Table 1.

Reconstruction methods considered

Method	Problem
Pseudoinverse	y=Ax (Moore–Penrose)
Ridge Regression	${min}_x\left\{{∣∣\mathbf{y}-\mathbf{Ax}∣∣}_2^2+{\alpha }_2{∣∣\mathbf{x}∣∣}_2^2\right\}$
LASSO	${min}_x\left\{{∣∣\mathbf{y}-\mathbf{Ax}∣∣}_2^2+{\alpha }_1{∣∣\mathbf{x}∣∣}_1\right\}$
BPDN	${min}_x\left\{\left(1∕2\right){∣∣\mathbf{y}-\mathbf{Ax}∣∣}_2^2+{\alpha }_1{∣∣\mathbf{x}∣∣}_1\right\}$
RBF Network	${min}_c\left\{{∣∣\mathbf{y}-{\mathbf{Ah}}_{\mathbf{c}}∣∣}_2^2\right\}$ with ${\mathbf{h}}_{\mathbf{c}}=\mathbf{Kc}=\sum _{d=1}^D{c}_d{e}^{-\beta {∣\lambda -{\lambda }_d∣}^2}$
Elastic-Net	${min}_{x,x>0}\left\{{∣∣\mathbf{y}-\mathbf{Ax}∣∣}_2^2+{\alpha }_1{∣∣\mathbf{x}∣∣}_1+{\alpha }_2{∣∣\mathbf{x}∣∣}_2^2\right\}$
Elastic-D1	${min}_{x,x>0}\left\{{∣∣\mathbf{y}-\mathbf{Ax}∣∣}_2^2+{\alpha }_1{∣∣\mathbf{x}∣∣}_1+{\alpha }_2{∣∣\mathbf{x}∣∣}_2^2+{\alpha }_3{∣∣{\mathbf{D}}_1\mathbf{x}∣∣}_2^2\right\}$

Spectral reconstruction techniques/methods considered in this work, and the corresponding problem they solve. Depending on the nature of the problem and input vector, various techniques are such as convex optimization and gradient descent are available to solve the problem. The c coefficients for the RBF Network are computed via c=(AK)⁺y, where K is the kernel matrix ${\mathbf{K}}_{\lambda ,{\lambda }_d}=e^{-\beta {∣\lambda -{\lambda }_d∣}^2}$ and λ_d are the centers of the radial basis functions