demeyer wavelet and MSPIHT (VDMM) and (vii) video coding using Mexican hat wavelet and MSPIHT (VMHM). Then we calculate the PSNR and compression ratio for knowing the performance of the system.

Video Coding of Various Decomposition with Encoding Techniques

In a period of past ten years, Compression or coding of video has been elaborated as a vital role in the part of total communication. Multi resolutions techniques play a vital part in the coding of image and video. Wavelet and curve let transform are one of the popular and efficient technique in video coding. In my paper, I am operate to implement various coding based methods with (EWT)empirical wavelet transform, different wavelets ,curvelets with various encoding techniques. They are video coding with EWT and H.264(VEWH), video coding with EWT and LZW(VEWL), video coding with EWT and Huffman with SPIHT(VEWHS), video coding with mexican hat wavelet transform and SPIHT(VMWS), video coding with dual tree wavelet and SPIHT(VDTS), video coding with 3D dual tree wavelet transform and SPIHT(V3DTS), video coding with curvelet transform and SPIHT(VCTS) and video coding with dual tree complex wavelet fractional transform and modified SPIHT(VDTCWFS). Next we implement these methods with the assist of matlab 2014 and 2015, and then analyze these techniques by using PSNR and compression ratio