Related Experiment Videos

Regularized total least squares approach for nonconvolutional linear inverse problems

W Zhu, Y Wang, N P Galatsanos

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |February 13, 2008
    PubMed

    Related Concept Videos

    Application of Linearization and Approximation01:29

    Application of Linearization and Approximation

    A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
    Residuals and Least-Squares Property01:11

    Residuals and Least-Squares Property

    The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
    If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
    The process of fitting the best-fit...
    Linearization and Approximation01:26

    Linearization and Approximation

    Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
    Calibration Curves: Linear Least Squares01:20

    Calibration Curves: Linear Least Squares

    A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
    For data that follow a straight line, the standard method for fitting is the linear...
    Linear Approximation in Time Domain01:21

    Linear Approximation in Time Domain

    Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
    For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
    Linear Approximations01:23

    Linear Approximations

    For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...