Reduction of MRI data acquisition time is an important goal in the MRI field. Undersampling k-t space is a solution to reduce acquisition time. MR images may have sparse or compressible presentations in appropriate transform domains, such as wavelets. According to the Compressive Sensing (CS) theory, they can be recovered from randomly undersampled k-t space data that guarantees incoherency bet...

We consider the problem of stably computing the K-sparse N -point Walsh-Hadamard Transform (WHT) of a noisy input vector of length N , where K = O(N δ) scales sub-linearly in the signal dimension N for some δ ∈ (0, 1). The most efficient way known by far for computing the WHT of an arbitraryN -length signal is the Fast Walsh-Hadamard Transform (FWHT), which usesN samples and O(N logN) operation...

Due to its simple and real arithmetic structure Number Theoretic Transform is attractive for computation of convolution. However, there exists a stringent relation between the choice of modulus M and convolution length. Choice of modulus as K.2+1, a prime, leads to relaxation of this constraint and wide choices of wordlength, with each of these associated with many choices of convolution length...

We present a simultaneous generalization of the well-known Karhunen-Loéve (PCA) and k-means algorithms. The basic idea lies in approximating the data with k affine subspaces of a given dimension n. In the case n = 0 we obtain the classical k-means, while for k = 1 we obtain PCA algorithm. Moreover, by our approach we can obtain clusters with different dimensionality which describe the structure...

This paper presents an integer discrete cosine transform (IntDCT) with only dyadic values such as k/2n (k, n ∈ N). Although some conventional IntDCTs have been proposed, they are not suitable for lossless-to-lossy image coding in low-bit-word-length (coefficients) due to the degradation of the frequency decomposition performance in the system. First, the proposed M-channel lossless Walsh-Hadama...

This paper extends the concepts of the Sparse Fast Fourier Transform (sFFT) Algorithm introduced in [1] to work with two dimensional (2D) data. The 2D algorithm requires several generalizations to multiple key concepts of the 1D sparse Fourier transform algorithm. Furthermore, several parameters needed in the algorithm are optimized for the reconstruction of sparse image spectra. This paper add...

Automatic Audio Segmentation aims at extracting information about type of audio i.e. silence, clean speech or speech with noise, music etc. The aim of this thesis is to find and extract different features of audio, segment the audio and combine them to form single type of audio. In this work, the audio signal is initially decomposed into non-overlapping frames. Then these frames are decomposed ...

Linear canonical transform is an integral transform with four parameters and has been proved to be powerful tool for optics, radar system analysis, filter design etc. Fractional Fourier transform and Fresnel transform can be seen as a special case of linear canonical transform with real parameters. Further generalization of linear canonical transform with complex parameters is also developed an...

Fast Fourier Transform (FFT) is one of the most important tools in digital signal processing. FFT costs O(N logN) for transforming a signal of length N . Recently, researchers at MIT have proposed Sparse Fast Fourier Transform (sFFT) [1][2] as a breakthrough with computational complexity O(K logN) and O(K logN log N K ) for exactly K-sparse signal (with only K non-zero frequency grids) and gene...

Intranasal route, ensuring suitable bioavailability of medicines under circumvention of the gastrointestinal degradation and hepatic first-pass elimination, has been a popular choice for drug delivery. Among nasal dosage forms, mucoadhesive solid inserts have been shown to resist mucociliary clearance and provide a prolonged nasal residence time. Hence, the purpose of this study was the prepara...