## 1 Introduction  
In diffuse optical imaging (DOI), near-infrared (NIR) light is used to noninvasively probe cm-thick biological tissues to map macroscopic structure and function. For example, DOI can identify the distribution and concentrations of NIR tissue optical absorbers, such as oxy-, deoxy- hemoglobin, water, and lipids, and has been widely explored in clinical breast cancer applications [1; 2; 3]. These studies have demonstrated quantitative analysis of breast tissue (tumor and normal) composition [2; 4; 5; 6], monitoring, and prediction of tumor response to chemotherapy [3; 7; 8] and differential diagnosis of malignant from benign lesions [9; 10; 11; 12; 13]. DOI techniques also provide advantages in terms of cost, safety, and accessibility as a point-of-care technology compared to other breast imaging methods [14]. Although many DOI systems use just a few optical wavelengths, several studies have shown that the accuracy of chromophore estimation is significantly affected by the lack of spectral information [15; 16]. This is especially true when a targeted chromophore lies in an undersampled spectral region [16]. Therefore, broadband methods have been developed in the field of diffuse optics to broaden the wavelength range and provide accurate assessments of additional tissue constituents. For example, a broadband time-resolved diffuse optical spectrometer that measures absorption and scattering spectra of turbid media over the 600 to 1350 nm range was recently described [17]. The optical bandwidth of discrete wavelength quantitative frequency-domain (FD) NIR spectroscopy has also been expanded by combining it with broadband continuous-wave (CW) NIR spectroscopy in a hybrid instrument [18; 16; 1; 19], or by using wavelength-tunable lasers [20]. However, because of instrument complexity, broadband DOI typically samples the tissue with limited (few or single) views and homogeneous models of tissue composition are employed. This results in a 2D spatial map of the optical \"topography\" of the tissue, and ignores any depth-dependent variations in tissue composition. This longstanding challenge in the field of diffuse optics leads to significant errors in optical property estimation of tissue inhomogeneities, such as breast tumors or in layered tissues such as the brain/skull/scalp. This error is the result of the partial volume effect, wherein the tissue inhomogeneity occupies only a small portion of the optically interrogated volume, and is one of the major limitations of employing homogeneous tissue models for optical property estimation [21; 22]. A common alternative approach to imaging more complex tissues is diffuse optical tomography (DOT), which requires many DOI measurements at different tissue views and source-detector separations to reconstruct the 3D optical properties with tomographic algorithms. Indeed, studies of DOT techniques and applications [23; 24] have employed spectrally constrained reconstruction techniques and have demonstrated improvements in the chromophore concentration recovery in the tissue. The spectral constraint DOT reconstruction algorithm, where instead of estimating optical properties at each wavelength independently, measurements at all wavelengths are coupled together to estimate chromophore concentrations directly given their known extinction spectra [25]. The spectral constraint in DOT reduces the number of unknowns, thereby making the inversion problem better posed, and is an excellent approach when the expected chromophores are known a priori. However, the spectral constraint approach is not suitable for applications when there are unknown chromophore contributions to the broadband absorption spectrum. For example, several studies have shown that the spectral shape and strength of unknown optical absorbers in breast tissue are a strong discriminator of benign and malignant breast lesions [9; 10; 11; 12; 13].