Tonal signals are shown as spectral peaks in the frequency domain. When the number of spectral peaks is small and the spectral signal is sparse, Compressive Sensing (CS) can be adopted to locate the peaks with a low-cost sensing system. In the CS scheme, a time domain signal is modelled as $oldsymbol{y}=Phi F^{-1}oldsymbol{s}$, where y and s are signal vectors in the time and frequency domains. In addition, F-1 and $Phi$ are an inverse DFT matrix and a random-sampling matrix, respectively. For a given y and $Phi$, the CS method attempts to estimate s with l0 or l1 optimization. To generate the peak candidates, we adopt the frequency-domain information of $ esmile{oldsymbol{s}}$ = $oldsymbol{F} esmile{oldsymbol{y}}$, where $ esmile{y}$ is the extended version of y and $ esmile{oldsymbol{y}}left(oldsymbol{n} ight)$ is zero when n is not elements of CS time instances. In this paper, we develop Gaussian statistics of $ esmile{oldsymbol{s}}$. That is, the variance and the mean values of $ esmile{oldsymbol{s}}left(oldsymbol{k} ight)$ are examined.

The noise in digital images acquired by image sensors has complex characteristics due to the variety of noise sources. However, most noise reduction methods assume that an image has additive white Gaussian noise (AWGN) with a constant standard deviation, and thus such methods are not effective for use with image signal processors (ISPs). To efficiently reduce the noise in an ISP, we estimate a unified noise model for an image sensor that can handle shot noise, dark-current noise, and fixed-pattern noise (FPN) together, and then we adaptively reduce the image noise using an adaptive Smallest Univalue Segment Assimilating Nucleus ( SUSAN ) filter based on the unified noise model. Since our noise model is affected only by image sensor gain, the parameters for our noise model do not need to be re-configured depending on the contents of image. Therefore, the proposed noise model is suitable for use in an ISP. Our experimental results indicate that the proposed method reduces image sensor noise efficiently.

The precise noise modeling of complementary metal oxide semiconductor image sensor (CMOS image sensor: CIS) is a significant key in understanding the noise source mechanisms, optimizing sensor design, designing noise reduction circuit, and enhancing image quality. Therefore, this paper presents an accurate random telegraph signal (RTS) noise analysis model and a novel quantitative evaluation method in motion picture for the visual sensory evaluation of CIS. In this paper, two main works will be introduced. One is that the exposure process of a video camera is simulated, in which a Gaussian noise and an RTS noise in pinned-photodiode CMOS pixels are modeled in time domain and spatial domain; the other is that a new video quality evaluation method for RTS noise is proposed. Simulation results obtained reveal that the proposed noise modeling for CIS can approximate its physical process and the proposed video quality evaluation method for RTS noise performs effectively as compared to other evaluation methods. Based on the experimental results, conclusions on how the spatial distribution of an RTS noise affects the quality of motion picture are carried out.