Speech enhancement in strong noise condition is a challenging problem. Low-rank and sparse matrix decomposition (LSMD) theory has been applied to speech enhancement recently and good performance was obtained. Existing LSMD algorithms consider each frame as an individual observation. However, real-world speeches usually have a temporal structure, and their acoustic characteristics vary slowly as a function of time. In this paper, we propose a temporal continuity constrained low-rank sparse matrix decomposition (TCCLSMD) based speech enhancement method. In this method, speech separation is formulated as a TCCLSMD problem and temporal continuity constraints are imposed in the LSMD process. We develop an alternative optimisation algorithm for noisy spectrogram decomposition. By means of TCCLSMD, the recovery speech spectrogram is more consistent with the structure of the clean speech spectrogram, and it can lead to more stable and reasonable results than the existing LSMD algorithm. Experiments with various types of noises show the proposed algorithm can achieve a better performance than traditional speech enhancement algorithms, in terms of yielding less residual noise and lower speech distortion.

Single Image Super-Resolution (SISR) through sparse representation has received much attention in the past decade due to significant development in sparse coding algorithms. However, recovering high-frequency textures is a major bottleneck of existing SISR algorithms. Considering this, dictionary learning approaches are to be utilized to extract high-frequency textures which improve SISR performance significantly. In this paper, we have proposed the SISR algorithm through sparse representation which involves learning of Low Resolution (LR) and High Resolution (HR) dictionaries simultaneously from the training set. The idea of training coupled dictionaries preserves correlation between HR and LR patches to enhance the Super-resolved image. To demonstrate the effectiveness of the proposed algorithm, a visual comparison is made with popular SISR algorithms and also quantified through quality metrics. The proposed algorithm outperforms compared to existing SISR algorithms qualitatively and quantitatively as shown in experimental results. Furthermore, the performance of our algorithm is remarkable for a smaller training set which involves lesser computational complexity. Therefore, the proposed approach is proven to be superior based upon visual comparisons and quality metrics and have noticeable results at reduced computational complexity.

Optimal random network coding is reduced complexity in computation of coding coefficients, computation of encoded packets and coefficients are such that minimal transmission bandwidth is enough to transmit coding coefficient to the destinations and decoding process can be carried out as soon as encoded packets are started being received at the destination and decoding process has lower computational complexity. But in traditional random network coding, decoding process is possible only after receiving all encoded packets at receiving nodes. Optimal random network coding also reduces the cost of computation. In this research work, coding coefficient matrix size is determined by the size of layers which defines the number of symbols or packets being involved in coding process. Coding coefficient matrix elements are defined such that it has minimal operations of addition and multiplication during coding and decoding process reducing computational complexity by introducing sparseness in coding coefficients and partial decoding is also possible with the given coding coefficient matrix with systematic sparseness in coding coefficients resulting lower triangular coding coefficients matrix. For the optimal utility of computational resources, depending upon the computational resources unoccupied such as memory available resources budget tuned windowing size is used to define the size of the coefficient matrix.

The zero attraction affine projection algorithm (ZA-APA) achieves better performance in terms of convergence rate and steady state error than standard APA when the system is sparse. It uses l1 norm penalty to exploit sparsity of the channel. The performance of ZA-APA depends on the value of zero attractor controller. Moreover a fixed attractor controller is not suitable for varying sparsity environment. This paper proposes an optimal adaptive zero attractor controller based on Mean Square Deviation (MSD) error to work in variable sparsity environment. Experiments were conducted to prove the suitability of the proposed algorithm for identification of unknown variable sparse system.